Frank Prioritized Aggregation Operators and WASPAS Method Based on Complex Intuitionistic Fuzzy Sets and Their Application in Multi-Attribute Decision-Making

Abstract

Complex intuitionistic fuzzy (CIF) information covers the degree of membership and the degree of non-membership in the form of polar coordinates with a valuable and dominant characteristic where the sum of the real parts (the same rule for the imaginary parts) of the pair must be contained in the unit interval. In this paper, we first derive the Frank operational laws for CIF information and then examine the prioritized aggregation operators based on Frank operational laws for managing the theory of CIF information. These are the CIF Frank prioritized averaging (CIFFPA) operator, the CIF Frank prioritized ordered averaging (CIFFPOA) operator, the CIF Frank prioritized geometric (CIFFPG) operator, and the CIF Frank prioritized ordered geometric (CIFFPOG) operator with properties of idempotency, monotonicity, and boundedness. Furthermore, we derive the WASPAS (weighted aggregates sum product assessment) under the consideration or presence of the CIF information and try to justify it with the help of a suitable example. Additionally, we illustrate some numerical examples in the presence of the MADM (multi-attribute decision-making) procedures for evaluating the comparison between the proposed operators with some well-known existing operators to show the validity and worth of the proposed approaches.

On Extended Lr-Norm-Based Derivatives to Intuitionistic Fuzzy Sets

“…Atanassov later conducted additional research to improve intuitionistic fuzzy set theory (IFST) [2,[6][7][8]. In recent years IFST has been increasingly used in applications of decision-making problems [9,10], medical diagnosis [11][12][13], software selection [14], environmental management [15], transport problems [16], predator prey [17], etc. Susanto et al [18] generated fuzzy interval data from crisp data using the Cheng et al [19] correlation method to determine the relationship between students' anxiety and mathematical self-efficacy, based on the concept of α-cut from a fuzzy set.…”