Novel Aczel–Alsina Operators for Pythagorean Fuzzy Sets with Application in Multi-Attribute Decision Making

Abstract

Multi-attribute decision-making (MADM) is usually used to aggregate fuzzy data successfully. Choosing the best option regarding data is not generally symmetric on the grounds that it does not provide complete information. Since Aczel-Alsina aggregation operators (AOs) have great impact due to their parameter variableness, they have been well applied in MADM under fuzzy construction. Recently, the Aczel-Alsina AOs on intuitionistic fuzzy sets (IFSs), interval-valued IFSs and T-spherical fuzzy sets have been proposed in the literature. In this article, we develop new types of Pythagorean fuzzy AOs by using Aczel-Alsina t-norm and Aczel-Alsina t-conorm. Thus, we give these new operations Aczel-Alsina sum and Aczel-Alsina product on Pythagorean fuzzy sets based on Aczel-Alsina t-norm and Aczel-Alsina t-conorm. We also develop new types of Pythagorean fuzzy AOs including Pythagorean fuzzy Aczel-Alsina weighted averaging and Pythagorean fuzzy Aczel-Alsina weighted geometric operators. We elaborate some characteristics of these proposed Aczel-Alsina AOs on Pythagorean fuzzy sets, such as idempotency, monotonicity, and boundedness. By utilizing the proposed works, we solve an example of MADM in the information of the multinational company under the evaluation of impacts in MADM. We also illustrate the comparisons of the proposed works with previously existing AOs in different fuzzy environments. These comparison results demonstrate the effectiveness of the proposed Aczel-Alsina AOs on Pythagorean fuzzy sets.

A Novel SIR Approach to Closeness Coefficient‐Based MAGDM Problems Using Pythagorean Fuzzy Aczel–Alsina Aggregation Operators for Investment Policy

“…Hussain et al [31] used the AA aggregation operators on TSFSs. Hussain et al [32] considered AA aggregation operators on PFSs using the MADM problems.…”

“…We suppose ΤΝ Ť and ΤCΝ Š represent AA product ŤA and AA sum ŠǍ , respectively. Ten, the generalization of intersection and union over two PFSs " _ P" and "Ṙ" turn out to be the AA product (represented by _ P ⊗ Ṙ) and AA sum (represented by _ P ⊕ Ṙ) over two PFSs " _ P" and "Ṙ," respectively, [32]:…”

“…Pythagorean Fuzzy Aczel-Alsina (PF-AA) Average Aggregation Operators (AOs). Hussain et al [32] introduced some PF-AA average AOs under PFNs. Additionally, some related properties are also discussed.…”

Applications of the Multiattribute Decision-Making for the Development of the Tourism Industry Using Complex Intuitionistic Fuzzy Hamy Mean Operators

“…Aggregation of information is a significant tool that has some widespread applications especially when it comes to MADM problems. There are several AOs that are used for MADM problems including weighted averaging (WA) and weighted geometric (WG) AOs [ 15 ], Einstein WA operator and Einstein WG AOs [ 16 , 17 ], Dombi WA and Dombi WG AOs [ 18 ], Pythagorean fuzzy (PyF) Aczel Alsina (PyFAA) AOs [ 19 ], interval-valued PyFAA AOs [ 20 ], Einstein geometric AOs [ 21 ], AOs of picture FSs [ 22 ], and Hamacher AOs [ 23 , 24 ]. In a decision-making (DM) problem, the mutual relationship of the information has created a certain impact on results.…”

Multiple Attribute Decision-Making Based on Bonferroni Mean Operators under Square Root Fuzzy Set Environment

“…Consequently, Yager [44] put forwarded the idea of Pythagorean fuzzy set (PyFS) which is a simplification of IFS. PyFS is a more effective tool to solve unclear and vagueness difficulties and applied in DM challenges [45,46,47,48].…”