Multi-attribute decision-making using Archimedean aggregation operator in T-spherical fuzzy environment

Abstract

As an extension of several fuzzy structures such as fuzzy sets, intuitionistic fuzzy sets, picture fuzzy sets, q-rung ortho-pair fuzzy sets, and T-spherical fuzzy (TSF) sets (TSFSs), are an effective tool for controlling the vagueness of data. Archimedean t-conorm (ATCN) and t-norm (ATN), which consists of the t-conorm (TCN) and t-norm (TN) families, is a crucial approach for fuzzy sets to produce extensive operational rules. In this manuscript, for TSF numbers some core operational laws are initiated based on ATCN and ATN, also some basic characteristics of these operational laws are investigated. Secondly, based on these operational laws TSF Archimedean weighted averaging (TSPFAWA) and TSF Archimedean weighted geometric (TSPFAWG) operators are initiated. Thirdly, we investigated special cases of these aggregation operators and some basic properties. On the behalf of the TSPFAWA and TSPFAWG operators, a novel method for solving multiple attribute decision-making (MADM) problems using TSF information is also devised. Lastly, a numerical example is provided to demonstrate the applicability of the suggested technique, and a comparison analysis is done to demonstrate its advantages.