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Normal fuzzy sets and Pythagorean cubic fuzzy sets are the best means to deal with fuzziness. Combining both of these structures in our current work, we establish the idea of Pythagorean cubic normal fuzzy set. We define some basic operational laws for Pythagorean cubic normal fuzzy set and introduce a number of aggregation operators, including Pythagorean cubic normal fuzzy weighted averaging operator, Pythagorean cubic normal fuzzy weighted geometric operator, Pythagorean cubic normal fuzzy order weighted averaging operator and Pythagorean cubic normal fuzzy order weighted geometric operator. We examine several favorable properties, including monotonicity, boundedness, and idempotency for the proposed operators. We develop an algorithm for the solution of multicriteria decision-making problems. Moreover, we propose an extended form of the TODIM (Portuguese acronym for Interactive Multi-Criteria Decision Making) method. We present a multicriteria decision-making example related to assessing the educational needs of students with disabilities. The techniques and operators defined in the current work provide greater generality and accuracy and give precise results. Ultimately, a detailed illustration is provided to show the closure process of these specified procedures and functions, demonstrating their credibility and efficacy. [ABSTRACT FROM AUTHOR]

Abstract In the current era, IoT-based healthcare solutions play a pivotal role in transforming the healthcare landscape by addressing key challenges and significantly enhancing the quality, accessibility, and efficiency of medical services, particularly for individuals in remote areas. This paper introduces innovative operations on fractional fuzzy sets (FFS), specifically the Hamacher sum and product, and establishes corresponding operational laws. Building upon these foundations, we propose novel aggregation operators (AoPs) leveraging Hamacher norms and rigorously analyze their properties within the FFS framework. Furthermore, we integrate these advancements into decision-making methodologies, including Extended TOPSIS, TODIM, and Extended GRA, tailored for applications in FFS. To illustrate the practicality and effectiveness of our approach, we present a detailed case study on healthcare system selection. Finally, a comparative analysis of the proposed methods with existing aggregation operators highlights the robustness and suitability of our solution in real-world scenarios.

With the acceleration of urbanization construction, the contradiction between supply and demand of urban public transportation resources is becoming increasingly prominent, resulting in increasingly serious problems such as traffic congestion and environmental pollution, which has a great impact on the sustainable development of cities. The experience of mature markets both domestically and internationally indicates that priority must be given to the development of public transportation networks with rail transit as the backbone. Due to the fact that the operation of the rail transit system should not only focus on market benefits but also meet social benefits as much as possible, evaluating efficiency has become a prerequisite for managing rail transit and an important topic in the performance evaluation of urban public transportation. The urban public transport operations evaluation is a multiple-attribute group decision-making (MAGDM). Then, the TODIM and EDAS method has been constructed to deal with MAGDM issues. The interval neutrosophic sets (INSs) are constructed as an effective tool for representing uncertain information during the urban public transport operations evaluation. In this manuscript, the interval neutrosophic number TODIM-EDAS (INN-TODIM-EDAS) method is constructed to solve the MAGDM under INSs. Finally, a numerical example study for urban public transport operations evaluation is constructed to validate the INN-TODIM-EDAS method. The main research contribution of this paper is constructed: (1) the INN-TODIM-EDAS method is put up for MAGDM with INSs; (2) the INN-TODIM-EDAS method is put up for urban public transport operations evaluation and were compared with existing methods; (3) Through the detailed comparison, it is evident that INN-TODIM-EDAS method for urban public transport operations evaluation proposed in this paper are effective. [ABSTRACT FROM AUTHOR]

Aiming at the defects of the existing probabilistic hesitation fuzzy distance measures, which require the number of membership degree to be consistent and the order to be rearranged, a probabilistic hesitation fuzzy multi-attribute decision making method based on the comprehensive characteristic distance measure is proposed. First, a new law of probability hesitant fuzzy number comparison is defined. Then four characteristics of aggregation, discreteness, fuzziness and consistency are defined, and a new comprehensive distance measure is defined based on definitions above. Finally, on the basis of traditional TODIM method and prospect theory, the validity and rationality of the distance measure and new probability hesitant fuzzy recognition method in this paper are verified by examples and comparative analysis.

The hesitant fuzzy linguistic term sets (HFLTSs) are capable of accurately capturing decision makers' subjective characteristics, thereby resolving the issue of uncertain ambiguity in decision-making concerning existing ship water pollutant receiving facilities (SWPRF). This paper introduces an enhanced TODIM approach that incorporates optimized dominance degrees to overcome the shortcomings associated with current research assumptions regarding known weights, artificial elements, and disregard for decision makers' psychological behavior. Firstly, we introduce a new HFLTS hesitancy degree (HFLTS-HD) and bidirectional projection model to handle the problem of unknown weights. Moreover, our proposed model incorporates attribute weights, decision maker weights, and hesitant fuzzy linguistic weighted operators. Secondly, considering the inconsistency in the cardinality of elements within the hesitant fuzzy linguistic term set, we define the hesitant fuzzy linguistic signed distance (HFLSD). Eventually, using Taizhou SWPRF and its disposal facilities as a case study, the effectiveness of the proposed scheme is demonstrated, while highlighting the superiority of the proposed method through a comparison with two existing approaches. [ABSTRACT FROM AUTHOR]

