Multi-attribute decision-making based on soft set theory: a systematic review

A novel stochastic group decision-making framework with dual hesitant fuzzy soft set for resilient supplier selection

Suppliers can be regarded as unavoidable sources of external risks in modern supply chains, which may cause disruption of supply chains. A resilient supplier usually has a high adaptive ability to reduce the vulnerability against disruptions and recover from disruption to keep continuity in operations. This paper develops an effective multi-attribute group decision-making (MAGDM) framework for resilient supplier selection. Because of the many uncertainties in resilient supplier selection, the dual hesitant fuzzy soft sets (DHFSSs), a very flexible tool to express uncertain and complex information of decision-makers, is utilized to cope with it. In order to obtain the resilient supplier’s partial order relationship and consider the psychological behavior of decision-makers, this paper proposes the MAGDM framework with DHFSSs based on the TOPSIS method and prospect theory for resilient supplier selection. Furthermore, we consider the consensus level among experts of different backgrounds and experiences and propose a consensus measure method based dual hesitant fuzzy soft numbers (DHFSNs) before selecting a resilient supplier. The expert weights are calculated by the group consensus level between the expert and the group opinions. Meanwhile, we define the entropy of DHFSSs to determine the attribute weights objectively in the decision-making process. Based on this, the proposed method is applied to a practical manufacturing enterprise with an international supply chain for a resilient supplier selection problem. Finally, by performing a sensitivity analysis and a comparative analysis, the results demonstrate the robustness and validity of the proposed method.

Venture capital project selection based on interval number grey target decision model

In this study, aiming at the multi-attribute decision-making problem with incomplete and uncertain attribute weight information and attribute value of interval numbers, a grey target decision-making model of interval numbers based on positive and negative clouts is proposed. Firstly, in this model, the linear transformation operator of interval number is used to normalize the original decision information, and the positive and negative clouts of interval number are designed. Secondly, after the space projection distance between each scheme and the positive and negative clouts is considered comprehensively, the off-target distance is taken as the basis of vector analysis in space to obtain a new comprehensive off-target distance. The existing interval number grey target decision-making model ignores the important influence of interval distribution and the correlation between the attributes in scheme evaluation, and there are some fuzzy errors when setting the weight of attributes. In order to solve the above problems, this paper combined with the uncertainty analysis of the attribute weights, a goal programming is constructed for the objective function based on the comprehensive off-target distance minimization to solve the attribute weight vector, and finally determine the order of the scheme. Finally, the feasibility and effectiveness of the proposed grey target decision model are verified by an example of venture capital projects. Compared with traditional models, the improved model fully considers the characteristics of interval data and the correlation between the attributes.

An Alternate Unsupervised Technique Based on Distance Correlation and Shannon Entropy to Estimate λ0-Fuzzy Measure

λ0-measure is a special type of fuzzy measure. In the context of multi-attribute decision making (MADM), the measure can be used together with Choquet integral to model the interdependencies that usually present between the decision attributes. Unfortunately, the range of techniques available to estimate λ0-measure values is too limited i.e., only four techniques are available to this date. Besides, the review on literature shows that each of these existing techniques either requires some initial data from the decision-makers or misrepresents the actual interdependencies held by the attributes. Thus, an alternate unsupervised technique is needed for the estimation of λ0-measure values. This study has developed such a technique by integrating the idea of distance correlation and Shannon entropy. In this technique, the two inputs required to estimate λ0-measure values, namely, the interdependence degrees and fuzzy densities are determined by utilizing the distance correlation measures and entropy weights, respectively. An evaluation to rank the websites owned by five different hospitals located in Sabah, Malaysia, was conducted to illustrate the usage of the technique. A similar evaluation was also performed with a few selected MADM techniques for comparison purposes, where the proposed technique is found to have produced the most consistent ranking. From the literature perspective, this study has contributed an alternate unsupervised technique that can estimate λ0-measure values without necessitating any additional data from the decision-makers, and at the same time can better capture the interdependencies held by the attributes.

Some Construction Methods of Aggregation Operators in Decision-Making Problems: An Overview

Aggregating data is the main line of any discipline dealing with fusion of information from the knowledge-based systems to decision-making. The purpose of aggregation methods is to convert a list of objects, all belonging to a given set, into a single representative object of the same set usually by an n-ary function, so-called aggregation operator. As the useful aggregation functions for modeling real-life problems are limited, the basic problem is to construct a proper aggregation operator, usually a symmetric one, for each situation. During the last decades, a number of construction methods for aggregation functions have been developed to build new classes based on the existing well-known operators. There are three main construction methods in common use: transformation, composition, and convex combination. This paper compares these methods with respect to the type of aggregating problems that can be handled by each of them.

Multi-Attribute Decision Making Based on Stochastic DEA Cross-Efficiency with Ordinal Variable and Its Application to Evaluation of Banks’ Sustainable Development

Multi-attribute decision making (MADM) is a cognitive process for evaluating data with different attributes in order to select the optimal alternative from a finite number of alternatives. In the real world, a lot of MADM problems involve some random and ordinal variables. Therefore, in this paper, a MADM method based on stochastic data envelopment analysis (DEA) cross-efficiency with ordinal variable is proposed. First, we develop a stochastic DEA model with ordinal variable, which can derive self-efficiency and the optimal weight of each attribute for all decision making units (DMUs). To further improve its discrimination power, cross-efficiency as a significant extension is proposed, which utilizes peer DMUs’ optimal weight to evaluate the relative efficiency of each alternative. Then, based on self-efficiency and cross-efficiency of all DMUs, we construct corresponding fuzzy preference relations (FPRs) and consistent fuzzy preference relations (FPRs). In addition, we obtain the priority weight vector of all DMUs by utilizing the row wise summation technique according to the consistent FPRs. Finally, we provide a numerical example for evaluating operation performance of sustainable development of 15 listed banks in China, which illustrates the feasibility and applicability of the proposed MADM method based on stochastic DEA cross-efficiency with ordinal variable.

Intertemporal Choice of Fuzzy Soft Sets

This paper first merges two noteworthy aspects of choice. On the one hand, soft sets and fuzzy soft sets are popular models that have been largely applied to decision making problems, such as real estate valuation, medical diagnosis (glaucoma, prostate cancer, etc.), data mining, or international trade. They provide crisp or fuzzy parameterized descriptions of the universe of alternatives. On the other hand, in many decisions, costs and benefits occur at different points in time. This brings about intertemporal choices, which may involve an indefinitely large number of periods. However, the literature does not provide a model, let alone a solution, to the intertemporal problem when the alternatives are described by (fuzzy) parameterizations. In this paper, we propose a novel soft set inspired model that applies to the intertemporal framework, hence it fills an important gap in the development of fuzzy soft set theory. An algorithm allows the selection of the optimal option in intertemporal choice problems with an infinite time horizon. We illustrate its application with a numerical example involving alternative portfolios of projects that a public administration may undertake. This allows us to establish a pioneering intertemporal model of choice in the framework of extended fuzzy set theories.