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This paper aims to support decision-makers improve their ability to accurately capture and represent their judgment in a wide range of situations. To do this, we propose a new type of fuzzy set called a p , q -cubic quasi-rung orthopair fuzzy set ( p , q -CQOFS). The p , q -CQOFS allows for a more flexible and detailed expression of incomplete information through the use of an additional parameter. The paper describes the concept of p , q -CQOFS and its relationship to other types of fuzzy sets, introduces score and accuracy functions for p , q -CQOFS and analyzes some of its mathematical properties, defines the Hamming distance measure between two p , q -CQOFSs and examines some of its important properties, investigates the basic operations of p , q -CQOFSs and extends these laws to aggregation operators, and introduces weighted averaging and geometric aggregation operators for combining p , q -cubic quasi-rung orthopair fuzzy data. [ABSTRACT FROM AUTHOR]

The large-scale multi-attribute group decision-making (LSMAGDM) problem has become a hot research topic in the field of decision science. An R-numbers large-scale multi-attribute group decision-making (R-LSMAGDM) model is proposed to be constructed in this paper based on the advantages of R-numbers in capturing risks. First, the most commonly used clustering method, k-means, is introduced to determine the sub-groups. Then, a new sub-group weighting determination model is constructed by considering sub-group size and sub-group entropy. Next, we also build an optimized consensus-reaching model by improving the calculation method of the mean value. Then, the R-numbers weighted Hamy mean (RNWHM) operator is proposed to aggregate the sub-group information. In addition, the logarithmic percentage change-driven objective weighting (LOPCOW) method and the compromise ranking of alternatives from distance to ideal solution (CRADIS) method are used for attribute weighting calculation and alternative ranking, respectively. Finally, the effectiveness of the model is verified by an application example of hydrogen fuel cell logistics path selection. [ABSTRACT FROM AUTHOR]

A T-spherical uncertain linguistic set (TSULS) is not only an expanded form of the T-spherical fuzzy set and the uncertain linguistic set but can also integrate the quantitative judging ideas and qualitative assessing information of decision-makers. For the description of complex and uncertain assessment data, TSULS is a powerful tool for the precise description and reliable processing of information data. However, the existing multi-attribute border approximation area comparison (MABAC) method has not been studied in TSULS. Thus, the goal of this paper is to extend and improve the MABAC method to tackle group decision-making problems with completely unknown weight information in the TSUL context. First, the cross-entropy measure and the interactive operation laws for the TSUL numbers are defined, respectively. Then, the two interactive aggregation operators for TSUL numbers are developed, namely T-spherical uncertain linguistic interactive weighted averaging and T-spherical uncertain linguistic interactive weighted geometric operators. Their effective properties and some special cases are also investigated. Subsequently, a new TSULMAGDM model considering the DM's behavioral preference and psychology is built by integrating the interactive aggregation operators, the cross-entropy measure, prospect theory, and the MABAC method. To explore the effectiveness and practicability of the proposed model, an illustrative example of Sustainable Waste Clothing Recycling Partner selection is presented, and the results show that the optimal solution is h3. Finally, the reliable, valid, and generalized nature of the method is further verified through sensitivity analysis and comparative studies with existing methods. [ABSTRACT FROM AUTHOR]

In large group decision-making, participators with different knowledge structures, backgrounds, and other characteristics are unlikely to accurately evaluate alternatives. For this, it is necessary to decompose alternatives into several elements, and consider the participators' preferences for elements of alternatives and the multiple classifications for participators according to their characteristics. However, related studies are still scarce. The objective of this paper is to propose a multi-elemental large group decision-making method, in which the desirable alternative(s) are selected from a set of feasible alternatives according to the preference information on multiple elements of alternatives provided by participators from multiple subgroups, and multiple classifications for participators are considered. In the method, according to the strict preference ordering of elements provided by participators, the percentage distributions on preferences of each subgroup concerning each element are firstly presented under each classification for participators. Secondly, the decision weight of each subgroup is determined by three factors, i.e., the consensus of preferences provided by each subgroup, the organizer's preference for each subgroup, and the number of participators in each subgroup. Then, the comprehensive preference concerning each element is determined by combing the preference information from multiple subgroups and the decision weights of multiple subgroups, the overall preference vector can be obtained under each classification, and the virtual alternatives are determined by normalizing the overall preference vector. Further, considering multiple classifications for participators, the overall dominant degrees of alternatives can be obtained by calculating the similarity degrees between each virtual alternative and each alternative, thus the ranking order of alternatives can be obtained based on the overall dominant degrees of alternatives. Finally, an example is given to confirm the feasibility of the proposed method. The results of the sensitivity and comparative analyses show that the proposed method is applicable and effective. The proposed method can further enrich and improve the theory and approach of large group decision-making with multiple elements considering multiple classifications for participators. [ABSTRACT FROM AUTHOR]

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]

