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Using multi-criteria decision making (MCDM) technique to rank alternatives is a well-known area of study in which aggregation operators, such as ordered weighted averaging (OWA) and induced OWA (IOWA) operators, play an important role in merging information and producing an overall ranking. The distance measures from ideal argument values in aggregation operators have gained attention in recent literature. Distance measures are traditionally used as argument variables, which leads to the depiction that the attribute cannot be aggregated directly. In this paper, a generalized form of distance-induced OWA (DIOWA) operators is proposed with distance measures used as order-inducing variables. A distinctive benefit of DIOWA operators is that they permit us to consider ideal argument values while simultaneously also taking the attribute values as argument variables. Three variants of DIOWA operators are proposed and investigated, namely a) the Hamming distance-induced OWA (HDIOWA) operator, b) the normalized Hamming distance-induced OWA (NHDIOWA) operator, and c) the weighted Hamming distance-induced OWA (WHDIOWA) operator. We highlight their important properties and provide proofs to necessary theorems, and also suggest the determination methods for calculating their associated weights. We discuss further extensions of the proposed DIOWA operators with the help of generalized and quasi-arithmetic means. We discuss the use of our proposed family of operators for two different decision making situations, and demonstrate their validity by an illustrative numerical example. Finally, we apply the proposed operators to a real-life problem of ranking Chinese provinces for their science and technology (S&T) development levels. The proposed operators are shown to be a useful addition to the aggregation toolbox for decision analysts. [ABSTRACT FROM AUTHOR]

The paper aims to present one of the extensions of the single-valued neutrosophic set, by utilizing the features of the exponential and logarithmic (EL) parameters. The present idea is to integrate the features of the EL operations into the standard neutrosophic set to enhance their diversity. The proposed set is named an exponential-logarithm single-valued neutrosophic set. The major feature of the proposed set is to include one attitude character parameter which can help the decision-maker to give their decision as per their needs. In the defined set, the uncertainties which are present during the analysis are handled with the help of the advancement of the neutrosophic set. Later on, we stated some basic operations to aggregate the information by defining the several weighted operators. The characteristics of these proposed operators are also illustrated in detail. In addition to it, we state the new exponential entropy measure and investigate the impact of the membership degrees of the proposed set. Finally, we construct a multi-attribute group decision-making algorithm to address the decision-making problems based on the stated concept. The attribute weights are derived by using exponential entropy measures. Several case studies are illustrated and the performance of the algorithm is compared with several existing studies. The sensitivity analysis and advantages of the proposed algorithm are also stated. • Presented a new exponential-logarithm-based SVNS to handle the uncertainties. • Define new entropy measure for weight extraction. • Proposed MAGDM algorithm based on proposed operations. • Several case studies are taken to illustrate the method. [ABSTRACT FROM AUTHOR]

We can formulate complex automation systems with advanced decision-making methods. This work proposes a new multi-criteria group-based decision-making (MCGDM) method based on the linguistic neutrosophic cloud (LNC). As an efficient linguistic expression, the linguistic neutrosophic set (LNS) introduces linguistic terminology into a neutrosophic set to make it more complex. However, there are inherent problems with linguistic values and neutrosophic sets. First, existing operators cannot handle linguistic neutrosophic numbers (LNN) with extreme values while producing distorted results. Second, the subscript-based computation of linguistic values does not reflect the change of ambiguity during the operation. Third, the literature review rarely considers the randomness of uncertain variables. To eliminate the drawbacks of previous studies, this paper proposes a multi-criteria group-based decision-making (MCGDM) method considering the linguistic neutrosophic cloud (LNC). The proposed method presents a distance measure for LNCs based on Wasserstein distance and develops an improved MCGDM method based on weighted modified partial Hausdorff distance. With an extensive simulation, the feasibility of the proposed method is verified by solving an auto part selection problem. Finally, we show the superiority of the proposed method through a comparison with four different aggregation operators of LNNs in the literature review. [ABSTRACT FROM AUTHOR]