The primary objective of this research is to examine how the Russia–Ukraine war impacted the global economy. To achieve this goal, we propose operational laws, a score and accuracy function, and a divergence measure for complex dual hesitant fuzzy sets. Furthermore, we investigate the challenges associated with multi-criteria decision-making (MCR) using aggregation operators and the TODIM method with complex dual hesitant fuzzy (CDHF) information. Drawing inspiration from arithmetic aggregation operations, we introduce several aggregation operators for complex dual hesitant fuzzy information, including the complex dual hesitant fuzzy weighted average (CDHFWA) operator, complex dual hesitant fuzzy ordered weighted average (CDHFOWA) operator, and complex dual hesitant fuzzy hybrid average (CDHFHA) operator. We thoroughly analyze the unique characteristics of these proposed operators and use them in conjunction with the TODIM method to develop practical approaches for solving complex dual hesitant fuzzy multi-criteria decision-making problems. To validate our approach and demonstrate its applicability, we provide a practical example of how the Russia–Ukraine war affected the global economy. Our study confirms the effectiveness of our approach and highlights how it can be used to solve real-world problems. [ABSTRACT FROM AUTHOR]

Abstract The primary objective of this research is to examine how the Russia–Ukraine war impacted the global economy. To achieve this goal, we propose operational laws, a score and accuracy function, and a divergence measure for complex dual hesitant fuzzy sets. Furthermore, we investigate the challenges associated with multi-criteria decision-making (MCR) using aggregation operators and the TODIM method with complex dual hesitant fuzzy (CDHF) information. Drawing inspiration from arithmetic aggregation operations, we introduce several aggregation operators for complex dual hesitant fuzzy information, including the complex dual hesitant fuzzy weighted average (CDHFWA) operator, complex dual hesitant fuzzy ordered weighted average (CDHFOWA) operator, and complex dual hesitant fuzzy hybrid average (CDHFHA) operator. We thoroughly analyze the unique characteristics of these proposed operators and use them in conjunction with the TODIM method to develop practical approaches for solving complex dual hesitant fuzzy multi-criteria decision-making problems. To validate our approach and demonstrate its applicability, we provide a practical example of how the Russia–Ukraine war affected the global economy. Our study confirms the effectiveness of our approach and highlights how it can be used to solve real-world problems.

In reality, decision-making is usually influenced by vague evaluation information and irrational psychology behavior of decision-makers. To solve the multi-attribute decision-making problem with completely unknown weight vague information, an extended hybrid decision-making method is proposed under the Fermatean hesitant fuzzy environment. Firstly, the weight information is determined from two levels of alternative and attribute based on the score function and entropy value. Secondly, the dominance matrix is constructed according to the dominance of each alternative obtained by the TODIM method. Then, the regret theory is introduced to compute the perception values, which is the factor to rank the alternatives by the VIKOR method. Afterwards, an illustrative example is provided to prove the effectiveness and validity of the proposed hybrid method. By sensitivity analysis and comparative analysis, this method is shown to be more advantageous in considering the regret psychological characteristics of the DM. [ABSTRACT FROM AUTHOR]

In recent years, employers have continuously raised their requirements for college students, not only requiring a solid professional foundation, but also emphasizing personal professional literacy. As the first base for cultivating college students, major universities should not only guide them in their correct employment and entrepreneurship, but also help them find employment and entrepreneurship faster and better. However, in the context of the new era, universities still face some problems in the process of carrying out employment and entrepreneurship education, which hinder the progress of employment and entrepreneurship education. The probabilistic hesitant fuzzy sets (PHFSs), as an extension of hesitant fuzzy sets (HFSs), can more effectively and accurately describe uncertain or inconsistent information during the quality evaluation of college student employment and entrepreneurship education. TODIM and TOPSIS methods are two commonly used multi-attribute decision-making (MADM) methods, each of which has its advantages and disadvantages. The quality evaluation of college student employment and entrepreneurship education is regarded as the defined multiple attribute group decision making (MAGDM). This paper proposes a novel method based on TODIM and TOPSIS to cope with multi-attribute group decision making (MAGDM) problems under PHFSs environment. After introducing the related theory of PHFSs and the traditional TODIM and TOPSIS methods, the novel method based on a combination of TODIM and TOPSIS methods is designed. And then, an illustrative example for quality evaluation of college student employment and entrepreneurship education proved the feasibility and validity of the proposed method. Finally, the result has been compared with some existing methods under the same example and the proposed method's superiority has been proved. [ABSTRACT FROM AUTHOR]

