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The mixed metric dimension of a graph is an important parameter in characterizing its structural complexity, specifically in nanoscale networks where precision is paramount. In this article, we calculate the mixed metric dimension of hexagonal nano-network, a modal with significant applications in nanotechnology and material science. Through rigorous analysis, we set up that the mixed metric dimension of the hexagonal nano-network is exactly three, highlighting its minimal but enough resolving set that uniquely identifies all vertices. Furthermore, we check out the exchange property within this context, demonstrating the robust adaptability of the hexagonal network's resolving sets. Our findings display that the alternate assets aren't the handiest preserved but stronger in these nano-networks, allowing for flexible adjustments in resolving sets without compromising the network's integrity. This examination offers critical insights into the fundamental properties of hexagonal nano-networks, offering a theoretical foundation for future research in nanomaterial design and optimization. The results underscore the potential of leveraging mixed metric dimensions and exchange properties to achieve efficient and scalable solutions in nano-network applications. [ABSTRACT FROM AUTHOR] more...

Improvements are necessary for the performance improvements of the digital twin technology developed for the virtual energy market on the Metaverse platform. However, more important factors need to be improved first to avoid excessive increases in costs. Thus, a priority analysis needs to be carried out to determine the variables that most affect the performance of technology investments. Accordingly, the purpose of this study is to evaluate the investments of digital twin technologies for virtual energy market in the Metaverse. A novel artificial intelligence-based fuzzy decision-making model is constructed to reach this objective. Firstly, the expert choices are prioritized with artificial intelligence-based decision-making method. Secondly, the investment priorities are analyzed for digital twin technologies with quantum picture fuzzy rough sets (QPFRS)-based Multi Stepwise Weight Assessment Ratio Analysis (M-SWARA). Finally, the alternatives for virtual energy market in the metaverse are ranked by VIKOR (VIsekriterijumska optimizacija i KOmpromisno Resenje). There are limited studies in the literature that computes the weights of the experts while generating a decision-making model. Therefore, the main contribution of this study is integrating the artificial intelligence approach and fuzzy multi-criteria decision-making methodology. Within this scope, an artificial intelligence-based application is performed when creating the decision matrix. Owing to this issue, the importance weights of experts are determined according to the qualifications of these people. This situation contributes to the results obtained being more realistic. The findings demonstrate that operational performance is the most important indicator for the improvements of the digital twin technology investments for virtual energy markets in metaverse platform because it has the greatest weight (0.267). Furthermore, integrated data production is another critical factor for the performance increase of these projects with the weight of 0.257. It is also concluded that optimization of energy consumption with smart grids has the best ranking performance among the alternatives. [ABSTRACT FROM AUTHOR] more...

Green supply chain management concerns the incorporation of globally sustainable methods into supply chain management techniques. The major goal is to decrease the environmental impact of the entire supply chain to increase the social, ecological, and economic relationships with other countries for business. In this manuscript, we aim to compute the Dombi operational laws based on the complex Pythagorean fuzzy (CPF) information. Furthermore, we construct the Dombi aggregation operators under the consideration of the CPF information, such as the CPF power Dombi averaging (CPFPDA) operator, CPF power weighted Dombi averaging (CPFPWDA) operator, CPF power Dombi geometric (CPFPDG) operator, and CPF power weighted Dombi geometric (CPFPWDG) operator. Some flexible properties for the invented operators are also discussed. Additionally, we develop the multi-attribute decision-making (MADM) method to evaluate the problem of green supply chain management based on the invented operators for CPF information. Finally, we use some numerical examples to show the supremacy and validity of the developed techniques by comparing their ranking results with the obtaining ranking results of the existing techniques. [ABSTRACT FROM AUTHOR] more...

Aggregation operators are used for aggregating the collection of finite information into a singleton set. The Aczel-Alsina t-norm and t-conorm are very useful for constructing any kind of new aggregation operators, which was presented by Aczel and Alsina in 1982. Moreover, complex Pythagorean fuzzy (CPF) sets and hesitant fuzzy (HF) sets are the most generalized and very useful techniques to cope with unreliable and awkward information in genuine life problems. In this manuscript, we combine the HF set and CPF set to derive the complex Pythagorean hesitant fuzzy (CPHF) set and its fundamental laws. Furthermore, we evaluate the Aczel-Alsina operational laws based on Aczel-Alsina norms and CPHF information. Additionally, based on the Aczel-Alsina operational laws for CPHF information, we investigate the CPHF Aczel-Alsina-weighted averaging (CPHFAAWA) operator, CPHF Aczel-Alsina-ordered weighted averaging (CPHFAAOWA) operator, CPHF Aczel-Alsina-weighted geometric (CPHFAAWG) operator, and CPHF Aczel-Alsina-ordered weighted geometric (CPHFAAOWG) operator. Some remarkable properties are also examined for the invented theory. Moreover, a multi-attribute decision-making (MADM) technique is presented based on discovered operators for CPHF information. Finally, we aim to illustrate some examples for comparing the proposed techniques with some existing ones to show the worth and feasibility of the discovered approaches. [ABSTRACT FROM AUTHOR] more...

In 1960, Schweizer and Sklar introduced the novel Schweizer-Sklar t-norm and t-conorm which is used in the construction of aggregation operators. Schweizer-Sklar norms are more general than algebraic norms and Einstein norms. Additionally, computing the power operators based on the Schweizer-Sklar norms for complex Atanassov intuitionistic fuzzy (CA-IF) set is very awkward and complicated. In this manuscript, firstly, we propose the Schweizer-Sklar operational laws for CA-IF values, and secondly, we develop the CA-IF Schweizer-Sklar power averaging (CA-IFSSPA) operator, CA-IF Schweizer-Sklar power ordered averaging (CA-IFSSPOA) operator, CA-IF Schweizer-Sklar power geometric (CA-IFSSPG) operator, and CA-IF Schweizer-Sklar power ordered geometric (CA-IFSSPOG) operator. Some suitable and dominant properties for the above operators are also discussed. Furthermore, to simplify the above operators, we develop the procedure of decision-making technique, called multi-attribute decision-making (MADM) methods based on the proposed operators based on CA-IF values. Finally, we compare the proposed methods with some existing methods to describe the efficiency and capability of the discovered approaches by some examples. [ABSTRACT FROM AUTHOR] more...

A complex intuitionistic fuzzy (CIF) set contains the membership and non-membership in the shape of a complex number whose amplitude term and phase term are covered in the unit interval. Moreover, Hamacher interaction aggregation operators are the combination of two major operators, called Hamacher aggregation operators and interaction aggregation operators, and they are used to aggregate the collection of information into one value. In this manuscript, we present the concept of Hamacher interaction operational laws for CIF sets (CIFSs). Further, we develop the CIF Hamacher interaction weighted averaging (CIFHIWA) operator, CIF Hamacher interaction ordered weighted averaging (CIFHIOWA) operator, CIF Hamacher interaction weighted geometric (CIFHIWG) operator, and CIF Hamacher interaction ordered weighted geometric (CIFHIOWG) operator. For these operators, we also discuss some basic properties, such as idempotency, monotonicity, and boundedness. Additionally, we develop a MADM method based on the developed operators and apply it to solve the green supply chain management problems, which can implement environmentally friendly practices to minimize carbon emissions, resource consumption, and waste generation while promoting long-term sustainability. Finally, we verify the superiority and effectiveness of the proposed method based on a comparative analysis between the proposed techniques and existing methods. [ABSTRACT FROM AUTHOR] more...

