Approach to solve multi-criteria group decision-making problems by exponential operational law in generalised spherical fuzzy environment

Abstract

The construction of generalised spherical fuzzy number (GSFN) is a reliable philosophy to design and understanding of vagueness and impreciseness. In this study, at first, the authors have defined the generalised spherical fuzzy set and discussed its several properties. Then, a new score and accuracy functions have been introduced in the generalised spherical fuzzy environment which leads to a new method of conversion of fuzzy number into a crisp number. New exponential operational law has been defined for GSFNs where the bases are positive real numbers & components are GSFNs and its various algebraic properties have been studied explicitly. Using this exponential operational law, a generalised spherical weighted exponential averaging operator has been proposed, which is used to develop a multi-criteria group decision-making (MCGDM) method in the generalised spherical fuzzy environment. The newly developed MCGDM has been demonstrated through a real-life problem and its effectiveness and rationality have been shown through sensitivity analysis.

Keywords

• fuzzy set theory
• decision making
• operations research
• sensitivity analysis
• algebra
• generalised spherical fuzzy set
• exponential operational law
• generalised spherical weighted exponential averaging operator
• multicriteria group decision-making method
• algebraic properties
• sensitivity analysis