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Fuzzy bipolar soft semiprime ideals in ordered semigroups
Aziz-Ul-Hakim1, H Khan1, I Ahmad1
1Department of Mathematics, University of Malakand, Chakdara Dir(L), Pakistan.
Heliyon
|April 29, 2021
Summary
This study introduces fuzzy bipolar soft semiprimality in ordered semigroups, exploring its properties and applications. The research characterizes ordered semigroups using this new concept and examines fuzzy bipolar soft semiprime ideals.
Area of Science:
- Algebraic Structures
- Fuzzy Mathematics
- Order Theory
Background:
- Ordered semigroups are fundamental in abstract algebra.
- Fuzzy set theory extends classical sets with degrees of membership.
- Soft set theory provides a framework for dealing with uncertainty.
Purpose of the Study:
- Introduce and define fuzzy bipolar soft semiprimality in ordered semigroups.
- Investigate the fundamental properties of this new concept.
- Characterize classes of ordered semigroups using fuzzy bipolar soft semiprimality.
Main Methods:
- Definition of fuzzy bipolar soft semiprimality within the context of ordered semigroups.
- Exploration of algebraic properties and theorems related to the defined concept.
- Characterization of specific types of ordered semigroups based on fuzzy bipolar soft semiprime ideals.
Main Results:
- Established the concept of fuzzy bipolar soft semiprimality in ordered semigroups.
- Identified and investigated key properties of fuzzy bipolar soft semiprimality.
- Provided characterizations of ordered semigroups and their subclasses using this concept.
- Examined the Cartesian product of fuzzy bipolar soft semiprime ideals.
Conclusions:
- Fuzzy bipolar soft semiprimality offers a novel approach to studying ordered semigroups.
- The characterized classes of ordered semigroups provide deeper structural insights.
- The findings contribute to the advancement of fuzzy algebraic structures and ideal theory.
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