The rapid development of global information technology, especially the emergence and widespread application of the Internet, has enabled information technology to quickly penetrate into various fields of the economy and society. Informatization and networking have become important features of today's era. However, while people enjoy the tremendous progress brought by information technology to humanity, the openness and security vulnerabilities of computer networks have also made network information security issues increasingly prominent. The invasion of hackers, the continuous generation and spread of computer virus, and the rampant use of rogue software have all caused great economic losses to individuals, enterprises, and countries. The computer network security evaluation is a multiple-attribute group decision making (MAGDM). Then, the TODIM and TOPSIS method has been established to deal with MAGDM issues. The interval neutrosophic sets (INSs) are established as an effective tool for representing uncertain information during the computer network security evaluation. In this manuscript, the interval neutrosophic number TODIM-TOPSIS (INN-TODIM-TOPSIS) method is established to solve the MAGDM under INSs. Finally, a numerical example study for computer network security evaluation is established to validate the INN-TODIM-TOPSIS method. The main research contribution of this paper is established: (1) the INN-TODIM-TOPSIS method is put up for MAGDM with INSs; (2) the INN-TODIM-TOPSIS method is put up for computer network security evaluation and were compared with existing methods; (3) Through the detailed comparison, it is evident that INN-TODIM-TOPSIS method for computer network security evaluation proposed in this paper are effective. [ABSTRACT FROM AUTHOR]

In the face of multi-attribute decision problems in complex situations, most traditional multi-attribute group decision methods are based on the assumption that the decision maker is perfectly rational, while in the face of complex decision problems, the decision maker usually has the psychological characteristics of limited rationality and may use more than one linguistic term to describe the decision information when expressing the decision information To this end, this paper selects probabilistic language term sets to describe complex preference information. First, to address the problem that the current probabilistic linguistic term set correlation coefficient cannot appropriately measure the degree of correlation among probabilistic linguistic term sets, this paper proposes a new probabilistic linguistic term set correlation coefficient from three characteristic factors of probabilistic linguistic term sets: mean, variance, and length rate. To integrate the attribute index weights, probabilistic linguistic term set weighted mixed correlation coefficients are proposed. Second, this paper introduces the TODIM method, which can consider the psychological behavior of decision makers, and proposes a TODIM multi-attribute decision making method based on probabilistic linguistic term sets with mixed correlation coefficients. Finally, through an empirical analysis of four Internet listed companies in a new first-tier city in China, this study verifies the rationality and validity of the proposed method. The results show that the mixed correlation coefficient can comprehensively measure the correlation between probabilistic linguistic term sets, which provides an important method for future multi-attribute decision making problems. [ABSTRACT FROM AUTHOR]

The probabilistic hesitant fuzzy sets (P-HFSs) allow experts to express their preferences regarding different membership degrees with probabilistic information. Fuzzy entropy is an important concept to measure the uncertainty of probabilistic hesitant fuzzy information. In this paper, we propose a novel fuzzy entropy named as the exponential probabilistic hesitant fuzzy entropy for the P-HFEs. This novel fuzzy entropy not only observes the basic property of fuzzy entropy, but also has the same characteristics and change tends with the existing fuzzy entropy proposed and studied by other scholars. Then, based on the cardinal reconciliation method and TODIM(Tomada de decisao interativa multicriterio) method, we propose a multi-criteria decision-making (MCDM) problem, where the attribute weight is determined by the exponential probabilistic hesitant fuzzy entropy of the integration results. Finally, a application case in green building is given for the sake of illustrating the efficiency of the MCDM problem. Numerical and theoretical results show that a MCDM problem based on the proposed novel fuzzy entropy and the TODIM method have a wide range of application.

Three-way decision models have received substantial interest grounded in decision-theoretic rough sets and Bayesian decision theory. Single-valued neutrosophic sets are extremely useful for handling uncertain and inconsistent information, making them a valuable tool that is commonly applied in decision-making. In a three-way decision problem involving a piece of single-value neutrosophic information, the losses of each equivalence class under different actions can usually be identified with some accuracy. A critical aspect of the three-way decision problem centers around appropriate handling of the loss function. This paper proposes a novel approach to rank loss functions in each equivalence class of three-way decisions, based on the TODIM method and operates within a singlevalued neutrosophic environment. Furthermore, a numerical experiment on the location of a breakfast restaurant is used to to assess the model compared to some existing related models, with the aim of demonstrating its validity and soundness. [ABSTRACT FROM AUTHOR]

The normal wiggly hesitant fuzzy set (NWHFS) is one of the latest extensions of hesitant fuzzy set (HFS). It can depict experts' preference information consisting of several possible values and the potential information dug in the traditional hesitant fuzzy set (HFS) at the same time. However, traditional aggregation operators of NWHFSs always ignore the influence of psychological behaviors. Therefore, to make use of the potential information and manage the applications with incomplete rationality, this paper combines the advantages of TODIM (TOmada deDecisão Iterativa Multicritério) method and NWHFSs. Considering the structures and characteristics of NWHFSs, we also provide the definition of distance measure of NWHFSs. Based on this, we develop an improved TODIM method. The specific implementation process is also provided. Finally, we apply the improved TODIM method to the environmental quality evaluation. The comparison result with traditional aggregation operators indicates that the proposed method can enlarge the competitive relationship better. It also demonstrates the rationality and accuracy of our method. [ABSTRACT FROM AUTHOR]