One of the most significant and complete approaches to accommodate greater uncertainty than current fuzzy structures is the T-Spherical Fuzzy Set (TSPFS). The primary benefit of TSPFS is that current fuzzy structures are special cases of it. Firstly, some novel TSPF power Heronian mean (TSPFPHM) operators are initiated based on Aczel–Alsina operational laws. These aggregation operators (AOs) have the capacity to eliminate the impact of uncomfortable data and can simultaneously consider the relationships between any two input arguments. Secondly, some elementary properties and core cases with respect to parameters are investigated and found that some of the existing AOs are special cases of the newly initiated aggregation operators. Thirdly, based on these AOs and Aczel–Alsina operational laws a newly advanced technique for order of preference by similarity to ideal solution (TOPSIS)-based method for dealing with multi-attribute group decision-making (MAGDM) problems in a T-Spherical fuzzy framework is established, where the weights of both the decision makers (DMs) and the criteria are completely unknowable. Finally, an illustrative example is provided to evaluate and choose the pharmaceutical firms with the capacity for high-quality, sustainable development in the TSPF environment to demonstrate the usefulness and efficacy. After that, the comparison analysis with other techniques is utilized to demonstrate the coherence and superiority of the recommended approach. [ABSTRACT FROM AUTHOR] more...

Due to the intense competition in the market today, choosing of an appropriate healthcare device vendor in long-term organ transplant networks has emerged as a key issue in raising life expectancy. A complicated multi-attribute group decision-making (MAGDM) process problem with several viable alternatives and sustainable criteria may be used for evaluating sustainable healthcare equipment vendors. The q-rung orthopair fuzzy set (QROFS) is more effective at expressing ambiguous and fuzzy information since it is a generalization of intuitionistic fuzzy sets (IFSs) and Pythagorean fuzzy sets (PFS). The fact that QROFSs provide a wider range of acceptable membership grades and give decision-makers more leeway to express their real thoughts is their most valued feature. The Heronian mean (HM) operator and power aggregation (PA) operator are instances of classic aggregation operators. They are preferable because they can replicate the correlations between attributes and remove the negative effects of awkward information. The Aczel-Alsina t-norms, which were put out by Aczel and Alsina in 1982, constitute a very successful and widely used method for creating any type of aggregation operators. Additionally, the parameter Φ ∈ 0 , + ∞ makes the Algebraic t-norms as a special case of the Aczel-Alsina t-norms. To take the above advantages, in this article, initially, the Aczel-Alsina (AA) operational laws are combined, with power average and Heronian mean operators to propose the QROFAA power Heronian aggregation (QROFPWHA) operator and QROFAA power geometric Heronian aggregation (QROFAAFPGHA) operator. Moreover, some core characteristics and various core cases with respect to the parameters are investigated and found that some of the existing aggregation defined on AA operational laws are special cases of the suggested aggregation operators. Secondly, the weighted forms of the suggested aggregation operators are initiated. Thirdly, based on these newly aggregation operators two novel MAGDM models with unknown weights of the decision makers and attributes are initiated. Finally, an illustrated example about evaluating sustainable healthcare equipment vendors is provided to assess the effectiveness of the suggested models, and a comparison analysis is provided to support and corroborate the suggested approaches. Additionally, assessment for key parameters in the proposed models is carried out to evaluate the implications on results. [ABSTRACT FROM AUTHOR] more...

In multi-attribute group decision-making (MAGDM), the attributes can be placed into independent groups based on their properties through partitioning. First, the partitioned dual Hamy mean (PDHM) operator is introduced, along with its essential properties. This operator integrates these separate groups while preserving the relationships between the attributes within each group. Furthermore, the partitioned Hamy mean (PHM) and the PDHM operators are also constructed in the generalized orthopair fuzzy environment, namely the q-rung orthopair fuzzy PHM (q-ROFPHM), the q-rung orthopair fuzzy PDHM (q-ROFPDHM), and their weighted forms. Their essential properties are verified to ensure the validity of the proposed aggregation operators (AOs). Subsequently, a new MAGDM approach is developed, employing the proposed AOs. The MAGDM problem of selecting the best person is examined. Moreover, the research includes a sensitivity analysis in three directions and a comparative analysis of the proposed MAGDM approach with five different approaches. The findings indicate that applying attribute partitioning in the proposed approach mitigates the adverse impact of irrelevant attributes, leading to more feasible and reliable outcomes. Additionally, a practical case study focuses on selecting a suitable industry for investment among the five available options. This case study demonstrates the approach's effectiveness by considering five distinct qualities and results that make the Internet industry the best place to invest. Furthermore, a comparative analysis with four similar papers is also performed, indicating that the developed method's results are more reliable and consistent. [ABSTRACT FROM AUTHOR] more...

Failure mode and effect analysis (FMEA) method is widely utilized as a powerful reliability management tool to effectively evaluate and prevent risk problems that occur in all aspects of production, service and transportation. Since FMEA experts have different professional backgrounds and the particularity of the risk assessment environment, they may show different risk attitudes and bounded rational behavior. Thus, this paper develops an FMEA framework based on the dynamic reference point cumulative prospect theory considering risk attitude. The linguistic distribution assessment (LDA) and linguistic scale function are utilized to indicate the risk attitude based personalized FMEA experts' evaluation information. Further, based on the idea of maximizing deviation and the LDA-EMD (earth mover's distance) formula, the criteria weight determination method considering the different risk attitudes of the FMEA expert is constructed. Then, a dynamic reference point cumulative prospect theory considering different risk attitudes is developed to obtain the prospect value of the failure modes (FMs) under each FMEA expert. The comprehensive expert weight determination method is established which takes the subjective and objective aspects of expert evaluation and revision factor into account. Finally, the numerical example is carried out to verify the validity and superiority performance of the proposed FMEA method. The improved FMEA method can enhance the flexibility and reliability of risk assessment. Findings proved that it is necessary to consider the different and dynamic risk attitudes of experts in the practical risk assessment. [ABSTRACT FROM AUTHOR] more...

