adjustable approaches to multi-criteria group decision making based on inverse fuzzy soft matrices

In this paper, we focus on the matrices representing the inverse fuzzy soft sets over both the universal object set and the universal parameter set. some basic operations and properties of these inverse fuzzy soft matrices are investigated. moreover, two adjustable approaches to multi-criteria group decision making (mcgdm), namely inverse fuzzy soft sum-product decision making (ifsspdm) and inverse fuzzy soft distributive if-difference decision making (ifsdif-ddm), are proposed. the ifsspdm approach achieves the optimal choice for the mcgdm problem based on the inverse fuzzy soft structures consisting of multiple-discrete parameter sets and common universal object sets. the objective of ifsdif-ddm approach is to present a solution for the mcgdm problem based on the inverse fuzzy soft structures consisting of a common universal parameter set and twodiscrete universal object sets. thus, the solutions can be obtained using the practicality of inverse fuzzy soft matrices for two different types of decision making problems. besides, the comparisons are presented showing that the proposed approaches produce more convincing outputs than the current fuzzy soft approaches.