The competitiveness evaluation of regional financial centers is frequently looked as the multiple attribute group decision-making (MAGDM) problem. Based on the TODIM method and fuzzy number intuitionistic fuzzy sets (FNIFS), this paper proposes a new FNIF-TODIM method to evaluate the competitiveness of regional financial centers. First, some basic theories related to FNIFS are briefly introduced. In addition, the weights of the attributes are obtained objectively using the CRITIC weighting method. Then, the traditional TODIM method is extended to FNIFS to obtain the final order of alternatives. As a result, all alternatives can be ranked and the best one for the competitiveness assessment of regional financial centers can be identified. Finally, an example for competitiveness evaluation of regional financial centers and some decision comparative analysis is listed. The results show that the established algorithmic approach is useful. The main works of this work are: (1) the paper constructs the FNIF-TODIM method for the evaluation of the competitiveness of regional financial centers; (2) the established method is illustrated by a case study for competitiveness evaluation of regional financial centers; and (3) some comparisons prove the rationality and advantages. [ABSTRACT FROM AUTHOR]

The probabilistic hesitant fuzzy sets (P-HFSs) allow experts to express their preferences regarding different membership degrees with probabilistic information. Fuzzy entropy is an important concept to measure the uncertainty of probabilistic hesitant fuzzy information. In this paper, we propose a novel fuzzy entropy named as the exponential probabilistic hesitant fuzzy entropy for the P-HFEs. This novel fuzzy entropy not only observes the basic property of fuzzy entropy, but also has the same characteristics and change tends with the existing fuzzy entropy proposed and studied by other scholars. Then, based on the cardinal reconciliation method and TODIM(Tomada de decisao interativa multicriterio) method, we propose a multi-criteria decision-making (MCDM) problem, where the attribute weight is determined by the exponential probabilistic hesitant fuzzy entropy of the integration results. Finally, a application case in green building is given for the sake of illustrating the efficiency of the MCDM problem. Numerical and theoretical results show that a MCDM problem based on the proposed novel fuzzy entropy and the TODIM method have a wide range of application. [ABSTRACT FROM AUTHOR]

The offshore floating wind-solar-aquaculture (WSA) system with its advantages such as strong seakeeping ability, considerable power generation, and full utilization of ocean space and water resources will have a bright prospect in the future. In order to accelerate the sustainable development of the energy industry, it is very important to build a reasonable investment decision-making framework. Therefore, this paper aims to build a multi-criteria group decision-making (MCGDM) framework for investment decision-making of this project. Firstly, a comprehensive criteria system has been established. Secondly, probabilistic language term sets (PLTSs) are introduced to describe the uncertainty and fuzziness of decision information. Thirdly, the expert weight determination model is established based on the correlation measure and correlation coefficient of PLTSs, and the PL-fuzzy decision-making trial and evaluation laboratory (DEMATEL) method and the information entropy method are introduced to determine the subjective and objective weights of the criteria. In addition, considering the decision maker's psychological behavior, we choose probabilistic language the interactive and multiple attribute decision-making (TODIM) method to determine the optimal investment alternative. Finally, we apply the proposed framework to a case study. The results illustrate that the alternative A3 possesses the optimal comprehensive performance with the overall value is 1. Then, we conduct sensitivity analysis and comparative analysis to verify its robustness and feasibility. Scenario analysis in TODIM method showed that it is reasonable to express decision preference by setting different recession coefficients in the actual decision-making environment. This study can provide some reference for decision-makers, and also extend the method of decision-making field. [ABSTRACT FROM AUTHOR]

In the context of the accelerated iteration of financial technology, the layout of financial technology in the banking industry is also accelerating and shifting gears. Actively cooperating with financial technology companies has become an important channel for banks to cope with challenges and achieve transformational development. Assessing and selecting the best financial technology company is one of the core issues that banks should address in establishing cooperative relationships. In this paper, an integrated decision-making framework based on the best-worst method (BWM) and TODIM (an acronym for interactive and multi-criteria decision making in Portuguese) is proposed for financial technology selection under the interval type-2 fuzzy (IT2F) environment. Within the proposed framework, the preference information of decision-makers for alternatives and pairwise comparison among criteria is captured by the interval type-2 fuzzy sets (IT2FSs), and the criteria weights are calculated by the IT2F-BWM method. Moreover, the IT2F-TODIM considering the psychological behavior state of decision-makers is introduced to determine the alternative ranking. The practicability and reliability of the proposed methodology are verified by a case study with sensitivity analysis and comparative analysis. This study contributes theoretically and practically to relevant literature by providing an effective framework capable of handling decision issues under uncertainty. [ABSTRACT FROM AUTHOR]

The need for energy sources in India has increased abnormally in recent years due to industrial and societal growth. To meet this demand, it was a necessary choice of renewable energy sources (RESs) as a solution to lack of nonrenewable energy sources. Due to the multiplicity of involved factors, selecting the most appropriate RESs is a multiattribute decision making (MADM) problem. There is a large number of work associated with the development of MADM techniques, especially under ambiguous and uncertain conditions. However, the effective embedding of uncertainty and ambiguity and in decision‐making remains a difficult challenge, and thus this study introduces a new framework for solving the problem of selecting the most suitable RESs which is based on the neutrosophic set and TODIM (an acronym in Portuguese of interactive and multicriteria decision‐making) method. It also reduces human intervention by being systematically applied. First, it transforms the linguistic terms presented into neutrosophic values and implements systematic techniques to compute missing values in the decision matrix using the case‐based technique. Second, it calculates the weight of every linguistic variable as well as those of the decision‐makers (DMs) and weighted attributes. Furthermore, it creates an aggregated single valued neutrosophic decision matrix for DMs. Finally, it calculates the overall dominance‐degree matrix, derives the overall values, and ranks the alternatives. It is applied to select RESs in Karnataka, India, and the obtained results show that wind energy is the most suitable RES for India, with small hydroenergy second most appropriate. [ABSTRACT FROM AUTHOR]

