Radial Distance Functions for Partitioning Soft Spaces

Abstract

In this paper, we introduce a scalar measure for soft sets and define reference-based radial distances from a fixed reference soft set to every soft set in a soft space. We establish their fundamental properties, including non-negativity, identity of indiscernibles, and conditional monotonicity. The normalized radial distances induce a partition of the soft space into clusters determined by prescribed distance intervals. We formulate the partitioning task as a computational problem, develop an algorithm for constructing the induced partition, and establish its worst-case time and space complexities. The proposed framework is illustrated through a course outcomes assessment example