Group Decision Making with Dual Hesitant Fuzzy Preference Relations

A new group decision making approach based on incomplete probabilistic dual hesitant fuzzy preference relations

As an enhanced version of probabilistic hesitant fuzzy sets and dual hesitant fuzzy sets, probabilistic dual hesitant fuzzy sets (PDHFSs) combine probabilistic information with the membership degree and non-membership degree, which can describe decision making information more reasonably and comprehensively. Based on PDHFSs, this paper investigates the approach to group decision making (GDM) based on incomplete probabilistic dual hesitant fuzzy preference relations (PDHFPRs). First, the definitions of order consistency and multiplicative consistency of PDHFPRs are given. Then, for the problem that decision makers (DMs) cannot provide the reasonable associated probabilities of probabilistic dual hesitant fuzzy elements (PDHFEs), the calculation method of the associated probability is given by using an optimal programming model. Furthermore, the consistency level for PDHFPRs is tested according to the weighted consistency index defined by the risk attitude of DMs. In addition, a convergent iterative algorithm is proposed to enhance the unacceptable consistent PDHFPRs’ consistency level. Finally, a GDM approach with incomplete PDHFPRs is established to obtain the ranking of the alternatives. The availability and rationality of the proposed decision making approach are demonstrated by analyzing the impact factors of haze weather.

Consensus-based group decision-making methods with probabilistic dual hesitant fuzzy preference relations and their applications

Probabilistic dual hesitant fuzzy sets (PDHFSs) have good flexibility and integrity in expressing fuzzy and uncertain information. However, some crucial problems related to PDHFSs remain unsolved, such as how to define probabilistic dual hesitant fuzzy preference relations (PDHFPRs) and solve group decision-making (GDM) problems with PDHFPRs. This paper establishes the concept of PDHFPRs and investigates consensus-based GDM methods with PDHFPRs. First, a new distance measure is proposed to quantify the difference between two PDHFPRs, which does not increase the virtual elements of membership and non-membership degrees, and can contain all distance combination of membership and non-membership elements. Therefore, the distance calculation results are not affected by the subjectivity of decision-makers (DMs). Second, the consensus measures for PDHFPRs are proposed, which are effective tool to measure the consensus level among DMs. Moreover, two consensus-based GDM methods are proposed, which can improve the group consensus level for PDHFPRs by changing the PDHFPR with the worst consensus level or modifying the weights of DMs. Finally, the proposed methods are applied to the location selection of large-scale industrial solid waste treatment facilities. The comparison with existing methods illustrates the validity and feasibility of the proposed methods.

Entropy Based Pythagorean Probabilistic Hesitant Fuzzy Decision Making Technique and Its Application for Fog-Haze Factor Assessment Problem

The Pythagorean probabilistic hesitant fuzzy set (PyPHFS) is an effective, generalized and powerful tool for expressing fuzzy information. It can cover more complex and more hesitant fuzzy evaluation information. Therefore, based on the advantages of PyPHFSs, this paper presents a new extended fuzzy TOPSIS method for dealing with uncertainty in the form of PyPHFS in real life problems. The paper is divided into three main parts. Firstly, the novel Pythagorean probabilistic hesitant fuzzy entropy measure is established using generalized distance measure under PyPHFS information to find out the unknown weights information of the attributes. The second part consists of the algorithm sets of the TOPSIS technique under PyPHFS environment, where the weights of criteria are completely unknown. Finally, in order to verify the efficiency and superiority of the proposed method, this paper applies some practical examples of the selection of the most critical fog-haze influence factor and makes a detailed comparison with other existing methods.

About Linda Again: How Narratives and Group Reasoning Can Influence Conjunction Fallacy

Conjunction fallacy (together with other systematic reasoning errors) is usually explained in terms of the dual process theory of reasoning: Biases should be ascribed to fast and automatic processes, whereas slow and deliberative processes are responsible of producing answers that are correct with respect of normative criterion. The dual process theory is related to Bruner’s distinction between narrative and paradigmatic thought: Both modes of thought can be characterized by the two different processes of reasoning. In this paper, we explore the role of Bruner’s mode of thought manipulating also the difference between group vs individual reasoning. We observed that the narrative strategy of response induces more wrong answers. However, narrative-based strategies have higher effectiveness in the case of group reasoning. Our results suggest that narrative reasoning and group reasoning may induce violations of the conjunction rule when acceptable by the verisimilitude of the story. Five models are also presented in order to predict answer correctness and strategy of reasoning using a text analysis software.

Algorithm for Probabilistic Dual Hesitant Fuzzy Multi-Criteria Decision-Making Based on Aggregation Operators With New Distance Measures

Probabilistic dual hesitant fuzzy set (PDHFS) is an enhanced version of a dual hesitant fuzzy set (DHFS) in which each membership and non-membership hesitant value is considered along with its occurrence probability. These assigned probabilities give more details about the level of agreeness or disagreeness. By emphasizing the advantages of the PDHFS and the aggregation operators, in this manuscript, we have proposed several weighted and ordered weighted averaging and geometric aggregation operators by using Einstein norm operations, where the preferences related to each object is taken in terms of probabilistic dual hesitant fuzzy elements. Several desirable properties and relations are also investigated in details. Also, we have proposed two distance measures and its based maximum deviation method to compute the weight vector of the different criteria. Finally, a multi-criteria group decision-making approach is constructed based on proposed operators and the presented algorithm is explained with the help of the numerical example. The reliability of the presented decision-making method is explored with the help of testing criteria and by comparing the results of the example with several prevailing studies.