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With the constant changes in the decision-making environment, various limitations have emerged in traditional decision-making methods, such as the inability to simultaneously consider multiple factors such as randomness, hesitation, and ambiguity, thus limiting a comprehensive grasp of the decision-maker's cognitive inputs. To address the above problems, we propose a multi-criteria decision-making (MCDM) model based on a new fuzzy set (FS). Firstly, we define a new Z hesitant fuzzy linguistic term set (ZHFLTS) and propose a visualization metric for mapping ZHFLTS into T-spherical fuzzy (T-SF) space to simplify the computation. The relevant properties of ZHFLTS are further investigated. In order to accurately measure the uncertainty of FSs, we propose the probabilistic-hesitation-fuzzy (PHF) entropy and use it as a basis to derive the potential probability distribution using the fruit fly optimization algorithm (FOA). Subsequently, an MCDM model is established based on the proposed ZHFLTS, visualization metric, and PHF entropy. The model can better solve complex decision-making problems such as TCM through example studies and comparative analyses. The research in this paper aims to cope with today's increasingly complex decision-making environments, and the introduced ZHFLTS framework and the corresponding methodology provide new ways to solve complex decision problems. • ZHFLTS is defined and a mapping method to visualize ZHFLTS in T-SF space is studied. • PHF entropy is proposed based on FOA for obtaining potential probability distribution. • A Novel MCDM model based on ZHFLTS is presented. • It proves the effectiveness of the model through instances and comparative analysis. [ABSTRACT FROM AUTHOR]

Fifth-generation (5G) technology provides new possibilities for a variety of applications, but it also comes with challenges influenced by distinct aspects, such as the size of organizations that use such technology. Therefore, it is important to understand which architecture of 5G-radio access networks (RANs) is best for a given purpose; this requires an evaluation platform for assessment. This paper tackles this problem by presenting a novel multi-criteria decision-making (MCDM) solution based on a new integrated fuzzy set. The proposed integrated approach, which is based on a Type-2 neutrosophic fuzzy environment, is developed to address the application challenges of 5G-RANs architecture evaluation, as also to face the MCDM theoretical challenge represented by ambiguities and inconsistencies among decision makers within the decision making context of the presented case study. Many MCDM techniques for weighting and selection were presented from the literature, yet many of them still suffer from inconsistencies and uncertainty. Therefore, the chosen methods in this research are unique in a way that previous issues are addressed, making them suitable for integration with Type-2 neutrosophic fuzzy environment, and therefore creating a more robust decision platform for the presented challenge in this research, as a theoretical contribution. First, a new "Type-2 Neutrosophic Fuzzy-Weighted Zero-Inconsistency" (T2NN-FWZIC) technique is formulated for weighting the evaluation criteria of RAN architectures. Second, another new method, namely, "Type-2 Neutrosophic Fuzzy Decision by Opinion Score Method" (T2NN-FDOSM), was formulated to select the optimal RAN architecture using the obtained weights. The weighting results by T2NN-FWZIC for the (n = 25) evaluation criteria revealed that (C 21 latency and C 22 reliability) as the most important criteria, with 0.06 value for each as opposed to (C 15 Data Processing) as the lowest weighted criteria with 0.0186 value. As for T2NN-FDOSM, a total of four 5G-RAN architectures were evaluated, including "virtualized cloud RAN" coming as the optimal one, followed by "fog RAN," "cloud RAN," and finally "heterogeneous cloud RAN." The results were confirmed by carrying out a sensitivity analysis. The outcome of this study can be used to assist future 5G-RAN developments according to business needs and to establish an assessment platform for 5G technology in different domains and applications. [ABSTRACT FROM AUTHOR]