In the consensus reaching process (CRP), experts are not infinitely compromising when adjusting opinions, and the "compromise limit" is used to reflect the limited compromise behaviors in the process of expert opinion adjustment. In complex and multiple social relations, experts tend to exhibit different behaviors according to their compromise limits. This paper aims to develop a novel CRP framework to promote a consensus that categorizes and manages experts based on their compromise limits. Firstly, the trust-interest network is defined to represent the multiple relations among experts, and the expert weights are calculated by considering the impact of interest manipulation on trust relations. Secondly, a novel cloud model-based minimum cost consensus model is established, which considers the mutual acceptance between the experts and the group, as well as the changes in the ranges of experts' hesitation and the collective acceptance. Thirdly, three behavior classifications are defined based on individual compromise limits and group acceptance ranges: cooperative behavior, hesitating non-cooperative behavior, and strong non-cooperative behavior, and a CRP optimization model is constructed to manage the three behaviors. Finally, a numerical example is given to illustrate the validity and superiority of the proposed model. [ABSTRACT FROM AUTHOR] more...

The Aczel-Alsina t-norms ware proposed by Aczel and Alsina in 1982, which are a very effective and dominant technique used in the construction of any kind of aggregation operators. Moreover, the Algebraic t-norms are a special case of the Aczel-Alsina t-norms because of the parameter 0 < p < + ∞ . Additionally, a complex intuitionistic fuzzy (COIF) set is an essential and valuable part of the fuzzy set to handle vague and awkward situations in many real-life problems. Motivated by the above valuable and dominant ideas, the major contribution of this study is to propose the aggregation operators by involving the priority degree based on Aczel-Alsina t-norms for managing the COIF values, such as COIF Aczel-Alsina prioritized weighted averaging (COIFAAPWA), COIF Aczel-Alsina prioritized ordered weighted averaging (COIFAPOWA), COIF Aczel-Alsina prioritized weighted geometric (COIFAAPWG), and COIF Aczel-Alsina prioritized ordered weighted geometric (COIFAAPOWG) operators. The fundamental properties of these operators are also examined. Afterward, we develop a decision-making technique to process the multi-attribute decision-making (MADM) problem based on the COIF information and proposed operators. Lastly, we use some examples to show the supremacy and effectiveness of the developed approaches by checking the influence of the parameters and the comparison between proposed techniques with some existing techniques. [ABSTRACT FROM AUTHOR] more...

The complex q-rung orthopair fuzzy (CQ-ROF) set can describe the complex uncertain information. In this manuscript, we develop the Yager operational laws based on the CQ-ROF information and Yager t-norm and t-conorm. Furthermore, in aggregating the CQ-ROF values, the power, averaging, and geometric aggregation operators have played a very essential and critical role in the environment of fuzzy set. Inspired from the discussed operators, we propose the CQ-ROF power Yager averaging (CQ-ROFPYA), CQ-ROF power Yager ordered averaging (CQ-ROFPYOA), CQ-ROF power Yager geometric (CQ-ROFPYG), and CQ-ROF power Yager ordered geometric (CQ-ROFPYOG) operators. These operators are the modified version of the Power, Yager, averaging, geometric, and the combination of these all based on fuzzy set (FS), intuitionistic FS, Pythagorean FS, q-rung orthopair FS, complex FS, complex intuitionistic FS, and complex Pythagorean FS. Moreover, we also discuss the main properties of the proposed operators. Additionally, we develop a multi-attribute decision-making (MADM) method based on the developed operators. To show the supremacy and validity of the proposed method, the comparison between the proposed method and some existing methods is done by some examples, and results show that the proposed method is better than the others in terms of generality and effectiveness. [ABSTRACT FROM AUTHOR] more...

Complex a-rung orthopair fuzzy soft (CQROFS) set is very famous and effective tool for depicting complex uncertain information because it is the combination of the complex q-rung orthopair fuzzy set (CQROFS) and soft set (SS), in which the truth grade and falsity grade are expressed by complex numbers. Furthermore, Einstein's t-norm and t-conorm are very useful and more dominant tools in aggregating the collection of information into a singleton one, where the algebraic t-norm and t-conorm are the specific case of the Einstein t-norm and t-conorm. In this paper, we aim to propose the complex q-rung orthopair fuzzy soft (CQROFS) information which is the modification or generation of the complex Pythagorean and complex intuitionistic fuzzy soft sets. Some specific operational laws are also derived for the proposed work based on algebraic t-norm and t-conorm. Additionally, we also develop the Einstein's operational laws in the presence of the CQROFS set. Consequently, based on the Einstein operational laws and CQROFS information, we derive the CQROFS Einstein weighted geometric (CQROFSEWG), CQROFS Einstein ordered weighted geometric (CQROFSEOWG), and CQROFS Einstein hybrid geometric (CQROFSEHG) operators. Some notable properties and valuable results are also explored. Moreover, we develop a multi-attribute decision-making (MADM) method based on the derived operators for CQROFS set. Finally, we do a comparative analysis between the proposed work and some existing operators to show the advantages and supremacy of the developed method. [ABSTRACT FROM AUTHOR] more...

Bipolar complex fuzzy set (BCFS) is an enlargement of the bipolar fuzzy set and complex fuzzy set. A bipolar complex fuzzy number (BCFN) is used to represent both the bipolarity of ambiguity and bipolarity of periodicity semantics. This paper develops an integrated BCF–CRITIC–WASPAS methodology to elucidate the multi-criteria decision-making (MCDM) problems with bipolar complex fuzzy (BCF) data. Firstly, we propose the idea of cross-entropy of BCFSs followed by the introduction of some Archimedean operations between the BCFNs. Secondly, we discuss some BCF-Archimedean weighted aggregation operators with the proposed Archimedean aggregation operators that are generalizations of many renowned operators' namely algebraic operator, Einstein operator, Hamachar operator and Frank operator to combine the BCF information. Thirdly, a procedure is given to estimate the decision expert's weights using proposed cross-entropy measure of BCFSs. Since cross-entropy measure quantifies the degree of uncertain information and hence it reflects the influence of each expert. Fourthly, criteria weights are estimated through CRITIC (criteria importance through inter-criteria correlation) method which is a well-known objective method based on aggregated score values of options, intensity contrast of every criteria and conflict among attributes. Further, a green supplier selection (GSS) problem is taken to show the applicability of the developed methodology in real decision problems. We also exhibit a sensitivity investigation with diverse parameter values and criteria weights sets to examine the stability of proposed approach. Finally, we draw attention towards a comparison between the proposed approach and the extant methods to show its superiority. [ABSTRACT FROM AUTHOR] more...

The economic implications from the COVID-19 crisis are not like anything people have ever experienced. As predictions indicated, it is not until the year 2025 may the global economy recover to the ideal situation as it was in 2020. Regions lacked of developing category is among the mostly affected regions, because the category includes weakly and averagely potential power. For supporting the decision of economic system recovery scientifically and accurately under the stress of COVID-19, one feasible solution is to assess the regional economic restorability by taking into account a variety of indicators, such as development foundation, industrial structure, labor forces, financial support and government's ability. This is a typical multi-criteria decision-making (MCDM) problem with quantitative and qualitative criteria/indicator. To solve this problem, in this paper, an investigation is conducted to obtain 14 indicators affecting regional economic restorability, which form an indicator system. The interval type-2 fuzzy set (IT2FS) is an effective tool to express experts' subjective preference values (PVs) in the process of decision-making. First, some formulas are developed to convert quantitative PVs to IT2FSs. Second, an improved interval type-2 fuzzy ORESTE (IT2F-ORESTE) method based on distance and likelihood are developed to assess the regional economic restorability. Third, a case study is given to illustrate the method. Then, robust ranking results are acquired by performing a sensitivity analysis. Finally, some comparative analyses with other methods are conducted to demonstrate that the developed IT2F-ORESTE method can supporting the decision of economic system recovery scientifically and accurately. [ABSTRACT FROM AUTHOR] more...