Cross-efficiency evaluation is an extended form of DEA evaluation. The main difference from other models is that the evaluation of cross-efficiency takes the self-evaluation value and other evaluation values as the final efficiency score, and then ranks the decision-making units (DMUs). However, the traditional cross-efficiency model cannot guarantee the uniqueness of input weights and output weights, and the final result does not reach Pareto optimal. Also, the simple average aggregation of cross-efficiency values ignores the relative weight of DMUs and loses a lot of decision-making information, which leads to the lack of credibility of the results. Considering the decision information carried by the data and the weight of the decision-makers (DMs), this paper proposes an aggregate method of interval cross-efficiency matrix to realize the relative efficiency evaluation and the accurate ranking of the DMUs. In which DMUs are regarded as DMs, and then the relative weights of DMUs are determined by using the method of Decision-making trial and evaluation laboratory (DEMATEL), and the relative advantage scores are obtained by considering the risk attitude of decision-makers based on the principle of the improved TODIM method. Finally, a numerical example is used to verify the feasibility and effectiveness of the proposed method, and the stability of the proposed method is verified by changing the value of θ . Compared with the simple average aggregation method of cross-efficiency values, the proposed method is more reasonable and feasible. [ABSTRACT FROM AUTHOR]

With the increasing complexity of decision making (DM) problems, powerful mathematical tools are needed to represent and process fuzzy and uncertain DM information, and Pythagorean fuzzy set (PFS) is such a mathematical tool. PFS has been successfully applied in the field of fuzzy multiple criteria decision making (MCDM). Correlation coefficient is an information measure of PFS, and plays an important role in the application of PFS. At present, there is a problem that the existing correlation coefficients cannot moderately measure the correlation degree between PFSs, so this paper proposes the new correlation coefficients of PFS. The TODIM method has been proved to be effective in dealing with MCDM problems that consider the psychological behavior of decision makers. This paper extends the TODIM method with the new correlation coefficients of PFS, and the extended TODIM method is called Pythagorean fuzzy CC-TODIM method. By numerical examples, it is verified that the new correlation coefficients of PFS are more reasonable and valid. By case analysis, it is verified that the Pythagorean fuzzy CC-TODIM method can effectively solve the MCDM problems, and the Pythagorean fuzzy CC-TODIM method based on the new correlation coefficients is more accurate and reliable. [ABSTRACT FROM AUTHOR]

The single-valued neutrosophic sets area unit powerful tool to describe uncertain data. TODIM method is usually accustomed solve multi-attributes decision-making issues. supported the cumulative prospect theory, this paper proposes an extended TODIM method that comprehensively reflects the psychological characteristics of decision makers. Firstly, we in short explain the definitions of cumulative prospect theory and single-valued neutrosophic sets. Secondly, we introduce the steps of the classical TODIM method of resolution multiple attributes decision-making issues. On the idea, we propose an extended TODIM method to comprehensively mirror the psychological state of decision makers. Finally, through the case analysis, it’s evidenced that extended TODIM method will higher think about the psychological characteristics of decision makers. [ABSTRACT FROM AUTHOR]

Failure mode and effects analysis (FMEA) is known to be a proactive reliability analysis model broadly utilized to recognize and evaluate potential failure modes in various industries. The normal risk priority number (RPN) method, however, has suffers from a lot of criticisms, such as requirement of precise risk estimation, lack of scientific basis in computing RPN, and neglecting the weights of risk factors. Therefore, this paper devises a new FMEA model to evaluate and prioritize the risk of failure modes by integrating probabilistic linguistic term sets and TODIM (an acronym in Portuguese for interactive multi-criteria decision making) method. The probabilistic linguistic term sets are utilized to handle the intrinsic ambiguity existed in the risk assessments of FMEA team members, whilst an extended TODIM method is employed for determining the priority ranking of the individuated failure modes. Further, based on the technique for order of preference by similarity to ideal solution (TOPSIS), an objective weighting method is presented to derive the relative weights of risk factors. Finally, two illustrative examples are implemented and comparisons with other existing methods are performed to demonstrate the rationality and superiority of our proposed FMEA model. [ABSTRACT FROM AUTHOR]

