New q-rung orthopair fuzzy Aczel–Alsina weighted geometric operators under group-based generalized parameters in multi-criteria decision-making problems

Abstract

The concept of q-rung orthopair fuzzy set (q-ROF) defined as generalization of intuitionistic fuzzy set (IFS) and Pythagorean fuzzy set (PyFS) has more flexible structure according to several clusters. Therefore, it is a benefit tool to obtain various results for different values of q. The basic benefit of generalized concepts is to rate level of truth and falsity and reduce to error margin. Thus, while the final decision is decided by experts, the most accuracy finding is to present. Aczel–Alsina t-norm (AA-TN) and t-conorm (AA-TCN) structures were defined by Aczel and Alsina in 1982. The both concepts include parameters changing according to prefer, decision, and request of experts. In this paper, q-rung orthopair fuzzy Aczel–Alsina weighted geometric operator (q-ROFAAWG) is produced and also ordered and hybrid concepts (q-ROFAAOWG, q-ROFAAHWG) are obtained using Aczel–Alsina operators (AAOs). Hence, this operator is expanded to generalized q-rung orthopair fuzzy Aczel–Alsina weighted geometric operator (Gq-ROFAAWG), ordered and hybrid concepts (Gq-ROFAAOWG, Gq-ROFAAHWG) using single parameter. Finally, group-based generalized q-rung orthopair fuzzy Aczel–Alsina weighted geometric operator (GGq-ROFAAWG), ordered and hybrid concepts (GGq-ROFAAOWG, GGq-ROFAAHWG) are proposed and their properties are worked. Moreover, an algorithm-based multi-criteria decision-making is given and applied over a numerical example to illustrate the effective of the proposed method. The results are evaluated for different values of parameters. In addition to, comparative analysis is developed to show the superiority of proposed approach than existing methods.