The MULTIMOORA is a relatively new multi-attribute decision-making (MADM) technique containing three major parts. It has partial and complete aggregation information. The MULTIMOORA procedure contains three major parts: the full multiplicative shape, ratio system, and reference point. Furthermore, the Muirhead mean (MM) operator can easily capture the interaction between any number of preferences. The main feature of this model is to evaluate the novel theory of complex Pythagorean fuzzy uncertain linguistic (CPFUL) settings and utilize their useful properties ("algebraic laws, score value, and accuracy value"). Additionally, we combined the main theory of MM operators with information taken from the theory of CPFUL to diagnose the major idea of the CPFUL Muirhead mean (CPFULMM), CPFUL weighted Muirhead mean (CPFULWMM), CPFUL dual Muirhead mean (CPFULDMM), and CPFUL dual weighted Muirhead mean (CPFULDWMM) operators. We then evaluated their valuable properties ("idempotency, Boundedness, and monotonicity"). Moreover, to enhance the worth and feasibility of the diagnosed approach, we elaborated the extension of the MULTIMOORA method under CPFUL information. We then diagnosed a procedure of the MADM scenario whilst considering the evaluated operators using the CPFUL set theory. Lastly, to compare the diagnosed information with some old operators, we used numerical examples to illustrate the flexibility and feasibility of the presented information. [ABSTRACT FROM AUTHOR] more...

In an uncertain and complex decision-making environment, limited by the scope of human cognition, traditional utility decision-making has a certain deviation to actual decision-making. The revision of behavioral decision-making (BDM) to traditional rational decision-making theory makes the new model more universal. In light of this point, we reveal a new three-way decision (3WD) model by virtue of prospect theory (PT) on multi-scale information systems (MS-ISs) for persuing multi-attribute decision-making (MADM) problems. By utilizing an expected evaluation, our newly designed value function can not only reflect the relative position of the object but also avoid the drawbacks of the reference point being too subjective. Through the value function, we obtain a more reasonable avail function to replace the loss function in the traditional 3WD model. At the same time, the weighting function of the object in different states can be calculated, by synthesizing avail function and the weighting function under different decision attitudes. The comprehensive prospect value and classification conditions of the object are calculated. Then, through data selected from the UCI database, we verify the effectiveness of the constructed method. Comparative and experimental analyses are also used to illustrate the superiority and stability of our designed method. [ABSTRACT FROM AUTHOR] more...

With the increasing complexity of real decision-making problems, some experts try to use multi-scale information to express expert opinions in group decision-making problems. Facing the problem of group decision-making with multi-scale information, this paper attempts to explore a multi-scale group decision-making method consisting of two stages to provide theoretical support and methodological basis for establishing a multi-scale decision analysis system. In the first stage, we introduce a newly ranking decision-making approach based on a reflexive fuzzy α-neighborhood operator to deal with single-scale ranking problems with a single expert, which greatly enriches the ranking decision analysis theory. We also use a numerical example and experimental analysis to detect the stability and validity of the method. In the second stage, considering that the decision-making opinions of multiple experts may appear at the same time in the decision-making process, we propose the score labeling approach and the decision fusion approach to obtain the comprehensive decision-making result, which provides a feasible research idea for the comprehensive analysis of group decision-making results. Combining these two stages, a complete multi-scale group decision-making method in a multi-scale environment is described in detail, which can effectively deal with multi-scale group decision-making problems. Moreover, a series of simulation calculations are conducted to test the validity and stability of the proposed group decision-making method. [ABSTRACT FROM AUTHOR] more...

In this manuscript, we firstly proposed a novel concept of complex interval-valued q-rung orthopair linguistic (CIVq-ROL) information by integrating the concepts of complex interval-valued q-rung orthopair fuzzy (CIVq-ROF) information and linguistic set (LS), and it is more generalized than most existing sets, and it is very feasible and valuable for depicting awkward and unreliable information in a difficult situation. Further, we developed some new operational laws of the CIVq-ROF information based on algebraic t-norm and t-conorm. It is also clear that it is a very challenging task to fuse the collection of data into a singleton set in information fusion and decision making, and the Heronian mean (HM) operator is an important aggregation operator, which can not only achieve the aggregation function from the collection of data into a singleton one, but also consider the relationship between any two data. Therefore, based on the CIVq-ROL information and HM operator, we proposed the CIVq-ROL Heronian mean (CIVq-ROLHM), CIVq-ROL weighted HM (CIVq-ROLWHM), CIVq-ROL geometric HM (CIVq-ROLGHM), and CIVq-ROL weighted geometric HM (CIVq-ROLWGHM) operators, and then, the various desirable properties and specific cases of them are also investigated. Furthermore, we developed a multi-attribute decision-making (MADM) procedure for evaluating the finest business in the country from the collection of four different types of electronics-related businesses based on the proposed operators. Finally, various examples are given to show the application of the invented techniques, and a comparative analysis is carried out for the parameters to show the advantages of the proposed approaches. [ABSTRACT FROM AUTHOR] more...

The emergency logistics provider selection (ELPS) is an important part of emergency logistics management. In an increasingly complex and highly uncertain evaluation environment, how to effectively select emergency logistics providers has become a hot topic in the field of emergency logistics management. In this paper, by integrating the double hierarchy hesitant fuzzy linguistic term set (DHHFLTS), the normalized projection measure and the improved ELECTRE II method, a practical integrated decision support model is proposed to handle the ELPS problem. First, DHHFLTSs are utilized to represent the complex and uncertain linguistic evaluation information provided by decision makers (DMs) to provide subjective judgments. Meanwhile, a distance measure for DHHFLTSs based on the proposed normalized projection is proposed to reflect both the included angle and the distance between evaluation objects, and a weight-determining method based on the proposed distance measure and the maximizing deviation method is constructed. Then a new decision support framework of double hierarchy hesitant fuzzy linguistic ELECTRE II based on positive and negative ideal solutions is put forward, in which three kinds of preference relations of the concordance and discordance sets are set up to rank the alternatives more reasonably. Finally, a practical example of ELPS is presented to illustrate the effectiveness of the proposed method, and detailed comparative analysis with other representative methods is also conducted to demonstrate the advantages of the proposed method. [ABSTRACT FROM AUTHOR] more...

