Fuzziness, Indeterminacy and Soft Sets: Frontiers and Perspectives
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 us...
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| Format: | Article |
| Language: | English |
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MDPI AG
2022-10-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/10/20/3909 |
| _version_ | 1827649096505098240 |
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| author | Michael Gr. Voskoglou |
| author_facet | Michael Gr. Voskoglou |
| author_sort | Michael Gr. Voskoglou |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-03-09T19:52:07Z |
| format | Article |
| id | doaj.art-5f0f1754d6b14282a8e4d76929471af8 |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-09T19:52:07Z |
| publishDate | 2022-10-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-5f0f1754d6b14282a8e4d76929471af82023-11-24T01:08:23ZengMDPI AGMathematics2227-73902022-10-011020390910.3390/math10203909Fuzziness, Indeterminacy and Soft Sets: Frontiers and PerspectivesMichael Gr. Voskoglou0Department of Applied Mathematics, Graduate Technological Educational Institute of Western Greece, 22334 Patras, GreeceThe 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.https://www.mdpi.com/2227-7390/10/20/3909fuzzy set (FS)fuzzy logic (FL)intuitionistic FS (IFS)indeterminacyneutrosophic set (NS)soft set (SS) |
| spellingShingle | Michael Gr. Voskoglou Fuzziness, Indeterminacy and Soft Sets: Frontiers and Perspectives Mathematics fuzzy set (FS) fuzzy logic (FL) intuitionistic FS (IFS) indeterminacy neutrosophic set (NS) soft set (SS) |
| title | Fuzziness, Indeterminacy and Soft Sets: Frontiers and Perspectives |
| title_full | Fuzziness, Indeterminacy and Soft Sets: Frontiers and Perspectives |
| title_fullStr | Fuzziness, Indeterminacy and Soft Sets: Frontiers and Perspectives |
| title_full_unstemmed | Fuzziness, Indeterminacy and Soft Sets: Frontiers and Perspectives |
| title_short | Fuzziness, Indeterminacy and Soft Sets: Frontiers and Perspectives |
| title_sort | fuzziness indeterminacy and soft sets frontiers and perspectives |
| topic | fuzzy set (FS) fuzzy logic (FL) intuitionistic FS (IFS) indeterminacy neutrosophic set (NS) soft set (SS) |
| url | https://www.mdpi.com/2227-7390/10/20/3909 |
| work_keys_str_mv | AT michaelgrvoskoglou fuzzinessindeterminacyandsoftsetsfrontiersandperspectives |