To express the opinions of decision-makers, q-rung orthopair hesitant fuzzy sets (q-ROHFSs) have been employed extensively. Therefore, it is necessary to construct q-rung orthopair hesitant fuzzy preference relations (q-ROHFPRs) as a crucial decision-making tool for decision-makers. The goal of this paper aims to define a new consistency and consensus approach for solving q-ROHFPR group decision-making (GDM) problems. To do this, we first state the definitions of q-ROHFPRs and additive consistent q-ROHFPRs based on q-ROHFSs, an additive consistency index and acceptable additive consistent q-ROHFPRs. Second, based on minimizing the deviation, we establish an acceptable goal programming model for unacceptable additive consistent q-ROHFPRs. Third, an iterative algorithm is created for achieving acceptable consistency and reaching a rational consensus. The degree of rational consensus among individual q-ROHFPRs is quantified by a distance-based consensus index. Afterward, a non-linear programming model is formulated to derive the priority vector of alternatives, which are q-rung orthopair hesitant fuzzy numbers (q-ROHFNs). Based on this model, a GDM model for q-ROHFPRs is then developed. To demonstrate the validity and utility of the proposed GDM model, a case study on the risk assessment of hypertension is provided. The finding of sensitivity and comparison analyses supports the feasibility and efficacy of the suggested approach. [ABSTRACT FROM AUTHOR]

Group decision-making and consensus modeling have always been important research topics. With the widespread use of the Internet, group decisions can be made online, in which a large number of decision-makers participate. Most of the existing studies on large-scale group decision-making consider 20–50 decision-makers. Therefore, there is a need for a framework that focuses on situations where thousands of decision-makers exist. As dimension reduction is one of the five primary challenges in large-scale group decision-making, in this study, after reviewing the existing approaches, a new model is presented using a statistical approach along with complex network analysis techniques. The opinions are generalized first, and then the network of opinions is built. This new method reduces the dimensions of the problem by considering a hierarchy of opinions. Different scenarios were designed for the evaluation. The results show that the effect of this generalization on dimension reduction depends on the parameters of the problem. We have shown that in a group decision scenario with 3000 decision-makers and 6 alternatives, 99% of the data was reduced. As dimension reduction is the main focus of the current research, the effect of consistency on the diversity of opinions has also been investigated, and the results show that opinion consistency affects opinion generalization, which in turn affects dimension reduction. In addition, in the performed simulations, three types of functions were used to calculate similarity. The aim was to determine the best similarity function for the decision problems whose purpose was to rank the available alternatives. The results show that Euclidean similarity is a strict criterion compared with Cosine similarity. [ABSTRACT FROM AUTHOR]

To solve difficulties involving various groups' decision-making problems, this work has been proposed to develop a logical aggregation approach to aggregate decision-makers' crisp data into Pythagorean fuzzy numbers. By combining the established strategy with the Pythagorean fuzzy TOPSIS method, a hybrid Pythagorean fuzzy multiple criteria group decision-making methodology is presented. Based on fuzzy rules inference and the Takagi–Sugeno technique, a novel function is created to represent the degrees of uncertainty in decision-makers' data. As an example, the material selection process in practical additive manufacturing designs is provided to show how the proposed methodology may be applied to actual applications. Sensitivity analysis is used to evaluate the effectiveness of the suggested methodology. The outcomes demonstrate that the plan was successful in producing a PFN that accurately reflects the decision-maker's knowledge. [ABSTRACT FROM AUTHOR]

The disaster caused by landslide is huge. To prevent the spread of the disaster to the maximum extent, it is particularly important to carry out landslide disaster treatment work. The selection of landslide disaster treatment alternative is a large scale group decision-making (LSGDM) problem. Because of the wide application of social media, a large number of experts and the public can participate in decision-making process, which is conducive to improving the efficiency and correctness of decision-making. A IF-TW-LSGDM method based on three-way decision (TWD) and intuitionistic fuzzy set (IFS) is proposed and applied to the selection of landslide treatment alternatives. First of all, considering that experts and the public participate in the evaluation of LSGDM events, respectively, the method of obtaining and handling the public evaluation information is given, and the information fusion approach of the public and experts evaluation information is given. Second, evaluation values represented by fuzzy numbers are converted into intuitionistic fuzzy numbers (IFNs), and the intuitionistic fuzzy evaluation decision matrix described by IFNs is obtained. Then, a new LSGDM method of alternatives classification and ranking based on IFS and TWD is proposed, the calculation steps and algorithm description are given. In this process, we first cluster the experts, then consider the identification and management of non-cooperative behavior of expert groups. This work provides an effective method based on LSGDM for the selection of landslide treatment alternatives. Finally, the sensitivity of parameters is analyzed, and the feasibility and effectiveness of this method are compared and verified. [ABSTRACT FROM AUTHOR]

