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Journals / Hacettepe Journal of Mathematics and Statistics / 2008 / Cilt: 37 - Sayı: 2

Fuzzy sets over the poset $Bbb{I}$

İsmail U. TİRYAKİ
Pages
143–166
Publication Date
2022-10-18
DOI
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AI Summary & Key Takeaways

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⚡ TL;DR(Too Long; Didn't Read)

In particular soft fuzzy points behave like the points of crisp set theory with respect to join, and moreover there exists a Lowen type functor from Top to the construct SF-Top that preserves both separation and compactness.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:The author studies fuzzy sets over the poset $Bbb {I}$ = [0, 1] with the usual order.
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Key Findings & Data:These form a canonical example of fuzzy sets over a poset dis- cussed in (Tiryaki, İ.U. and Brown, L.M.
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Conclusion & Impact:In particular soft fuzzy points behave like the points of crisp set theory with respect to join, and moreover there exists a Lowen type functor from Top to the construct SF-Top that preserves both separation and compactness.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Domain Parameters

Abstract

The author studies fuzzy sets over the poset $Bbb {I}$ = [0, 1] with the usual order. These form a canonical example of fuzzy sets over a poset dis- cussed in (Tiryaki, İ.U. and Brown, L.M. Plain textures and fuzzy sets via posets, preprint). Characterizations of these so called “soft fuzzy sets” are obtained, and soft fuzzy sets are shown to have a richer mathematical theory than classical I-fuzzy sets. In particular soft fuzzy points behave like the points of crisp set theory with respect to join, and moreover there exists a Lowen type functor from Top to the construct SF-Top that preserves both separation and compactness.

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Cite This Article

TİRYAKİ, İ. U. (2022). Fuzzy sets over the poset $Bbb{I}$. Hacettepe Journal of Mathematics and Statistics, Cilt: 37 - Sayı: 2, 143–166. https://ajindex.com/articles/530725

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