As a more massive feasible and prominent tool than the complex interval-valued Pythagorean fuzzy (CIVPF) set and complex interval-valued intuitionistic fuzzy (CIVIF) set, the complex interval-valued q-rung orthopair fuzzy (CIVQROF) set has been usually used to represent ambiguity and vagueness for real-life decision-making problems. In this paper, we firstly proposed some distance measures, Yager operational laws, and their comparison method. Further, we developed CIVQROF Yager weighted averaging (CIVQROFYWA), CIVQROF Yager ordered weighted averaging (CIVQROFYOWA), CIVQROF Yager weighted geometric (CIVQROFYWG), CIVQROF Yager ordered weighted geometric (CIVQROFYOWG) operators with CIVQROF information, and some certain well-known and feasible properties and outstanding results are explored in detail. Moreover, we proposed a new and valuable technique for handling multi-attribute decision-making problems with CIVQROF information. Lastly, a practical evaluation regarding the high blood pressure diseases of the patient is evaluated to illustrate the feasibility and worth of the proposed approaches. [ABSTRACT FROM AUTHOR] more...

As an important link of marine dumping management, reasonable selection of the location of temporary marine dumping areas is of great significance to the high-quality development of the marine economy. To solve the problem of multi-attribute decision-making (MADM) for the location selection of temporary marine dumping areas, firstly, a fuzzy ELECTRE II model based on S-shaped utility function and the combined weight of game theory was proposed, which fully considered the direct influence of human bounded rationality and combination weight on the decision-making results. In the next part, based on constructing the evaluation index system of the preselected location of the temporary marine dumping marines, the fuzzy ELECTRE II model is applied to the q-order orthopair fuzzy environment to rank the alternative locations of the temporary marine dumping areas. Finally, the effectiveness and advantages of the model are proved compared with other existing methods. This paper provides a new and effective framework for the location selection of temporary marine dumping areas and possesses reference significance for marine dumping management. [ABSTRACT FROM AUTHOR] more...

Complex q-rung orthopair fuzzy (CQROF) set is very feasible to depict the complex uncertain information in real-life problems because it is the modified concept from the complex Pythagorean and complex intuitionistic fuzzy sets. In this manuscript, we concentrate to analyze the improved Einstein operational laws for CQROF information. Then, based on the improved Einstein operational laws, we develop the complex q-rung orthopair fuzzy Einstein interaction weighted geometric (CQROFEIWG) operator, complex q-rung orthopair fuzzy Einstein interaction ordered weighted geometric (CQROFEIOWG) operator, and complex q-rung orthopair fuzzy Einstein interaction hybrid geometric (CQROFEIHG) operator. Furthermore, we analyze their major results and main three properties such as idempotency, boundedness, and monotonicity. Additionally, a decision-making approach with complex q-rung orthopair fuzzy information is developed, in which weights are handled objectively. Finally, some illustrated examples are used to demonstrate the supremacy and feasibility of the proposed approaches by comparing them with some existing ones. [ABSTRACT FROM AUTHOR] more...

As an important technique in safety and reliability analysis, failure mode and effects analysis (FMEA) has been widely utilized to identify and eliminate existing and potential failure. When evaluating the failure modes (FMs), the weights of different FMs are always incompletely known, and different information forms are used to describe the risk assessment issues. The objective of the paper is developing a new approach to solve risk assessment problems faced by four transportation forms in fuzzy and complex environment. In the process of the assessment, the unbalanced double hierarchy linguistic term set (UDHLTS) is used as a linguistic technique to describe the information reasonably and practically. The contributions of this paper are reflected in the following four aspects. Firstly, three linguistic scale functions (LSFs) of the UDHLTS are improved and a semantic model with distinct linguistic cognitive bias parameters is constructed and unified. Secondly, multi-attribute decision-making (MADM) method is applied to FMEA, and an FMEA-MACBETH model is presented to address the risk assessment problems under UDHLTS environment. Meanwhile, weight determination method is built based on the CRITIC method under the situation of completely unknown weights. Finally, a case study of risk assessment in different transportation forms is used to explain the feasibility and rationality of the presented method. Comparison and discussion are conducted to further demonstrate the advantages of the proposed method. [ABSTRACT FROM AUTHOR] more...

The diagnosed complex Pythagorean fuzzy (CPF) set is a more valuable and dominant tool than the Pythagorean and intuitionistic fuzzy sets to describe awkward and unreliable information more effectively. Further, Archimedean t-norm and t-conorm have a significant influence to depict the relation among aggregated values. To take advantage of the CPF set and Archimedean t-norm and t-conorm, and assume the relation among Archimedean norms and algebraic, Einstein, Hamacher, and frank norms at the same time, in this analysis, first, we proposed the fundamental Archimedean operational laws. Second, based on these laws, we developed confidence CPF Archimedean-weighted averaging (CCPFSAWA), confidence CPF Archimedean-ordered weighted averaging (CCPFSAOWA), confidence CPF Archimedean-weighted geometric (CCPFSAWG), confidence CPF Archimedean-ordered weighted geometric (CCPFSAOWG) operators and implemented their valuable results and properties. We know that Archimedean t-norm and t-conorm are the general form of the all-aggregation operators, so by using different values of t-norm and t-conorm, we explored the confidence CPF-weighted averaging (CCPFWA), confidence CPF-ordered weighted averaging (CCPFOWA), confidence CPF Einstein-weighted averaging (CCPFEWA), confidence CPF Einstein-ordered weighted averaging (CCPFEOWA), confidence CPF Hamacher-weighted averaging (CCPFHWA), confidence CPF Hamacher-ordered weighted averaging (CCPFHOWA), confidence CPF frank-weighted averaging (CCPFFWA), confidence CPF frank-ordered weighted averaging (CCPFFOWA), confidence CPF-weighted geometric (CCPFWG), confidence CPF-ordered weighted geometric (CCPFOWG), confidence CPF Einstein-weighted geometric (CCPFEWG), confidence CPF Einstein-ordered weighted geometric (CCPFEOWG), confidence CPF Hamacher-weighted geometric (CCPFHWG), confidence CPF Hamacher-ordered weighted geometric (CCPFHOWG), confidence CPF frank-weighted geometric (CCPFFWG), and confidence CPF frank-ordered weighted geometric (CCPFFOWG) operators. Then, we developed a multi-attribute decision-making (MADM) method based on the proposed operators. Finally, many examples are used to do comparative analysis among proposed and existing methods to show the validation of the new approaches. [ABSTRACT FROM AUTHOR] more...

Pythagorean fuzzy set (PFS), an extended version of intuitionistic fuzzy set (IFS), is verified to be fastest emerging research discipline and is a significant mode to tackle the imprecise and vague information. It provides a broader representation domain than the IFS. Similarity and divergence measures play paramount role in the field of IFSs' doctrine as well as PFSs' doctrine. These measures are integral aspects of utilizing generalized fuzzy sets in real-life problems. In this manuscript, novel similarity and divergence measures for PFSs are developed and compared with extant measures to illustrate their efficiency and reliability. Further, an extended version of multi-objective optimization based on the ratio analysis (MOORA) with the full multiplicative form (MULTIMOORA) approach is introduced by employing developed similarity and divergence measures on PFSs information. To reveal the feasibility and usefulness of the presented approach, a problem of medical equipment supplier selection is discussed from Pythagorean fuzzy perspective. Finally, a comparison with previously developed models is studied to certify the applicability and stability of the introduced MULTIMOORA technique. The outcomes of the work indicate that the present approach is more applicable and efficient than existing techniques under PFSs' context. [ABSTRACT FROM AUTHOR] more...

