Fuzziness, Indeterminacy and Soft Sets: Frontiers and Perspectives
This work addresses foundational mathematical extensions for fuzzy and soft sets, which is incremental in advancing theoretical frameworks in uncertainty modeling.
The paper reviews the evolution from fuzzy sets to soft sets and presents hybrid methods for assessment and decision-making under fuzzy conditions, improving an earlier method by Maji et al., while extending topological concepts like limit and continuity to fuzzy and soft structures with illustrative examples.
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.