In the era of uncertain information everywhere, the Probabilistic Hesitant Fuzzy sets (PHFs), utilizing the possible numbers and its possible membership degrees to descript decision-makers' behavior, has been brought about widespread attention. Scholars from all over the world applied numerous approaches in this environment since Probabilistic Hesitant Fuzzy sets (PHFs) has been come up with, and there are still untapped territories. The TODIM (TOmada deDecisão Iterativa Multicrite´rio) method is a common decision-making method which is based on the prospect theory (PT). Unlike the other multiple criteria decision making (MCDM) methods, the TODIM method think over the bounded rationality of decision makers to choose the optimal alternative according to the decision maker's psychological reality. In this essay, we introduce the Extended TODIM Based on Cumulative Prospect Theory (CPT) for probabilistic hesitant fuzzy multiple attributes group decision-making (MAGDM). In addition, the entropy is applied to calculate the weights between attributes. Finally, the developed method is used to solve the decision-making case study. To test the reasonability of this new method, we utilize a numerical case to compare the extended TODIM method with other methods. [ABSTRACT FROM AUTHOR]

Recently, the TODIM has been used to deal with multiple attribute decision making (MADM) problems. The intuitionistic 2-tuple linguistic sets (I2TLSs) are useful tools to depict uncertainty in MADM. This paper use TODIM method to solve MADM with the intuitionistic 2-tuple linguistic numbers (I2TLNs). Firstly, the concepts of I2TLNs are briefly presented, and classical TODIM for MADM are introduced. Then, the classical TODIM method is used to solve MADM with I2TLNs, and its important characteristic is to fully consider the decision makers' bounded rationality which is a real action in MADM. And a comparative analysis is also given. Finally, a numerical example for service outsourcing providers selection is proposed. [ABSTRACT FROM AUTHOR]

Green supplier selection (GSS) is a crucial issue in green supply chain management. CAPS indicate that industries spend yearly USD 25 million per procurement, which is a huge amount that necessitates a systematic GSS to avoid financial catastrophes. Literatures on GSS reveal that researchers have not addressed the issue of missing preferences, consistency of decision matrices, and repairing inconsistencies. Moreover, handling of complex linguistic expressions is another open challenge in GSS. Motivated by these research gaps, a two-stage decision framework was proposed. From the analysis of different linguistic models, it is clear that a double-hierarchy linguistic model is flexible for handling complex expressions. In the preprocessing stage, preferences were imputed using the case-based method. Later, consistency of matrices was determined using the Cronbach's coefficient, and inconsistent matrices were repaired using the iterative method. In the next stage, new mathematical models were formulated to calculate weights of experts and criteria. Preferences were sensibly aggregated by using the Maclaurin symmetric mean operator, which captures the criteria interrelationship. Green suppliers were prioritized by using the TODIM method. Finally, the practicality, strengths, and weaknesses of the proposed framework were realized by demonstrating a case study of GSS and comparison with other methods. Results infer that the proposed framework (i) is consistent with the existing models, and the values are 0.60, 0.86, and 0.75, respectively; (ii) is robust with 100% rank-order stability even after adequate weight alterations; and (iii) finally can better discriminate suppliers with a broad deviation range of 0.34–0.35. [ABSTRACT FROM AUTHOR]

The selection of a suitable reform model for provincial rural credit cooperatives unions (PRCCUs) is a pivotal aspect of China's ongoing financial reform endeavors. This involves optimizing internal processes, enhancing efficiency, minimizing operational costs, elevating service quality, strengthening financial innovation capabilities, and promoting the healthy growth of rural financial markets. However, current research on this matter primarily concentrates on qualitative analysis. As of yet, a scientifically grounded decision-making framework from a quantitative standpoint has not been developed. This absence of quantitative analysis results in inaccuracies in research findings, thereby hindering the practical applicability of outcomes. To tackle this formidable challenge, we propose an innovative quantitative analysis framework employing the multi-criteria group decision-making method. This framework, which builds upon the cumulative prospect theory (CPT), the TODIM method, and the most recent advances in type-2 fuzzy numbers (T2FNs), is referred to as the T2FNs-CPT-TODIM. Initially, we define a novel score function, followed by the introduction of a fresh method for computing the distance between the T2FNs. Subsequently, our model pioneers an exclusive weight allocation strategy for decision-makers, grounded in the principles of Dice Similarity. Furthermore, the objective weights of criteria can be computed utilizing the Distance Correlation-based CRITIC approach. We then optimize the rankings by applying the advantage of gains and losses preference in the CPT-TODIM. Ultimately, we apply our proposed model to the practical task of selecting the optimal reform model for a specific PRCCU. Thorough comprehensive sensitivity and comparative analyses, the results validate the theoretical robustness and practical efficacy of our proposed method. • We developed a novel quantitative decision making analysis framework for the PRCCUs. • The new score function, distance measure, and Dice Similarity measure are introduced. • Apply the proposed framework to the selection of a PRCCU's reform models. [ABSTRACT FROM AUTHOR]

In modern business environments, a competitive Supply Chain Management is crucial to business continuity. In this context, Lean, Agile, Resilient and Green (LARG), are advocated as the fundamental paradigm for a competitive Supply Chain as a whole. Various paradigms have emerged in the supply chain from the beginning, from among which there are four paradigms lean, agile, resilient and green that are important in supply chain performance and competitiveness, which are referred to as the LARG supply chain. Each of these paradigms pursues a specific mission and purpose in the supply chain. The choice of best supplier in each supply chain is based on different decision-making criteria, but the weight of each criteria varies according to the supplier's priorities. The purpose of this research is to provide a hybrid model of multi-criteria decision for selecting suppliers in the LARG paradigms of tile and ceramic industry. In this research, in first, supplier selection indicators are identified and then weighted by the Best Worst Method. Subsequently, suppliers are ranked by piecewise linear value function and multi-criteria decision-making technique TODIM. This system can play an important role in improving supply chain performance in effective decision making by managers in the supplier selection process and provide results based to reality.

