Shapeless Intuitionistic Fuzzy Sets and Their Application in Decision Making

Objects in nature tend to occupy the minimum volume (or minimum area in two-dimensional space). In decision making processes, decisions involve the grouping of decision points within a given environment, and the existence of a closed-form representing this group decision is noteworthy. Current group decision-making models often rely on arithmetic and geometric operators, neglecting the inherent spatial information embedded within the decision space. When the structure formed by decision groups is associated with a convex structure representing it that occupies the least volume or area; the decision-making structure also needs to be re-evaluated geometrically in addition to operations in the literature. In this context, this article is a novel perspective on the introduction of the Shapeless Intuitionistic Fuzzy Set (S-IFS) which is an extension of intuitionistic fuzzy sets. The operations and structure of these sets, which are a new extension with the convex structure formed by the IF decision points, are examined. A numerical micromobility risk assessment case is presented to demonstrate the application of S-IFS in multi criteria decision making procedures. To compare S-IFS with the literature, a new score function has also been proposed to Circular Intuitionistic Fuzzy Set (C-IFS) with the perspective of the proposed fuzzy set. The effect of including the uncertainty in the geometric structure of group decisions into the result is clearly revealed by comparing the point group decisions of IFS, the circle covering group decisions of C-IFS, and the convex group decisions occupying the smallest area in two dimensions of the proposed S-IFS. This article aims to lead the examination of the geometric structure of fuzzy sets in group decisions, the inclusion of uncertainty in decision-making processes in a geometric sense, and the structure of group decisions in n-dimensions according to convex and concave formations for future studies.