The complexity and significance of decision-making in selecting suppliers highlight the need for a systematic and transparent approach. The more organizations rely on suppliers, the more harmful the direct and indirect consequences of poor decision-making are. This study attempted to identify factors affecting supplier selection and develop a system dynamics model for supplier selection by taking into account social corporate responsibility (CSR) practices. This model aims to increase CSR practices when selecting suppliers and thus help supply chain members gain competitive power and satisfy customer demands optimally. The system dynamics model for supplier selection was developed by considering profitability, productivity, social transparency, and customer satisfaction. To this end, first, the indicators affecting supplier selection were identified. Then, a cause–effect model was extracted by surveying subject-matter experts. Finally, the system dynamics model was developed. The final output of the third stage was a dynamic model of a supplier selection system that considers CSR practices. The results showed that profitability increases only by implementing the policy of reducing the average distance between suppliers and increasing the number of suppliers. This issue causes lower costs, reduced delivery time due to reduced average distance between suppliers, and increased suppliers, resulting in increased customer satisfaction and increased demand. [ABSTRACT FROM AUTHOR] more...

The q-rung orthopair 2-tuple linguistic numbers (q-RO2TLNs) are helpful tools to represent fuzzy or indeterminate evaluation information. The classical PROMETHEE II is a flexible outranking method for complete ranking and provides different preference functions for decision-makers to choose from. Considering the superiority of the PROMETHEE II method and q-RO2TLNs, in this paper, we propose an extended PROMETHEE II method for multi-attribute group decision-making with the q-RO2TLNs. First, the distance measure of q-RO2TLNs is defined, and then the similarity degree of q-RO2TLNs based on distance is defined to determine the experts' weights. Besides, the comprehensive weights are determined for attributes, in which the subjective and objective weights are derived using the group best–worst method and the deviation maximization method respectively. Then, the PROMETHEE II method is extended to q-RO2TLNs. Finally, the demonstration and discussion of two examples are conducted to illustrate the feasibility and superiority of our proposed method. [ABSTRACT FROM AUTHOR] more...

As more attention is given to environmental protection, sustainable development has become a hot topic for the international community and the companies are motivated to focus on reverse logistics (RL) in their operations for resource conservation and sustainability. However, many enterprises are limited by their economic strength and resources so that outsourcing RL to third-party reverse logistics provider (3PRLP) is their best choice. Therefore, how to effectively assess and select the 3PRLP has been a crucial issue. Given that the preference and optimism of decision makers (DMs) should be exhibited, in this paper, an improved ELECTRE II method with double attitude parameters under linguistic Z-number (LZN) environment is proposed to deal with such decision problems. Firstly, the LZN is in use to describe experts' assessments as well as the reliability of evaluations qualitatively. Then an improved ELECTRE II model based on ideal point method is presented to rank alternatives accurately, in which the main concept of ideal point method is pressed into service in determining the preference levels of alternatives and identifying the outranking relations. Meanwhile, two attitude parameters are introduced, which can express DMs' preference for risk as well as profit and their optimism for decision making, thereby making the decision process more practical and the ranking more reasonable. Then a numerical example on the selection of 3PRLP is shown to minutely explain procedures of the presented method and a sensitivity analysis on the double attitude parameters is conducted to illustrate effects of the two indexes and verify the robustness of the proposed method. Finally, some comparisons are carried out to prove its effectiveness and meliority. [ABSTRACT FROM AUTHOR] more...

Green supplier selection (GSS) plays an irreplaceable role in green supply chain management and environmental protection. Simultaneously, it is widely studied as a typical multi-attribute decision-making (MADM) problem. In this paper, the qualitative flexible multiple criteria (QUALIFLEX) method is used to solve the problem of green suppliers which the number of alternatives is far smaller than the number of attributes. Firstly, the normal q-rung orthopair fuzzy numbers (q-RONFNs) is proposed to overcome the limitation of normal intuitionistic fuzzy numbers (NIFNs) that it cannot handle situation where the sum of the membership degree and non-membership degree is greater than or equal to 1. Secondly, we adopt the combination weight which takes into account subjective and objective weights in MADM, where the subjective weight and objective weight are calculated by fuzzy best–worst method (FBWM) and q-RONF criteria importance through inter-criteria correlation (q-RONFNs-CRITIC) method, respectively, and the combination weight is calculated based on the maximum comprehensive evaluation values. Furthermore, based on QUALIFLEX as the decision-making framework, the q-RONFNs-QUALIFLEX method for GSS is proposed. Finally, this model is applied to the GSS, and the effectiveness and superiority of this model are proved by the comparison with the existing methods. [ABSTRACT FROM AUTHOR] more...

Industry commitments include inventory planning and control, aiming to find the most appropriate purchasing and managing inventory policies by examining the conditions and costs. The Economic Order Quantity (EOQ) is a mathematical model for inventory control in manufacturing systems. As a result, they should be developed from several perspectives to effectively utilize classic models' findings. The current study employs an EOQ model that involves creating new demand and on-time and regulated production variables while considering market demand in two-sided markets. The cost of the inventory-production system in the multi-echelon Supply Chain (SC) was reduced Using game theory and fuzzy demand forecasting. The findings revealed that the level of inventory maturity control has a strong relationship with accurate forecasting of fuzzy demand. As a result, precise forecasting of the ambiguous demands related to increasing price elasticity inevitably lowers retailer performance in SC. As price elasticity rises in response to market demand, all retailers should take the required steps to avoid losing sales. This problem boosts retailers' net profits as well as the overall management system's profitability while also lowering inventory control costs. [ABSTRACT FROM AUTHOR] more...

Hesitant fuzzy linguistic term sets (HFLTSs) and double hierarchy hesitant fuzzy linguistic term sets (DHHFLTSs) are two frequently used linguistic information forms in uncertain decision-making environments. However, they only include membership grades and cannot yield fuzzy information from a negative aspect. A bipolar fuzzy set can quantify evaluation information from positive and negative sides using positive and negative memberships, respectively. To address this issue, double hierarchy bipolar hesitant fuzzy linguistic term sets (DHBHFLTSs) are proposed, which can highlight the importance of the negative membership degree, and the objects can be evaluated from positive and negative aspects. Furthermore, DHBHFLTSs increase the reasonableness and comprehension of the evaluation information in the process of optimal talent selection. This paper proposed a framework involving the stepwise weight assessment ratio analysis (SWARA) method and the extended weighted aggregated sum product assessment (WASPAS) method. The extended WASPAS method is utilized to aggregate the evaluation information of all the alternatives under the DHBHFLTSs context. So, this proposed method increases the ranking accuracy. The SWARA method is extended to DHBHFLTSs to rank and determine the criteria. This weight determination method is helpful for coordinating and gathering data from experts. Therefore, the proposed method can obtain the weight values efficiently. Subsequently, a case of talent selection is utilized to show the feasibility and applicability of the proposed framework. Finally, the accuracy and comparison analyses with other methods illustrate the superiority of this framework. [ABSTRACT FROM AUTHOR] more...

