Plithogenic Set, an Extension of Crisp, Fuzzy, Intuitionistic Fuzzy, and Neutrosophic Sets - Revisited
In this paper, we introduce the plithogenic set (as generalization of crisp, fuzzy, intuitionistic fuzzy, and neutrosophic sets), which is a set whose elements are characterized by many attributes’ values. An attribute value v has a corresponding (fuzzy, intuitionistic fuzzy, or neutrosophic) degree...
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| Format: | Article |
| Language: | English |
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University of New Mexico
2018-09-01
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| Series: | Neutrosophic Sets and Systems |
| Subjects: | |
| Online Access: | http://fs.unm.edu/NSS/PlithogenicSetAnExtensionOfCrisp.pdf |
| _version_ | 1811269186171699200 |
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| author | Florentin Smarandache |
| author_facet | Florentin Smarandache |
| author_sort | Florentin Smarandache |
| collection | DOAJ |
| description | In this paper, we introduce the plithogenic set (as generalization of crisp, fuzzy, intuitionistic fuzzy, and neutrosophic sets), which is a set whose elements are characterized by many attributes’ values. An attribute value v has a corresponding (fuzzy, intuitionistic fuzzy, or neutrosophic) degree of appurtenance d(x,v) of the element x, to the set P, with respect to some given criteria. In order to obtain a better accuracy for the plithogenic aggregation operators in the plithogenic set, and for a more exact inclusion (partial order), a (fuzzy, intuitionistic fuzzy, or neutrosophic) contradiction (dissimilarity) degree is defined between each attribute value and the dominant (most important) attribute value. The plithogenic intersection and union are linear combinations of the fuzzy operators tnorm and tconorm, while the plithogenic complement, inclusion (inequality), equality are influenced by the attribute values contradiction (dissimilarity) degrees. This article offers some examples and applications of these new concepts in our everyday life. |
| first_indexed | 2024-04-12T21:36:29Z |
| format | Article |
| id | doaj.art-2f423d14f2524aaea64d6ee7b5eb5506 |
| institution | Directory Open Access Journal |
| issn | 2331-6055 2331-608X |
| language | English |
| last_indexed | 2024-04-12T21:36:29Z |
| publishDate | 2018-09-01 |
| publisher | University of New Mexico |
| record_format | Article |
| series | Neutrosophic Sets and Systems |
| spelling | doaj.art-2f423d14f2524aaea64d6ee7b5eb55062022-12-22T03:15:52ZengUniversity of New MexicoNeutrosophic Sets and Systems2331-60552331-608X2018-09-0121153166doi.org/10.5281/zenodo.1408740Plithogenic Set, an Extension of Crisp, Fuzzy, Intuitionistic Fuzzy, and Neutrosophic Sets - RevisitedFlorentin SmarandacheIn this paper, we introduce the plithogenic set (as generalization of crisp, fuzzy, intuitionistic fuzzy, and neutrosophic sets), which is a set whose elements are characterized by many attributes’ values. An attribute value v has a corresponding (fuzzy, intuitionistic fuzzy, or neutrosophic) degree of appurtenance d(x,v) of the element x, to the set P, with respect to some given criteria. In order to obtain a better accuracy for the plithogenic aggregation operators in the plithogenic set, and for a more exact inclusion (partial order), a (fuzzy, intuitionistic fuzzy, or neutrosophic) contradiction (dissimilarity) degree is defined between each attribute value and the dominant (most important) attribute value. The plithogenic intersection and union are linear combinations of the fuzzy operators tnorm and tconorm, while the plithogenic complement, inclusion (inequality), equality are influenced by the attribute values contradiction (dissimilarity) degrees. This article offers some examples and applications of these new concepts in our everyday life.http://fs.unm.edu/NSS/PlithogenicSetAnExtensionOfCrisp.pdfPlithogenyPlithogenic SetNeutrosophic Set |
| spellingShingle | Florentin Smarandache Plithogenic Set, an Extension of Crisp, Fuzzy, Intuitionistic Fuzzy, and Neutrosophic Sets - Revisited Neutrosophic Sets and Systems Plithogeny Plithogenic Set Neutrosophic Set |
| title | Plithogenic Set, an Extension of Crisp, Fuzzy, Intuitionistic Fuzzy, and Neutrosophic Sets - Revisited |
| title_full | Plithogenic Set, an Extension of Crisp, Fuzzy, Intuitionistic Fuzzy, and Neutrosophic Sets - Revisited |
| title_fullStr | Plithogenic Set, an Extension of Crisp, Fuzzy, Intuitionistic Fuzzy, and Neutrosophic Sets - Revisited |
| title_full_unstemmed | Plithogenic Set, an Extension of Crisp, Fuzzy, Intuitionistic Fuzzy, and Neutrosophic Sets - Revisited |
| title_short | Plithogenic Set, an Extension of Crisp, Fuzzy, Intuitionistic Fuzzy, and Neutrosophic Sets - Revisited |
| title_sort | plithogenic set an extension of crisp fuzzy intuitionistic fuzzy and neutrosophic sets revisited |
| topic | Plithogeny Plithogenic Set Neutrosophic Set |
| url | http://fs.unm.edu/NSS/PlithogenicSetAnExtensionOfCrisp.pdf |
| work_keys_str_mv | AT florentinsmarandache plithogenicsetanextensionofcrispfuzzyintuitionisticfuzzyandneutrosophicsetsrevisited |