An Efficient Approach to Approximate Fuzzy Ideals of Semirings Using Bipolar Techniques

Muhammad Shabir, Ahmad N. Al-Kenani, Fawad Javed and Shahida Bashir
Additional contact information
Muhammad Shabir: Department of Mathematics, Quaid-e-Azam University Islamabad, Islamabad 44000, Pakistan
Ahmad N. Al-Kenani: Department of Mathematics, Faculty of Science, King Abdulaziz University, P.O. Box 80219, Jeddah 21589, Saudi Arabia
Fawad Javed: Department of Mathematics, Quaid-e-Azam University Islamabad, Islamabad 44000, Pakistan
Shahida Bashir: Department of Mathematics, University of Gujrat, Gujrat 50700, Pakistan

Mathematics, 2022, vol. 10, issue 7, 1-16

Abstract: The bipolar fuzzy (BF) set is an extension of the fuzzy set used to solve the uncertainty of having two poles, positive and negative. The rough set is a useful mathematical technique to handle vagueness and impreciseness. The major objective of this paper is to analyze the notion of approximation of BF ideals of semirings by combining the theories of the rough and BF sets. Then, the idea of rough approximation of BF subsemirings (ideals, bi-ideals and interior ideals) of semirings is developed. In addition, semirings are characterized by upper and lower rough approximations using BF ideals. Further, it is seen that congruence relations (CRs) and complete congruence relations (CCRs) play fundamental roles for rough approximations of bipolar fuzzy ideals. Therefore, their associated properties are investigated by means of CRs and CCRs.

Keywords: semirings; bipolar fuzzy subsets; bipolar fuzzy ideals; congruence relations; complete congruence relation; upper rough sets; lower rough sets (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
https://www.mdpi.com/2227-7390/10/7/1009/pdf (application/pdf)
https://www.mdpi.com/2227-7390/10/7/1009/ (text/html)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:gam:jmathe:v:10:y:2022:i:7:p:1009-:d:776451

Access Statistics for this article

Mathematics is currently edited by Ms. Emma He

More articles in Mathematics from MDPI
Bibliographic data for series maintained by MDPI Indexing Manager ().