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

Abstract

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.

Multiattribute decision making based on power operators for linguistic intuitionistic fuzzy set using set pair analysis

“…Also, the superiority and advantages of the proposed method are discussed which show that the proposed approach is more flexible and versatile. For the future work, we will develop some more MADM method using soft sets or probabilities hesitant fuzzy information (Garg & Kaur, ; Khalil, Li, Garg, Li, & Ma, ; Kaur & Garg, ; Nancy & Garg, ; Rani & Garg, ).…”

Multi‐criteria group decision‐making method based on TODIM with probabilistic interval‐valued hesitant fuzzy information

“…Researchers focus on the operators, and some operations have been proposed (Garg, ; Garg & Kaur, ; Kaur & Garg, ; Xu et al, ). For example, based on distance measures and the Einstein norm operations, Garg and Kaur () discussed basic operational laws for the proposed structure and explore various relationships. One of the principles of combining fuzzy sets with operators is that the fuzzy sets fit each other.…”

“…Take the linguistic intuitionistic fuzzy set (LIFS) and set pair analysis theory for example, and the LIFS can better addresses uncertain and imprecise information and the set pair analysis theory provides a quantitative analysis to integrate certainty and uncertainties as a combined system (Garg & Kumar, ). Hence, the linguistic connection number (LCN) and various operational laws were defined (Garg & Kaur, ). Other fuzzy sets follow this principle (Garg, , , ; Garg & Arora, ).…”

“…Hao, Xu, Zhao, and Su () proposed the new probabilistic dual hesitant fuzzy set and investigated their operation to solve problems with aleatory uncertainty and epistemic uncertainty. Garg and Kaur () utilized Einstein norm operations to reduce data. In this paper, the convex combination operation is extended (Wei, Na, & Tang, ).…”

Some results on information measures for complex intuitionistic fuzzy sets

“…Zhang et al 26 studied hybrid monotonic inclusion measure under IFS theory and interval-valued intuitionistic FS theory. Besides this, many researchers [27][28][29][30][31][32][33][34][35][36][37] worked on various information measures and showed their applications by applying them to DM problems.…”