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 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.

Keywords

• Fuzzy sets
• T-spherical fuzzy sets
• t-norm
• t-conorm
• Aczel-Alsina operations
• aggregation operators