The probabilistic hesitant fuzzy set (PHFS) is an important extension of hesitant fuzzy set (HFS), which can more accurately describe the uncertainty of elements and can show more flexibility of decision maker (DM) in the process of decision-making. Taxonomy method is a useful tool for grading, classifying, and comparing different activities with respect to their advantages and utility degree from studied attributes. In this paper, a probabilistic hesitant fuzzy Taxonomy method based on Best–Worst-Method (BWM) and Indifference Threshold-based Attribute Ratio Analysis (ITARA) for multi-attributes decision-making (MADM) is presented. First, the definitions about PHFS and probabilistic hesitant fuzzy element (PHFE) are introduced, and some corresponding operations are given. Second, we adopt BWM to obtain subjective weights and ITARA approach to obtain objective weights, by combining the subjective weights and objective weights together; we can derive the final weights. Furthermore, we extend the Taxonomy method to the PHFS. Finally, an example of selecting research topic is given to illustrate the usefulness of our proposed method. Compared with other useful methods, the validity and superiority of our proposed method can be showed. [ABSTRACT FROM AUTHOR] more...

The q-rung Orthopair fuzzy set (QROFS) is one of the fuzzy structures which can introduce more fuzzy information than other fuzzy frames proposed by Ronald R. Yager. In this article, the dynamic multiple attribute decision making (DMADM) approach with complex q-rung Orthopair fuzzy (CQROF) information has been introduced. The ideas of CQROF variable and uncertain CQROF variables are defined and introduced new dynamic weighted averaging (DWA) operators called dynamic complex q-rung Orthopair fuzzy weighted average (DCQROFWA) operator and uncertain dynamic complex q-rung Orthopair fuzzy weighted average (UDCQROFWA) operator. For the moment, a procedure has been developed based on DCQROFWA and CQROFWA operator to solve DMADM problems where all attribute information are used in complex q-rung Orthopair fuzzy numbers (CQROFNs) collected at distinct periods, and another procedure is developed based on UDCQROFWA and CIVQROFWA operators to solve uncertain DMADM problems for interval uncertainty in which all attribute information takes in the form of complex interval-valued q-rung Orthopair fuzzy numbers (CIVQROFNs) collected at distinct periods. Finally, a comprehensive comparative analysis has been made for the proposed approach for testing its applicability and efficiency by considering a numerical example. [ABSTRACT FROM AUTHOR] more...

The complex q-rung orthopair fuzzy set (Cq-ROFS) is the extension of complex Pythagorean fuzzy set (CPFS) in which the sum of the q-power of the real part (imaginary part) of the support for and the q-power of the real part (imaginary part) of the support against is limited by one; however, it is difficult to express the hesitant information. In this study, the conception of complex q-rung orthopair hesitant fuzzy set (Cq-ROHFS) by combining the Cq-ROFS and hesitant fuzzy set (HFS) is proposed, and its properties are discussed, obviously, Cq-ROHFS can reflect the uncertainties in structure and in detailed evaluations. Further, some distance measures (DMs) and cross-entropy measures (CEMs) are developed based on complex multiple fuzzy sets. Moreover, these proposed measures are utilized to solve a multi-criteria decision-making problem based on TOPSIS (technique for order preference by similarity to ideal solution) method. Then, the advantages and superiority of the proposed measures are explained by the experimental results and comparisons with some existing methods. [ABSTRACT FROM AUTHOR] more...

How to effectively reflect the randomness and reliability of decision information under uncertain circumstances, and thereby improve the accuracy of decision-making in complex decision scenarios, has become a crucial topic in the field of uncertain decision-making. In this article, the loss –aversion behavior of decision-makers and the non-compensation between attributes are considered. Furthermore, a novel generalized TODIM-ELECTRE II method under the linguistic Z-numbers environment is proposed based on Dempster–Shafer evidence theory for multi-criteria group decision-making problems with unknown weight information. Firstly, the evaluation information and its reliability are provided simultaneously by employing linguistic Z-numbers, which have the ability to capture the arbitrariness and vagueness of natural verbal information. Then, the evaluation information is used to derive basic probability assignments in Dempster–Shafer evidence theory, and with the consideration of both inner and outer reliability, this article employed Dempster's rule to fuse evaluations. Subsequently, a generalized TODIM-ELECTRE II method is conceived under the linguistic Z-numbers environment, which considers both compensatory effects between attributes and the bounded rationality of decision-makers. In addition, criteria weights are obtained by applying Deng entropy which has the ability to deal with uncertainty. Finally, an example of terminal wastewater solidification technology selection is offered to prove this framework's availability and robustness. The predominance is also verified by a comparative analysis with several existing methods. [ABSTRACT FROM AUTHOR] more...

The q-rung orthopair fuzzy sets (q-ROFSs), originally proposed by Yager, can express uncertain data to give decision-makers more space. The q-ROFS is a useful tool for describing imprecision, ambiguity, and inaccuracy, and the point operator is a useful aggregation operator which can manage the uncertainty and thus obtain intensive information within the decision-making process. In the latest realization, the linguistic q-rung orthopair fuzzy number (Lq-ROFN) is suggested where the linguistic variables are expressed as membership and non-membership of the Lq-ROFN. In this article, we propose the q-rung orthopair fuzzy linguistic family of point aggregation operators for linguistic q-rung orthopair fuzzy sets (Lq-ROFSs). Firstly, with the arithmetic and geometric operators, we introduce a new class of point-weighted aggregation operators to aggregate linguistic q-rung orthopair fuzzy information such as linguistic q-rung orthopair fuzzy point weighted averaging (Lq-ROFPWA) operators, linguistic q-rung orthopair fuzzy point weighted geometric (Lq-ROFPWG) operators, linguistic q-rung orthopair fuzzy generalized point weighted averaging (Lq-ROFGPWA) operators and linguistic q-rung orthopair fuzzy generalized point weighted geometric (Lq-ROFGPWG) operators. Then, we discuss some special cases and study the properties of these proposed operators. Based on Lq-ROFPWA and Lq-ROFPWG operators, a novel multi attribute group decision-making (MAGDM) methodology is designed to process the linguistic q-rung orthopair fuzzy information. Finally, we provide an example to demonstrate the applicability of the MAGDM. Consequently, the outstanding superiority of the developed methodology is assisted in a variety of ways by parameter exploration and thorough comparative analysis. [ABSTRACT FROM AUTHOR] more...