In practical decision‐making problems, the coexistence of several complex situations increases the difficulty for decision makers to make reasonable decision, such as attributes outnumber alternatives, heterogeneous relationships among multiple attributes, and individual risk tendency of decision maker. In view of the advantage of probabilistic linguistic term sets (PLTSs) in presenting qualitative information, a novel decision‐making approach with PLTSs is constructed to deal with the above special situations simultaneously. To realize this goal, some basic models have been proposed. First of all, to truly reflect the importance of attributes from the heterogeneous relationships, a weight determination model with generalized Banzhaf values is developed to analyze the interaction between combinations of attributes. Then, for analyzing the individual risk tendency of decision maker, the generalized Banzhaf TODIM method with PLTSs is constructed. Moreover, based on the above research results, the generalized Banzhaf TODIM‐QUALIFLEX method with PLTSs is developed to solve decision‐making problems where the number of attributes exceeds the number of alternatives, the combinations of attributes are interacted with each other, and decision maker is affected by individual risk propensity. Lastly, smartphones selection through online ratings is a typical case of decision‐making problems with the above situations, which is designed to illustrate the performance of the proposed method. And its rationality and advantages are further demonstrated through some comparative analyses with other methods. [ABSTRACT FROM AUTHOR]

The prosperity of online mobile phone recycling platforms has brought convenience to waste mobile phone recycling. This study aims to propose a novel decision-making method to evaluate the recycling channels of mobile phones in an uncertain environment using the probabilistic linguistic term set (PLTS) to represent uncertain information. Given that each PLTS is associated with a probability distribution, the differences of different PLTSs can be represented by comparing different probability distributions. The Hellinger distance is a widely-used index to measure the similarity of two probability distributions, but it cannot be directly used to express the semantic differences of PLTSs. In this regard, we introduce a cumulative probability-based Hellinger distance measure of PLTSs. Then, we propose an extension of TODIM (an acronym in Portuguese of Interactive and Multicriteria Decision Making) method considering the bounded rationality and psychology of decision-makers based on the proposed distance measure of PLTSs and a criterion weight determination method, the Simos-Roy-Figueira method. Finally, an illustrative example of evaluating the recycling channels of mobile phones is given with sensitive and comparative analyses, showing the efficiency of the proposed method. This method can also be applied to other various fields. [ABSTRACT FROM AUTHOR]

It is impossible for agents on both sides to achieve complete rationality in the decision-making process of two-sided matching (TSM). The TODIM (an acronym in Portuguese of interactive and multi-criteria decision-making) method considering the psychological behavior of decision-makers is well applied in the multiple criteria decision making (MCDM) problems. The TSM is a MCDM problem. Therefore, in this paper, a method based on TODIM technique is introduced to solve the TSM problem, in which the intuitionistic linguistic numbers are utilized to describe the mutual evaluation between candidates and hiring managers. The focus of this paper is to develop a method for the multi-criteria TSM problem under intuitionistic linguistic environment. First, the evaluation matrices of each agent with respect to each criterion are provided by agents on the opposite side, and the weight assigned to each criterion is determined according to the importance of the evaluation criterion to the matching agent. Then, the dominance measurement of each agent over another one can be calculated based on the intuitionistic linguistic TODIM method. Next, a bi-objective optimization model which aims to maximize the overall satisfaction degree of agents on both sides is constructed to attain the optimal matching pair. Furthermore, the feasibility of the solution method is verified by a case study of person-position matching (PPM), and the matching result demonstrates that the proposed method is effective in dealing with multi-criteria PPM problem. Finally, the sensitivity of parameters and some comparative studies are discussed. [ABSTRACT FROM AUTHOR]

A scientific evaluation model can be effectively used for the evaluation of regional talent development level. This paper proposes a set of scientific index systems for evaluating rural science and technology talents, which can be used for understanding the development status and level of rural science and technology talents in various regions; putting forward the corresponding talent cultivation and introduction policies, and; promoting the development of rural economic construction. Moreover, in order to avoid the shortcoming of over-subjective indicator weight in analytic hierarchy process (AHP), this paper uses the entropy weight method to determine indicator weight. Furthermore, giving the fact that the evaluation experts may have individual personal preferences, this paper proposes an extended TODIM method based on hybrid index values, for achieving more scientific and effective evaluation results of rural science and technology talents. Finally, the proposed methods are evaluated on an actual case, where relevant analysis and suggestions are given. [ABSTRACT FROM AUTHOR]