A useful tool for expressing fuzziness and uncertainty is the recently developed n,m-rung orthopair fuzzy set (n,m-ROFS). Due to their superior ability to manage uncertain situations compared to theories of q-rung orthopair fuzzy sets, the n,m-rung orthopair fuzzy sets have variety of applications in decision-making in daily life. To deal with ambiguity and unreliability in multi-attribute group decision-making, this study introduces a novel tool called k m n -rung picture fuzzy set ( k m n -RPFS). The suggested k m n -RPFS incorporates all of the benefits of n,m-ROFS and represents both the quantitative and qualitative analyses of the decision-makers. The presented model is a fruitful advancement of the q-rung picture fuzzy set (q-RPFS). Furthermore, numerous of its key notions, including as complement, intersection, and union are explained and illustrated with instances. In many decision-making situations, the main benefit of k m n -rung picture fuzzy sets is the ability to express more uncertainty than q-rung picture fuzzy sets. Then, along with their numerous features, we discover the basic set of operations for the k m n -rung picture fuzzy sets. Importantly, we present a novel operator, k m n -rung picture fuzzy weighted power average ( k m n -RPFWPA) over k m n -rung picture fuzzy sets, and use it to multi-attribute decision-making issues for evaluating alternatives with k m n -rung picture fuzzy information. Additionally, we use this operator to pinpoint the countries with the highest expat living standards and demonstrate how to choose the best option by comparing aggregate findings and applying score values. Finally, we compare the outcomes of the q-RPFEWA, SFWG, PFDWA, SFDWA, and SFWA operators to those of the k m n -RPFWPA operator. [ABSTRACT FROM AUTHOR]

In current piece of writing, we bring in the new notion of induced bipolar neutrosophic (BN) AOs by utilizing Einstein operations as the foundation for aggregation operators (AOs), as well as to endow having a real-world problem-related application. The neutrosophic set can rapidly and more efficiently bring out the partial, inconsistent, and ambiguous information. The fundamental definitions and procedures linked to the basic bipolar neutrosophic (BN) set as well as the neutrosophic set (NS), are presented first. Our primary concern is the induced Einstein AOs, like, induced bipolar neutrosophic Einstein weighted average (I-BNEWA), induced bipolar neutrosophic Einstein weighted geometric (I-BNEWG), as well as their different types and required properties. The main advantage of employing the offered methods is that they give decision-makers a more thorough analysis of the problem. These strategies whenever compare to on hand methods, present complete, progressively precise, and accurate result. Finally, utilizing a numerical representation of an example for selection of robot, for a problem involving multi-criteria community decision making, we propose a novel solution. The suitability ratings are then ranked to select the most suitable robot. This demonstrates the practicality as well as usefulness of these novel approaches. [ABSTRACT FROM AUTHOR]

With consideration for the extensive resources consumption and environmental degradation being on the rise today, implementing green development strategy to pursue both socioeconomic growth and the coordinated of environment sustainability, has become an increasingly important issue in modern enterprise supply chain operations management. Hence, the appropriate green supplier selection (GSS), viewed as a core issue in green supply chain management (GSCM), requires continuous research in this field to obtain a complete perception on GSS practices. It can be regarded as a multi-attribute group decision-making (MAGDM) problem that involves many conflict and unmeasurable evaluation criteria. In view of the superiority of multi-granularity extended probabilistic linguistic term sets (MGEPLTSs) in modeling such issues on potential ambiguity, complexity and uncertainty in actual GSS practices, we propose a novel integrated MAGDM methodology for GSS problems, by integrating the BWM (best–worst method) with the VIKOR (VIšekriterijumsko KOmpromisno Rangiranje) technique under the MGEPLTSs environment. First, by introducing the multi-granularity and probabilistic linguistic term sets, the MGEPLTSs are proposed to represent and quantify the decision information of GSCM practitioners. Then, the BWM is introduced to the MGEPLTSs environment to compute the weights of decision-making panels and evaluation attributes in GSS problems, by building the fuzzy mathematical programming model, respectively. Finally, we extend a multi-granularity extended probabilistic linguistic VIKOR method to calculate the compromise measure of alternatives considering the group utility maximization and the individual regret minimization, thereby achieving the full ranking of alternatives. A GSS case is conducted to illustrate the feasibility of the proposed approach, and the sensitivity analysis and comparative analysis with other similar approaches are presented to demonstrate its effectiveness and advantages. [ABSTRACT FROM AUTHOR]

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]

In this article, we introduce logarithmic operations on bipolar fuzzy numbers (BFNs). We present some new operators based on these operations, namely, the logarithm bipolar fuzzy weighted averaging (L-BFWA) operator, logarithm bipolar fuzzy ordered weighted averaging (L-BFOWA) operator, and logarithm bipolar fuzzy weighted geometric (L-BFWG) operator, and logarithm bipolar fuzzy ordered weighted geometric (L-BFOWG) operator. Further, develop a multi-attribute group decision-making (MAGDM) methodology model based on logarithm bipolar fuzzy weighted averaging operator and logarithm bipolar fuzzy weighted geometric operators. To justify the proposed model's efficiency, MABAC (the multiple attribute border approximation area comparison) methods are applied to construct MAGDM with BFNs established on proposed operators. To demonstrate the proposed approach's materiality and efficiency, use the proposed method to solve supply chain management by considering numerical examples for supplier selection. The selection of suppliers is investigated by aggregation operators to verify the MABAC technique. The presented method is likened to some existing accumulation operators to study the feasibility and applicability of the proposed model. We concluded that the proposed model is accurate, effective, and reliable. [ABSTRACT FROM AUTHOR]