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Fuzziness, Indeterminacy and Soft Sets: Frontiers and Perspectives

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  • Michael Gr. Voskoglou

    (Department of Applied Mathematics, Graduate Technological Educational Institute of Western Greece, 22334 Patras, Greece)

Abstract

The present paper comes across the main steps that were laid from Zadeh’s fuzziness and 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 using suitable examples that use soft sets and real intervals as tools. The decision making method improves on 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 kinds of structures. In particular, fuzzy and soft topological spaces are defined and examples are given to illustrate these generalizations.

Suggested Citation

  • Michael Gr. Voskoglou, 2022. "Fuzziness, Indeterminacy and Soft Sets: Frontiers and Perspectives," Mathematics, MDPI, vol. 10(20), pages 1-15, October.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:20:p:3909-:d:949492
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    References listed on IDEAS

    as
    1. Athar Kharal & B. Ahmad, 2011. "Mappings On Soft Classes," New Mathematics and Natural Computation (NMNC), World Scientific Publishing Co. Pte. Ltd., vol. 7(03), pages 471-481.
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