On the basis of previous scholars' research, we improve the traditional TOmada de Decisão Interativa e Multicritério (TODIM) along with Cumulative Prospect Theory (CPT) under the 2‐tuple linguistic Pythagorean fuzzy sets (2TLPFSs) in this article. First of all, we give some definitions of Pythagorean fuzzy sets, 2TLPFSs, and the 2‐tuple linguistic Pythagorean fuzzy weighted average as well as 2‐tuple linguistic Pythagorean fuzzy weighted geometric operators. After that, according to the existing researches, we simply introduce the TODIM method and TODIM method under 2TLPFSs. Furthermore, we propose the TODIM method based on CPT (CPT–TODIM) for multiple attribute group decision‐making (MAGDM) with 2TLPFSs. Finally, a numerical example about company credit risk assessment is used to explain the new proposed method. Comparing with other methods, there is no doubt that this new method has superiority. To be exact, because the new method fully considers the mental factors of decision makers, it can better solve the uncertainty of MAGDM and improve the rationality of decision‐making. [ABSTRACT FROM AUTHOR]

Project management has been proven to be an effective tool to manage sophisticated activities. Various techniques of project management have played an essential role for successful project implementation in different areas. Managing projects, especially in a multi-project environment, involves a complex situation because of its distinguishing feature in which a number of projects are being executed simultaneously, that is, they are followed in parallel. Therefore, applying human resources will be more effective and more idle time will be eliminated as well. More so, it can enable people to share their lessons learned from one project to another. With respect to handling a number of projects at the same time by most firms, it is sophisticated for contractors to cope with financial issues of projects, which involve different project cash inflows and outflows. Thus, taking an accurate cash flow prediction into account for projects has been changed into a crucial matter for firms, and lack of this consideration may result in the failure of projects as well. Moreover, there is a desperate need for uncertainties to be addressed thoroughly regarding their vital role for suitable project management. With these in mind, an innovative approach is proposed in this paper to anticipate the cash flow of project by considering type-2 fuzzy extension of both critical chain project management (CCM) for project scheduling and TODIM (an acronym in Portuguese for interactive Multi-Criteria Decision Making) method for selecting the best scenario in a multi-project environment. Hence, type-2 fuzzy numbers are utilized in order to state uncertainties. Eventually, a real-world project in a petro-refinery firm is applied to indicate the capability of the presented approach. [ABSTRACT FROM AUTHOR]

TODIM method (an acronym in Portuguese of Interactive and Multicriteria Decision Making) has attracted the attention of many scholars and achieved much success in multi-criteria decision making. Linguistic expression, as a qualitative information representation form, is much closer to human's cognition than specific numerical values. This paper combines the classical TODIM method with the continuous interval-valued linguistic term set to solve multi-criteria group decision-making problems. A distance measure of the continuous interval-valued linguistic term set is developed and then applied to develop a criteria-weighting method. In addition, the consensus level among experts are taken into account and an improved consensus reaching method is introduced to help experts reach an agreement. Subsequently, the framework of the continuous interval-valued linguistic TODIM method is introduced to show how to derive the optimal decision-making result with complicated and precise linguistic assessments in the qualitative situation. A case study concerning the green supplier selection for a food company is provided to verify the feasibility and practicality of the proposed method. Finally, the comparisons with other ranking methods are provided to demonstrate the advantages of the proposed method.

The paper focuses on the application of TODIM (TOmada de Decisao Interativa Multicriterio), which means in Portuguese ‘interactive and multi-criteria decision making’) method in identify-ing the most attractive and affordable under-construction housing project in the city of Kolkata in India. In this decision making problem, 14 under-construction housing projects spanning in and around Kolkata are evaluated with respect to ten important criteria. The deployment of TODIM method can well be validated with respect to its ability to deal with both qualitative and quantitative criteria in the presence of risk factors. This method is also acknowledged to be a robust tool being almost unaffected by the varying values of the attenuation factor of losses. Using TODIM method, an under-construction housing project at Rajarhat in the eastern fringes of Kolkata city is selected as the optimal choice while meeting the requirements of investors, inhabitants and other stakeholders.

This paper investigates the diversified multi-attribute group decision-making problem which means that the different decision-makers have different evaluation attribute sets for all candidate alternatives. We analyze the diversified multi-attribute group decision-making problem from the perspective of granular computing models and creatively combine soft sets with multigranulation fuzzy rough sets to construct the multigranulation soft fuzzy rough set model. Subsequently, we define the optimistic upper and lower approximations and pessimistic upper and lower approximations with respect to multigranulation soft fuzzy rough set model. Meanwhile, we discuss some important mathematical conclusions and properties based on the established model. Then, we propose a novel approach to the diversified multi-attribute group decision-making problem based on multigranulation soft fuzzy rough set and TODIM method, which fully consider the reference dependence and loss aversion of decision-makers in the decision-making process. Finally, we use a numerical example of evaluation for the policy selection group decision-making problem to describe and explain the calculation principle and process and compare the results with existing related work, and our approach has great stability and rationality. And the contributions of this paper include the following two points: (1) construct the multigranulation soft fuzzy rough set model; (2) combine the established model with TODIM method to provide a novel perspective to solve the diversified multi-attribute group decision-making problem. [ABSTRACT FROM AUTHOR]

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