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On fuzzy positive implicative filters in BE-algebras.
Sun Shin Ahn1, Jeong Soon Han2
1Department of Mathematics Education, Dongguk University, Seoul 100-715, Republic of Korea.
Thescientificworldjournal
|July 1, 2014
Summary
This study defines fuzzy positive implicative filters, a generalized concept of fuzzy filters within BE-algebras, enhancing algebraic structure understanding.
Area of Science:
- Algebraic Structures
- Fuzzy Set Theory
Background:
- BE-algebras are algebraic structures with specific properties.
- Fuzzy filters are a generalization of filters in algebraic structures using fuzzy set theory.
Purpose of the Study:
- To define and study fuzzy positive implicative filters in BE-algebras.
- To explore the properties and generalizations of fuzzy filters within this algebraic context.
Main Methods:
- Utilizing concepts from fuzzy set theory.
- Applying definitions and properties of BE-algebras.
- Investigating the generalization of fuzzy filters to fuzzy positive implicative filters.
Main Results:
- Established the definition of fuzzy positive implicative filters.
- Analyzed several degrees of these filters.
- Demonstrated their relationship as a generalization of fuzzy filters.
Conclusions:
- Fuzzy positive implicative filters offer a broader framework within BE-algebras.
- The study contributes to the understanding of fuzzy structures in abstract algebra.
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