From Zadeh’s Fuzziness to Smarandache’s Neutrosophy: A Review-Reference-Cited by-同舟云学术

From Zadeh’s Fuzziness to Smarandache’s Neutrosophy: A Review

Published:2022-12-31 Issue: Volume:4 Page:98-104
ISSN:2766-9823
Container-title:International Journal of Applied Mathematics, Computational Science and Systems Engineering
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Author:

Voskoglou Michael. Gr.¹^ORCID

Affiliation:

1. Mathematical Sciences University of Peloponnese (ex School of Technological Applicatiions of the Graduate TEI of Western Greece) Patras, GREECE

Abstract

The present paper reviews the process that led from Zadeh’s fuzziness to Smarandache’s neutrosophy. Starting from fuzzy sets and logic and Atanassov’s intuitionistic fuzzy sets, it proceeds to a detailed study of the concept of neutrosophic set, which takes in account the existing in real life indeterminacy. The basic operations on neutrosophic sets are defined and the classical notion of topological space is extended to the notion of neutrosophic topological space, where fundamental properties and concepts like convergence, continuity, compactness and Hausdorff topological spaces are naturally extended.

Publisher

World Scientific and Engineering Academy and Society (WSEAS)

Reference36 articles.

1. G.J. Klir and T.A. Folger, Fuzzy sets, uncertainty and information, Prentice-Hall, London, 1988.

2. B. Kosko, “Fuzziness vs probability”, Int. J. of General Systems, Vol. 17(2-3), pp. 211-240, 1990.

3. M.Gr. Voskoglou, “Fuzzy systems, extensions and relative theories”, WSEAS Transactions on Advances in Engineering Education, Vol. 16, pp. 63-69, 2019.

4. S. Korner, Laws of thought, Encyclopedia of Philosophy; Mac Millan: NY, USA, Volume 4, pp. 414–417, 1967.

5. M.Gr. Voskoglou, “Methods for assessing human-machine performance under fuzzy conditions”, Mathematics, Vol. 7(3), article 230, 2019.