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Fuzzy γ-hyperideals in γ-hypersemirings by using triangular norms
B A Ersoy1, B Davvaz2, S Onar1
1Department of Mathematics, Yildiz Technical University, 81270 Istanbul, Turkey.
Thescientificworldjournal
|June 27, 2014
Summary
This study introduces triangular fuzzy sub-Γ-semihyperrings and triangular fuzzy Γ-hyperideals using triangular norms. These concepts generalize existing algebraic structures like Γ-semihyperrings.
Area of Science:
- Algebraic Structures
- Fuzzy Mathematics
Background:
- Γ-semihyperrings generalize semirings and semihyperrings.
- Previous work established Γ-semihyperrings by Dehkordi and Davvaz.
Purpose of the Study:
- To define and investigate triangular fuzzy sub-Γ-semihyperrings.
- To introduce and study triangular fuzzy Γ-hyperideals within Γ-semihyperrings.
- To explore properties related to these new fuzzy concepts.
Main Methods:
- Utilizing the concept of triangular norms.
- Applying fuzzy set theory to Γ-semihyperring structures.
- Developing theoretical results based on these definitions.
Main Results:
- Definition of triangular fuzzy sub-Γ-semihyperrings.
- Definition of triangular fuzzy Γ-hyperideals.
- Exploration of initial properties and relationships.
Conclusions:
- The study successfully extends Γ-semihyperring theory with fuzzy concepts.
- Triangular fuzzy norms provide a framework for new algebraic investigations.
- Further research can explore more advanced properties and applications.
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