Complex intuitionistic fuzzy preference relations and their applications in individual and group decision‐making problems

Abstract

This paper aspires to present single and group decisionmaking methods based on complex intuitionistic fuzzy (CIF) preference relations (CIFPRs). The presented work is divided into three folds. The first fold is that the concept of CIFPRs is introduced in this study in which the pairwise comparison values are represented using CIF numbers which have the characteristic of portraying membership and nonmembership degrees over the unit disc of the complex plane. The conditions for additive consistent CIFPR are defined and the related results are explored. In addition, an algorithm for rectifying inconsistent CIFPR is also developed. The second fold is that two goal programming models are established for generating CIF normalized priority weights corresponding to individual and group decision-making problems. The third fold is to develop the algorithms for handling individual and group decision-making problems with CIFPRs. The practicality of the proposed algorithms is shown by applying them to real-life decision-making problems. The results of the presented methods are compared with several existing studies.

A Multicriteria Selection Framework for Wireless Communication Infrastructure with Interval‐Valued Pythagorean Fuzzy Assessment

“…We look forward to proposing more practical decision methods and enriching fuzzy decision theory in the future. We will refer to the current research status of q-rung orthopair fuzzy decision-making and its application [52,53] and consider expanding more ranking functions in q-rung orthopair fuzzy environment. Then, we integrate the extending function into the decision-making method of multidimensional preference linear programming to solve multicriteria decision-making problems.…”

“…According to formula (53), the matrix of individual regret value R i ði = 1, 2, 3, 4Þ is showed in Table 4.…”

Investigation of Cyber-Security and Cyber-Crimes in Oil and Gas Sectors Using the Innovative Structures of Complex Intuitionistic Fuzzy Relations

“…These sets discuss the relationship in the environment of intuitionistic fuzzy set theory through the membership and non-membership grades. De et al [ 26 ] applied IFSs in medical diagnosis; Szmidt and Kacprzyk [ 27 ] found the distances between IFSs; De et al [ 28 ] defined some operations on IFSs; Gerstenkorn and Manko [ 29 ] gave the correlation of IFSs; Buyukozkan and Uzturk [ 30 ] used interval-valued IFQFD for designing a smart fridge; Rani and Garg [ 31 ] applied the CIFRs in individual and group decision-making problems; Bustince and Burillo [ 32 ] proposed structures on IFRs, and Deschrijver and Kerre [ 33 ] studied the composition of IFRs.…”

Power Aggregation Operators Based on t-Norm and t-Conorm under the Complex Intuitionistic Fuzzy Soft Settings and Their Application in Multi-Attribute Decision Making

“…CIFS takes the TG ℳ ℭ 𝔵̿ ℳ ℭ 𝔵̿ 𝑒 ℳ ℭ 𝔵̿ and FG 𝒩 ℭ 𝔵̿ 𝒩 ℭ 𝔵̿ 𝑒 𝒩 ℭ 𝔵̿ , with 0 ℳ ℭ 𝔵̿ 𝒩 ℭ 𝔵̿ 1 and 0 ℳ ℭ 𝔵̿ 𝒩 ℭ 𝔵̿ 1. Numerous scholars have expended effort employing the principle of CIFS in the circumstances of distinct fields-as illustrated by information measures [22], correlation measures [23], geometric aggregation operators (AOs) [24], robust AOs [25], generalized AOs [26], PAOs [27], and preference relations [28]. The concept of soft set (SS) was elaborated by Molodtsov [29], after which every scholar has employed it in the environment of distinct fields; for illustration, Maji et al [30] initiated the fuzzy SS (FSS).…”