Abstract
One recent generalization of Zadeh’s fuzzy sets is the concept of multidimensional fuzzy sets. This work extends this concept further by introducing a generalized form of multidimensional fuzzy algebra. By focusing on multidimensional t-norms and t-conorms, we develop a comprehensive theory. This includes the notion of strong multidimensional fuzzy algebras and explores their properties, such as multidimensional groupoids, monoids, and groups. Additionally, we introduce equivalence relations on the collection of all multidimensional fuzzy sets and present an example of specific monoids within this collection. Finally, we demonstrate how a group structure can be imposed on a subcollection of orderless multidimensional fuzzy sets.
| Original language | English |
|---|---|
| Pages (from-to) | 1-15 |
| Number of pages | 15 |
| Journal | Turkish World Mathematical Society Journal of Applied and Engineering Mathematics |
| Volume | 16 |
| Issue number | 1 |
| Publication status | Published - 2026 |
All Science Journal Classification (ASJC) codes
- Statistics and Probability
- Numerical Analysis
- Mathematical Physics
- Discrete Mathematics and Combinatorics
- Control and Optimization
- Computational Mathematics
- Applied Mathematics
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