This paper introduces and investigates ranked hesitant fuzzy sets, a novel extension of hesitant fuzzy sets that is less demanding than both probabilistic and proportional hesitant fuzzy sets. This new extension incorporates hierarchical knowledge about the various evaluations submitted for each alternative. These evaluations are ranked (for example by their plausibility, acceptability, or credibility), but their position does not necessarily derive from supplementary numerical information (as in probabilistic and proportional hesitant fuzzy sets). In particular, strictly ranked hesitant fuzzy sets arise when no ties exist, i.e., when for any fixed alternative, each submitted evaluation is either strictly more plausible or strictly less plausible than any other submitted evaluation. A detailed comparison with similar models from the literature is performed. Then in order to produce a natural strategy for multi-criteria multi-agent decisions with ranked hesitant fuzzy sets, canonical representations, scores and aggregation operators are designed in the framework of ranked hesitant fuzzy sets. In order to help implementation of this model, Mathematica code is provided for the computation of both scores and aggregators. The decision-making technique that is prescribed is tested with a comparative analysis with four methodologies based on probabilistic hesitant fuzzy information. A conclusion of this numerical exercise is that this methodology is reliable, applicable and robust. All these evidences show that ranked hesitant fuzzy sets are an intuitive extension of the hesitant fuzzy set model designed by V. Torra, that can be implemented in practice with the aid of computationally assisted algorithms. • We introduce a new model called ranked hesitant fuzzy sets. • We develop scores in this framework. • An algorithm produces information fusion of ranked information under hesitancy. • Mathematica codes facilitate reproducibility of these computations. • We apply these elements to multi-criteria multi-agent decisions. [ABSTRACT FROM AUTHOR]

[Display omitted] • Proposes a novel quantification of two key concepts in expert/intelligent systems. • These concepts are the knowledge and ignorance levels. • Some theoretical results are developed to provide a holistic and in-depth treatment. • Some illustrative examples demonstrate key computational issues. • These results can become an integral foundation for more important developments. People use knowledge on several cognitive tasks such as when they recognize objects, rank entities such as the alternatives in multi-criteria decision making, or for classification tasks of decision making / expert / intelligent systems. When people have sufficient relevant knowledge, they can make well-distinctive assessments among entities. Otherwise, they may exhibit some uncertainty. This paper establishes two differential equations, of which one is for the interaction between the knowledge level and the uncertainty level, and the other is for the interaction between the ignorance level and the uncertainty level. By solving these two differential equations under certain boundary conditions, one can derive that the proposed knowledge level indicator is equivalent to Wierman's knowledge granularity measure up to a constant (exactly, ln2). Moreover, the knowledge level indicator and the ignorance level indicator are found to be in a complementary relationship with each other. That is, more knowledge implies less ignorance, and vice-versa. The results of this study bridge a critical gap that exists in the understanding of the concepts of knowledge and ignorance. [ABSTRACT FROM AUTHOR]

• We define a geometric score and geometric variance function of the PHFE. • We propose a novel comparison law between two PHFEs. • We develop a new distance measure of PHFEs. • We introduce an optimization-based model to measure the risk aversion coefficient. • We develop a Choquet integral-based probabilistic hesitant fuzzy TODIM method. A probabilistic hesitant fuzzy set (PHFS) is a generalization of the hesitant fuzzy set (HFS) that adds the probability of occurrence to each possible value of the hesitant fuzzy element (HFE). It is a powerful tool for handling uncertain information, especially when there is no complete consensus or full dissensus among decision-makers. The TODIM (an acronym in Portuguese for interactive and multiple attribute decision-making) approach is a multi-attribute decision-making (MADM) technique based on prospect theory. In this paper, we developed a Choquet integral-based TODIM method under a probabilistic hesitant fuzzy environment. Firstly, we introduced both a geometric score function and a geometric variance function of the probabilistic hesitant fuzzy element (PHFE). Furthermore, we proposed a novel comparison law between two PHFEs, and we defined a new distance measure of PHFEs. Considering the interaction between the criteria, we calculated the degree of importance of the criteria with the Shapley value. Next, we introduced the principles and steps of the developed TODIM method. One of the prominent components of the TODIM method is its risk aversion coefficient. However, it has not been sufficiently addressed in the research literature. In this regard, a novel optimization-based method is proposed to calculate the attenuation factor of the TODIM method. Finally, we verify the effectiveness of the Choquet integral-based probabilistic hesitant fuzzy-TODIM (PHF-TODIM) method using a supplier selection problem in the dairy industry. [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]