Complex intuitionistic fuzzy power aggregation operators and their applications in multicriteria decision‐making

Abstract

The objective of this manuscript is to present some aggregation operators for aggregating the different complex intuitionistic fuzzy (CIF) sets by considering the dependency between the pairs of its membership degrees. In the existing studies of fuzzy and its extensions, the uncertainties present in the data are handled with the help of degrees of membership that are the subset of real numbers, which may lose some useful information and hence consequently affect the decision results. A modification to these, complex intuitionistic fuzzy set handles the uncertainties with the degrees whose ranges are extended from real subset to the complex subset with unit disc and hence handle the two‐dimensional information in a single set. Thus, motivated by this, we developed some new power aggregation operators, namely, CIF power averaging, CIF weighted power averaging, CIF ordered weighted power averaging, CIF power geometric, CIF weighted power geometric, and CIF ordered weighted power geometric. Also, some of the desirable properties of these are investigated. Further, based on these operators, a multicriteria decision‐making approach is presented under the CIF set environment. An illustrative example related to the selection of the best alternative(s) is considered to demonstrate the efficiency of the proposed approach and is validated it by comparing their results with the several existing approaches results.

Generalized intuitionistic fuzzy soft power aggregation operator based ont‐norm and their application in multicriteria decision‐making

“…From the existing approaches, our proposed approach also delivers a benefit over the existing approaches when the prioritized relationship between the parameters and the experts is considered. In the future, the result of this paper can be extended to Pythagorean fuzzy environment and other uncertain environment …”

“…In the future, the result of this paper can be extended to Pythagorean fuzzy environment and other uncertain environment. [44][45][46][47]…”

Some results on information measures for complex intuitionistic fuzzy sets

“…Kumar and Bajaj proposed some distance and entropy measures for CIF soft sets. Rani and Garg developed some distance measures and power aggregation operators, respectively, for CIFSs along with their various properties and gave their applications in DM problems. Garg and Rani proposed generalized averaging aggregation operators based on t‐norms and conorms and novel correlation coefficients, respectively, under CIFS environment.…”

Multi-criteria decision making method based on Bonferroni mean aggregation operators of complex intuitionistic fuzzy numbers

“…In the aspect of the MCDM problem, researchers have impersonated some AOs and information measures for CIFS for to solve the DMPs. For instance, in the AOs domain, Rani and Garg [37] given power AOs while in [19,21], authors had performed AOs based on the operational laws. Based on the Archimedean t-norm operations, authors in [18] examined the generalized BM operators for CIFSs.…”

“…Definition 2.7. [19,37] The score and accuracy functions of CIFN H = ((r, wr), (k, w k )) are stated as…”