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Fuzzy rank functions in the set of all binary systems
Hee Sik Kim1, J Neggers2, Keum Sook So3
1Department of Mathematics, Hanyang University, Seoul, 04763 Korea.
Springerplus
|November 9, 2016
Summary
This study introduces fuzzy rank functions for groupoids, exploring their impact on binary systems and semigroups using novel parallelism and shrinking groupoid concepts.
Area of Science:
- Algebraic Structures
- Fuzzy Mathematics
Background:
- Groupoids are fundamental algebraic structures.
- Semigroups of binary systems are crucial in abstract algebra.
- Fuzzy set theory offers tools to generalize algebraic concepts.
Purpose of the Study:
- To introduce and define fuzzy rank functions for groupoids.
- To investigate the role of these functions within the semigroup of binary systems.
- To utilize right parallelisms and [Formula: see text]-shrinking groupoids as analytical tools.
Main Methods:
- Development of fuzzy rank function definitions for groupoids.
- Application of right parallelism concepts.
- Utilisation of [Formula: see text]-shrinking groupoid properties.
Main Results:
- Fuzzy rank functions are established for groupoids.
- Their significance in the context of binary system semigroups is demonstrated.
- The interplay between fuzzy rank, right parallelisms, and shrinking groupoids is elucidated.
Conclusions:
- Fuzzy rank functions provide a new perspective on groupoid analysis.
- These functions have implications for understanding the structure of binary system semigroups.
- The study highlights the utility of fuzzy algebraic tools in exploring complex mathematical structures.
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