Abstract
In this paper, a new approach to order relation between fuzzy sets is provided, which is called well inclusion order between fuzzy sets. Based on this new order relation, the concept of algebraic fuzzy closure operators is introduced. It is shown that there is a categorical isomorphism between algebraic fuzzy closure operators and fuzzy convex structures. Also, the relationship between fuzzy closure systems and fuzzy convex structures is investigated. It is proved that the category of fuzzy convex spaces is a bicoreflective subcategory of the category of fuzzy closure system spaces.
| Original language | English |
|---|---|
| Pages (from-to) | 87-96 |
| Number of pages | 10 |
| Journal | International Journal of Approximate Reasoning |
| Volume | 92 |
| DOIs | |
| Publication status | Published - Jan 2018 |
Keywords
- Fuzzy closure operator
- Fuzzy closure system
- Fuzzy convex structure
- Fuzzy set