Fuzziness, Indeterminacy and Soft Sets: Frontiers and Perspectives

TL;DR

This paper reviews the development of fuzzy, indeterminacy, and soft set theories, introduces hybrid decision-making methods, and explores topological generalizations within fuzzy and soft structures.

Contribution

It presents new hybrid assessment methods using soft sets and real intervals, and extends topological concepts to fuzzy and soft spaces.

Findings

Improved decision-making method using soft sets and real intervals.

Extension of topological concepts to fuzzy and soft spaces.

Illustrative examples of fuzzy and soft topological spaces.

Abstract

The present paper comes across the main steps that laid from Zadeh's fuzziness ana Atanassov's intuitionistic fuzzy sets to Smarandache's indeterminacy and to Molodstov's soft sets. Two hybrid methods for assessment and decision making respectively under fuzzy conditions are also presented through suitable examples that use soft sets and real intervals as tools. The decision making method improves an earlier method of Maji et al. Further, it is described how the concept of topological space, the most general category of mathematical spaces, can be extended to fuzzy structures and how to generalize the fundamental mathematical concepts of limit, continuity compactness and Hausdorff space within such kind of structures. In particular, fuzzy and soft topological spaces are defined and examples are given to illustrate these generalizations.