[Display omitted] • Main developments on sorting approaches. • The categorization of multiple-criteria decision-making sorting methods. • Applications of the multiple-criteria decision-making sorting methods. • Trends and future directions of MCDM Sorting. Multi-Criteria Decision Making (MCDM) is a complex process. It aims to support decision makers in making their decisions more effective and consistent. MCDM provides a useful and successful alternative for handling three main types of MCDM problems, namely, choosing, ranking and sorting. The first two are the most common problems studied but the third offers a way to deal with real world MCDM problems that require alternatives to be assigned to ordered categories. The practitioners are currently developing and applying sorting methods to solve problems from different application areas. In spite of its interest and applicability, there is only one previous review on Multiple-Criteria sorting, performed almost 20 years ago. Hence, because of its interest this paper presents a new and systematic review of MCDM sorting methods that includes 30 years of research in the field. This review has systematically analyzed the conventional and non-classical methods of MCDM sorting and then classified the papers published into 16 application areas. The analysis reveals that the methodological development is still in growth phase for MCDM sorting and discovers the applied methods' trends. It also shows the complete spectrum of the areas of the application addressed, the state of knowledge about methods, the type of contribution to the knowledge, and the application area for the four categories of the MCDM approaches. The systematic review scrutinizes each selected article in order to find out which approach from the multi-criteria sorting presents the most development based on its contribution and application of the methods. We also aim to discover which Multiple-Criteria sorting methods are the most studied in MCDM. The relevant finding is the relation between the most applied methods and the application areas together with future directions for further research. [ABSTRACT FROM AUTHOR]

• A new form of the ranking based on optimal points MCDM method is developed. • A new weighting method is developed called Win, Loss, Draw method. • RBOP imitates the decision maker's behavioral pattern to find the best alternative. Supplier evaluation is a complex multi-criteria decision-making (MCDM) problem that deals with assessment of suppliers as the potential alternatives against various types of criteria. We consider the context where decision makers (DMs) have complete information about the suppliers and criteria. To address the needs of decision makers, a multi-criteria evaluation method named Ranking based on optimal points (RBOP) is developed in this paper. By imitating and simulating human decision-making behavioural patterns, the developed MCDM method selects the best alternative that is closer to what the DM desires. Furthermore, a novel subjective MCDM weighting method s called win-loss-draw (WLD) method is also developed, which is also based on human behavioural pattern. A real case study of domestic cheese brands is considered to apply the developed methods to select the best cheese supplier for an Iranian hypermarket. Compared to other MCDM methods, outputs of the RBOP method show some differences due to the impact of WLD method, which intensified divergence and optimal points during the decision-making process. [ABSTRACT FROM AUTHOR]

• Define Choquet integral based intuitionistic fuzzy arithmetic aggregation operator. • Combine the defined operator with ordered weighted aggregation operator. • Propose a decision-making method based on the combined operator. Intuitionistic fuzzy set (IFS), a classical extension of fuzzy set, is a powerful tool to describe fuzzy information in multi-criteria decision-making (MCDM) because of its membership and non-membership functions. Intuitionistic fuzzy aggregation operators are the standard mathematical tools for the combination of several inputs with respect to criteria into one unique output. The traditional intuitionistic fuzzy aggregation operator-based methods have been criticized because of reasons that include disregard for comprehensive correlative relationships of criteria and ignorance for combination of fuzzy measures of criteria and weights of positions. In this paper, the effectiveness of traditional aggregation operator-based MCDM techniques is improved by a novel method to select the best alternative(s) under the intuitionistic fuzzy environment. We begin by defining the Choquet integral-based intuitionistic fuzzy arithmetic aggregation (CIIFAA) operator, the remarkable properties of which are proved in details. Further, the Choquet integral based intuitionistic fuzzy hybrid arithmetic aggregation (CIIFHAA) operator is defined as well as the proofs of its properties. The CIIFHAA operator can not only capture the comprehensive correlative relationships of criteria in a simpler manner, but also combine the weights of positions. Then, we put forward a MCDM method based on CIIFHAA operator with intuitionistic fuzzy evaluations. An illustrative example is solved, the best alternative and the ranking of alternatives are obtained, which can verify the feasibility of the proposed method. Finally, two comparisons are conducted to illustrate the stability and advantages of the proposed method. [ABSTRACT FROM AUTHOR]