A novel probabilistic hesitant fuzzy rough set based multi-criteria decision-making method

A novel MCDM approach for design concept evaluation based on interval-valued picture fuzzy sets

The assessment of design concepts presents an efficient and effective strategy for businesses to strengthen their competitive edge and introduce market-worthy products. The widely accepted viewpoint acknowledges this as a intricate multi-criteria decision-making (MCDM) approach, involving a multitude of evaluative criteria and a significant amount of data that is frequently ambiguously defined and subjectively influenced. In order to tackle the problems of uncertainty and fuzziness in design concept evaluation, our research creatively combines interval-valued picture fuzzy set (IVPFS) with an MCDM process of design concept evaluation. Firstly, this study draws on the existing relevant literature and the experience of decision makers to identify some important criteria and corresponding sub-criteria and form a scientific evaluation indicator system. We then introduce the essential operational concepts of interval-valued picture fuzzy numbers (IVPFNs) and the interval-valued picture fuzzy ordered weighted interactive averaging (IVPFOWIA) operator. Thirdly, an entropy weighting method based on IVPFS is proposed in this research to calculate the weights of criteria and sub-criteria, and based on this, an integrated IVPF decision matrix is further constructed based on the presented IVPFOWIA operator. Finally, the best design concept alternative is selected by applying the extended TOPSIS (Technique for Order of Preference by Similarity to Ideal Solution) approach with IVPFS. The IVPFS combined with improved MCDM method have been proven to be superior in complex and uncertain decision-making situations through experiments and comparative assessments. The information ambiguity in the evaluation of design concept is well characterized by our augmentation based on IVPFS.

Extended Multicriteria Group Decision Making with a Novel Aggregation Operator for Emergency Material Supplier Selection

How to ensure the normal production of industries in an uncertain emergency environment has aroused a lot of concern in society. Selecting the best emergency material suppliers using the multicriteria group decision making (MCGDM) method will ensure the normal production of industries in this environment. However, there are few studies in emergency environments that consider the impact of the decision order of decision makers (DMs) on the decision results. Therefore, in order to fill the research gap, we propose an extended MCGDM method, whose main steps include the following: Firstly, the DMs give their assessment of all alternatives. Secondly, we take the AHP method and entropy weight method to weight the criteria and the DMs. Thirdly, we take the intuitionistic fuzzy hybrid priority weight average (IFHPWA) operator we proposed to aggregate evaluation information and take the TOPSIS method to rank all the alternatives. Finally, the proposed method is applied in a case to prove its practicability and effectiveness. The proposed method considers the influence of the decision order of the DMs on the decision results, which improves the accuracy and efficiency of decision-making results.

Hesitant fuzzy β-covering ( T , I ) rough set models: An application to multi-attribute decision-making

Covering rough sets have been successfully applied to decision analysis because of the strong representing capability for uncertain information. As a research hotspot in decision analysis, hesitant fuzzy multi-attribute decision-making (HFMADM) has received increasing attention. However, the existing covering rough sets cannot handle hesitant fuzzy information, which limits its application. To tackle this problem, we set forth hesitant fuzzy β-covering rough set models and discuss their application to HFMADM. Specifically, we first construct four types of hesitant fuzzy β-covering ( T , I ) rough set models via hesitant fuzzy logic operators and hesitant fuzzy β-neighborhoods, which can handle hesitant fuzzy information without requiring any prior knowledge other than the data sets. Then, some intriguing properties of these models and their relationships are also discussed. In addition, we design a new method to deal with HFMADM problems by combining the merits of the proposed models and the TOPSIS (Technique for Order Preference by Similarity to Ideal Solution) method. In this method, we not only consider the risk preferences of decision-makers, but also present a new hesitant fuzzy similarity measure expressed by hesitant fuzzy elements to measure the degree of closeness between two alternatives. Finally, an enterprise project investment problem is applied to illustrate the feasibility of our proposed method. Meanwhile, the stability and effectiveness of our proposed method are also verified by sensitivity and comparative analyses.

Various aggregation operators of the generalized hesitant fuzzy numbers based on Archimedean t-norm and t-conorm functions

This paper intends to introduce mathematical tools for aggregation of the generalized hesitant fuzzy numbers in order to increase the use of them in the real world. The proposed operators, are based on general form of t-norm and t-conorm functions, enable us to do some mathematical computations and aggregate the given generalized hesitant fuzzy numbers. At first, some famous Archimedean t-norms and t-conorms, i.e., Algebraic, Einstein, Hamacher, and Frank t-norms and t-conorms, and their properties, have been developed to be employed with generalized hesitant fuzzy numbers. Then, several averaging and geometric-based aggregation operators for generalized hesitant fuzzy numbers have been proposed. Later on, a decision-making algorithm has been defined based on such operators to address the problems. The necessity and application of the proposed concepts have been explained by some numerical examples.

Logarithmic Negation of Basic Probability Assignment and Its Application in Target Recognition

The negation of probability distribution is a new perspective from which to obtain information. Dempster–Shafer (D–S) evidence theory, as an extension of possibility theory, is widely used in decision-making-level fusion. However, how to reasonably construct the negation of basic probability assignment (BPA) in D–S evidence theory is an open issue. This paper proposes a new negation of BPA, logarithmic negation. It solves the shortcoming of Yin’s negation that maximal entropy cannot be obtained when there are only two focal elements in the BPA. At the same time, the logarithmic negation of BPA inherits the good properties of the negation of probability, such as order reversal, involution, convergence, degeneration, and maximal entropy. Logarithmic negation degenerates into Gao’s negation when the values of the elements all approach 0. In addition, the data fusion method based on logarithmic negation has a higher belief value of the correct target in target recognition application.