Aczel-Alsina Aggregation Operators on T-Spherical Fuzzy (TSF) Information With Application to TSF Multi-Attribute Decision Making

Abstract

Aczel-Alsina t-norm (TN) and t-conorm (TCN) were proposed by Aczel and Alsina in 1982 where they are more flexible than the other TN and TCN. Since Aczel-Alsina TN and TCN have a great impact due to the variableness of involved parameters, they have good applications in multi-attribute decision making (MADM) under fuzzy sets (FSs) construction. Recently, Senapati et al. (2022) developed Aczel-Alsina aggregation operators (AOs) under intuitionistic FSs (IFSs) and interval-valued IFSs (IVIFSs) with their applications in solving IFS and IVIFS MADM problems. We know that T-spherical FSs (TSFSs) are a recently developed approach to uncertain information with less information loss and more reliability than IFSs and IVIFSs. In this paper, we develop these AOs on TSFSs as a new approach to solve MADM problems by using Aczel-Alsina TN and Aczel-Alsina TCN under T-spherical fuzzy (TSF) information. Furthermore, the basic operations of TSF numbers (TSFNs) are developed and exemplified. Based on these operations, two types of AOs, i.e. TSF Aczel-Alsina weighted average (TSFAAWA), and TSF Aczel-Alsina weighted geometric (TSFAAWG) operators, are introduced and investigated. The reliability and accuracy of the newly developed AOs are tested numerically and theoretically by the induction methods. To further give applications and also study the sensitivity of these TSF Aczel-Alsina operators, the problem of project evaluation using these proposed operators is comprehensively observed. The results obtained by using these TSF Aczel-Alsina operators are compared with some previously existing AOs of TSFSs. According to comparison results, we observe the reliability and efficiency of the proposed methods.

Archimedean Aggregation Operators Based on Complex Pythagorean Fuzzy Sets Using Confidence Levels and Their Application in Decision Making

“…In the future, it is necessary to extend the proposed operators to the Maclaurin operators [ 47 ], Aczel-Alsina operators [ 48 ], Bonferroni operators [ 49 ], TOPSIS technique [ 50 ], fuzzy N-soft sets [ 51 ], Hesitant fuzzy N-soft sets [ 52 ], complex Pythagorean fuzzy N-soft sets [ 53 ], Pythagorean m-polar fuzzy sets [ 54 ], q-rung orthopair m-polar fuzzy sets [ 55 ], ELECTRE-1 technique [ 56 ], and m-polar fuzzy graphs [ 57 ] in the environment CPF information.…”

An Uncertain Multiple-Criteria Choice Method on Grounds of T-Spherical Fuzzy Data-Driven Correlation Measures

“…In intervalvalued T-SF circumstances, Hussain et al (2022a) utilized Frank aggregation operators to propose a method of assessing business proposals. Hussain et al (2022b) exploited Aczel-Alsina t-norms and t-conorms to evolve Aczel-Alsina weighted average and geometric operation in T-SF settings for resolving decision-making issues. Karaaslan and Al-Husseinawi (2022) presented arithmetic and geometric averaging operations in hesitant T-spherical Dombi fuzzy settings for group decision-making.…”

“…In particular, based on Table 1, it can be easily observed that many researchers discussed the modularization of multiple-criteria choice methods in the context of T-SF sets with aggregation operations or averaging (i.e. mean) operations, such as Akram and Martino (2022), Al-Quran (2021), Chen et al (2021), Gurmani et al (2022), Hussain et al (2022aHussain et al ( , 2022b, Karaaslan and Al-Husseinawi (2022), Khan et al (2022), Liu et al (2021c), Mahnaz et al (2022), Wang (2021), Wang and Zhang (2022), Yang and Pang (2022), Yang et al (2021), Zedam et al (2022), andZeng et al (2021). That is, many of the above works of literature focus on models of aggregating or averaging operations, which belong to a measurement of the central tendency of a finite set of T-SF information.…”

Complex q-Rung Orthopair Fuzzy Aczel–Alsina Aggregation Operators and Its Application to Multiple Criteria Decision-Making With Unknown Weight Information

“…Senapati et al [44], [45] constructed Aczel-Alsina aggregation operators for a framework of IFSs and also for interval-valued IFSs (IVIFSs), and then used them to address MCDM issues, while Senapati [46] examined Aczel-Alsina aggregation operators based on picture fuzzy sets with application to MCDM. Recently, Hussain et al [47] defined the fundamental T-spherical fuzzy aggregation operators in terms of Aczel-Alsina operations. Simultaneously, Naeem and Ali [48] investigated spherical fuzzy Aczel-Alsina aggregation operators and their application to solar energy cells.…”