One of the serious supply chain management (SCM) challenges is the effective selection of suppliers and the right allocation of orders to achieve an SCM's suitable financial and technical status. This paper introduced a multi-objective linear programming model to prioritize and weigh suppliers using the modified best–worst method (BWM). The proposed model uses evaluation criteria and used fuzzy variables to determine the right numbers of suppliers as well as order quantity of raw materials each supplier should provide. The model has been made up of four objective functions, and the required constraints have been solved using the goal programming method. The proposed model can take a set of opposing goals into account and prioritize the goals to maximize access to each goal. The uncertain concepts such as fuzzy and rough theories in some criteria enabled the proposed model to use the imprecise information in the best possible manner. This study has solved an example using the proposed model through analytic network process and BWM. Then, the obtained results were compared with our findings for adopting interval-valued fuzzy-rough numbers BWM (IVFRN-BWM) and it was shown that the modified BWM approach generates lower costs and better criteria. [ABSTRACT FROM AUTHOR] more...

Probabilistic linguistic Z number (PLZN) is considered as an effective information representation model. It not only describes the decision-making information, but also demonstrates its reliability. To handle the increasing problems of complexity and uncertainty in real-life, PLZN is widely used to indicate qualitative information. In this paper, a novel decision-making method with PLZNs is proposed, focusing on multiple attribute group decision-making (MAGDM) problems with fewer alternatives and more interacted attributes in PLZN environment. Firstly, all basic theories of PLZNs are shown, where the possibility degree of PLZNs is defined. Then, an integration model based on evidential reasoning theory is constructed to aggregate numerous PLZNs, which fully considers the incomplete probability distributions in PLZNs. The mathematical programming model with the generalized Shapley function is introduced to determinate the important degrees of attributes and reflect the interactive characteristics among them. In addition, the probabilistic linguistic Z QUALIFLEX (PLZ-QUALIFLEX) method with the generalized Shapley function is proposed to rank small numbers of alternatives with respect to large numbers of attributes with heterogeneous relationships. Lastly, after demonstrating the rationalities and superiorities of the proposed method, it is applied to solve some numerical cases, in which is compared with other methods. [ABSTRACT FROM AUTHOR] more...

T-spherical fuzzy set (T-SFS) is suitable for the situation where human opinions are not limited to yes or no, but include abstinence and refusal, and can be viewed as a generalization of fuzzy set (FS), intuitionistic FS and picture FS. Normal fuzzy number (NFN) is a useful tool to character phenomenon with normal distribution. Based on the advantages of T-SFS and NFN, we first propose the normal T-spherical fuzzy numbers (NT-SFNs) which can depict both normal distribution phenomenon and neutral information with a considerably large expression domain. Then, we define the operational laws, score function, accuracy function, expectation as well as distance measure of NT-SFNs. To deal with multiple-attribute decision-making (MADM) problems with NT-SFNs and unknown weights of attributes, we use the best worst method (BWM) to obtain the subjective weights, the criteria importance through intercriteria correlation (CRITIC) method to obtain the objective weights, and the minimum total deviation method to calculate the combination weights of attributes. Then, the Taxonomy method is used to rank the alternatives and the normal T-spherical fuzzy Taxonomy (NTSF-Taxonomy) method is proposed. Finally, two numerical examples and comparative analysis are conducted to verify the validity of the NTSF-Taxonomy method. [ABSTRACT FROM AUTHOR] more...

New energy investment assessment has a significant effect on facilitating the new energy industry's development. Reasonable evaluation methods can effectively reduce the risk of new energy investment and push forward the sustainable development of new energy resources. However, there are few research results in this area, especially in the complex decision-making environment. Thus, to make up for that, an integrated multi-attribute group decision-making (MAGDM) framework is developed to assess the new energy investment problems. First, considering the complex decision-making environment of new energy investment, hesitant fuzzy dual linguistic term sets (HFDLTSs) are applied to represent the new energy alternative evaluation values. Due to the cloud models can reflect the fuzziness and uncertainties of linguistic information, an algorithm is proposed to realize the quantitative transformation from HFDLTSs to cloud models. Second, in view of the heterogeneity of decision makers (DMs) regarding to different attributes, a cloud model similarity-based method is proposed to derive the weight information of DMs. Then, an integrated TOPSIS–ORESTE method with cloud model is established to rank the new energy investment alternatives. The proposed method could overcome the information loss due to Besson's ranks. In addition, the global preference score considers the ideal and negative solutions relative to the traditional ORETSE method. Finally, a case study on new energy investment of Shandong province, China is conducted to illustrate the application of the established MAGDM model. The effectiveness and superiority of the introduced method are further demonstrated through the sensitivity analysis of parameters and the comparison with other representative methods. [ABSTRACT FROM AUTHOR] more...

In this paper, our aim is to consider the new class of log-convex fuzzy-interval-valued function known as log-s-convex fuzzy-interval-valued functions (log-s-convex fuzzy-IVFs). By this concept, we have introduced Hermite–Hadamard inequalities (HH-inequalities) by means of fuzzy order relation. This fuzzy order relation is defined level-wise through Kulisch–Miranker order relation defined on interval space. Moreover, some new Hermite–Hadamard–Fejér inequalities (HH–Fejér-inequalities) and Jensen's inequalities via log-s-convex fuzzy-IVFs are also established and verified with the support of useful examples. Some special cases are also discussed which can be viewed as applications of fuzzy-interval HH-inequalities. The concepts and approaches of this paper may be the starting point for further research in this area. [ABSTRACT FROM AUTHOR] more...

The 2-dimensional uncertain linguistic variable (2DULV) can depict decision-makers' subjective assessments on the reliability of given evaluation results, which is a valid and practical tool to express decision information. In this study, we develop an improved MABAC method with 2DULVs to handle multiattribute group decision-making (MAGDM) problems where the weight information of attributes is unknown. First, some related theories of 2DULVs and the basic procedure of the MABAC method are briefly reviewed. Then, the maximum comprehensive evaluation value method is extended to 2DULVs to obtain combination weights of attributes, in which the subjective weights are determined according to the best–worst method (BWM) and the objective weights are calculated by the maximum deviation method. Besides, the generalized weighted average operator for 2DULVs (2DULGWA) is utilized to aggregate the evaluation information given by all experts. Finally, an improved MABAC for 2DULVs (2DUL-MABAC) is proposed, and an example is carried out to explain the validity of the proposed approach. [ABSTRACT FROM AUTHOR] more...

Then, a series of group consensus cost robust optimization models are constructed under asymmetric unit adjustment cost constraints and the aforesaid four uncertainty sets. Sensitivity analysis shows that the proposed group consensus cost robust optimization models are superior to the existing minimum cost consensus models. Finally, data-driven group consensus cost robust optimization models are developed based on the uncertainty set of asymmetric unit adjustment costs calibrated by using the pricing information of the new product MACUBE 550 in the DEEPCOOL company. [Extracted from the article] more...