Dual hesitant fuzzy rough set and its application

Three-way decisions in generalized intuitionistic fuzzy environments: survey and challenges

Enhancing decision-making under risks is crucial in various fields, and three-way decision (3WD) methods have been extensively utilized and proven to be effective in numerous scenarios. However, traditional methods may not be sufficient when addressing intricate decision-making scenarios characterized by uncertain and ambiguous information. In response to this challenge, the generalized intuitionistic fuzzy set (IFS) theory extends the conventional fuzzy set theory by introducing two pivotal concepts, i.e., membership degrees and non-membership degrees. These concepts offer a more comprehensive means of portraying the relationship between elements and fuzzy concepts, thereby boosting the ability to model complex problems. The generalized IFS theory brings about heightened flexibility and precision in problem-solving, allowing for a more thorough and accurate description of intricate phenomena. Consequently, the generalized IFS theory emerges as a more refined tool for articulating fuzzy phenomena. The paper offers a thorough review of the research advancements made in 3WD methods within the context of generalized intuitionistic fuzzy (IF) environments. First, the paper summarizes fundamental aspects of 3WD methods and the IFS theory. Second, the paper discusses the latest development trends, including the application of these methods in new fields and the development of new hybrid methods. Furthermore, the paper analyzes the strengths and weaknesses of research methods employed in recent years. While these methods have yielded impressive outcomes in decision-making, there are still some limitations and challenges that need to be addressed. Finally, the paper proposes key challenges and future research directions. Overall, the paper offers a comprehensive and insightful review of the latest research progress on 3WD methods in generalized IF environments, which can provide guidance for scholars and engineers in the intelligent decision-making field with situations characterized by various uncertainties.

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.

The determination and elimination of hidden inherent preference using q-ROFNs multicriteria group decision making problem

 The group decision-making problem usually involves decision makers (DMs) from different professional backgrounds, which leads to a considerable point, that it is the fact that there will be a certain difference in the professional cognition, risk preference and other hidden inherent factors of these DMs to the objective things that need to be evaluated. To improve the reasonability of decision-making, these hidden inherent preference (HIP) of DMs should be determined and eliminated prior to decision making. As a special form of fuzzy set, q-rung orthopair fuzzy numbers (q-ROFNs) is a useful tool to process uncertain information in decision making problems. Hence, under the environment of q-ROFNs, the determination of HIP based on distance from average score is proposed and a risk model is established to eliminate the HIP by analyzing the possible impact. Meanwhile, a dominant function is proposed, which extends the comparison method between q-ROFNs and an integrated decision-making method is provided. Finally, considering the application background of double carbon economy, an example by selecting the best design of electric vehicles charging station (EVCS) is conducted to illustrate the proposed method, and the feasibility and efficiency are verified.

A novel approach on spherical fuzzy rough set based-EDA𝒮 method for group decision support system

In daily life, the decision making problem is a complicated work related to uncertainties and vagueness. To overcome this vagueness and uncertainties, many fuzzy sets and theories have been presented by different scholars and researchers. EDA𝒮 (Evaluation based on distance from average solution) method plays a major role in decision-making problems. Especially, when multi-attribute group decision-making (MAGDM) problems have more conflicting attribute. In this paper, a new approach known as Spherical fuzzy rough-EDA𝒮 (SFR-EDA𝒮) method is used to handle these uncertainties in the MAGDM problem. The aggregation operators have the ability to combine different sources of information, which plays an essential role in decision making (DM) problem. Keeping in view the increasing complexity of the DM problem, it will be useful to combine the aggregation operators with the fuzzy sets in solving DM problem. Therefore, an aggregation operator known as SFR-EDA𝒮 method is utilized. For this propounded some new averaging and geometric aggregation is investigated. Moreover, the essential and desirable properties with some particular cases are deliberated and discussed detail. To evaluate the emergency program, a MAGDM approach is used based on the new introduced operators. Later on, the viability and applicability the proposed method is certified by a detailed analysis with the other existing approaches.

New distances for dual hesitant fuzzy sets and their application in clustering algorithm

Compared to hesitant fuzzy sets and intuitionistic fuzzy sets, dual hesitant fuzzy sets can model problems in the real world more comprehensively. Dual hesitant fuzzy sets explicitly show a set of membership degrees and a set of non-membership degrees, which also imply a set of important data: hesitant degrees.The traditional definition of distance between dual hesitant fuzzy sets only considers membership degree and non-membership degree, but hesitant degree should also be taken into account. To this end, using these three important data sets (membership degree, non-membership degree and hesitant degree), we first propose a variety of new distance measurements (the generalized normalized distance, generalized normalized Hausdorff distance and generalized normalized hybrid distance) for dual hesitant fuzzy sets in this paper, based on which the corresponding similarity measurements can be obtained. In these distance definitions, membership degree, non-membership-degree and hesitant degree are of equal importance. Second, we propose a clustering algorithm by using these distances in dual hesitant fuzzy information system. Finally, a numerical example is used to illustrate the performance and effectiveness of the clustering algorithm. Accordingly, the results of clustering in dual hesitant fuzzy information system are compared using the distance measurements mentioned in the paper, which verifies the utility and advantage of our proposed distances. Our work provides a new way to improve the performance of clustering algorithms in dual hesitant fuzzy information systems.

Novel Parameterized Utility Function on Dual Hesitant Fuzzy Rough Sets and Its Application in Pattern Recognition

Based on comparative studies on correlation coefficient theory and utility theory, a series of rules that utility functions on dual hesitant fuzzy rough sets (DHFRSs) should satisfy, and a kind of novel utility function on DHFRSs are proposed. The characteristic of the introduced utility function is a parameter, which is determined by decision-makers according to their experiences. By using the proposed utility function on DHFRSs, a novel dual hesitant fuzzy rough pattern recognition method is also proposed. Furthermore, this study also points out that the classical dual tool is suitable to cope with dynamic data in exploratory data analysis situations, while the newly proposed one is suitable to cope with static data in confirmatory data analysis situations. Finally, a medical diagnosis and a traffic engineering example are introduced to reveal the effectiveness of the newly proposed utility functions on DHFRSs.