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SOFT INTERSECTION AND SOFT UNION k-IDEALS OF HEMIRINGS AND THEIR APPLICATIONS
Anjum, Rukhshanda,Lodhi, Aqib Raza Khan,Munir, Mohammad,Kausar, Nasreen The Kangwon-Kyungki Mathematical Society 2022 한국수학논문집 Vol.30 No.2
The main aim of this paper is to discuss two different types of soft hemirings, soft intersection and soft union. We discuss applications and results related to soft intersection hemirings or soft intersection k-ideals and soft union hemirings or soft union k-ideals. The deep concept of k-closure, intersection and union of soft sets, ∧-product and ∨-product among soft sets, upper 𝛽-inclusion and lower 𝛽-inclusion of soft sets is discussed here. Many applications related to soft intersection-union sum and soft intersection-union product of sets are investigated in this paper. We characterize k-hemiregular hemirings by the soft intersection k-ideals and soft union k-ideals.
A characterization of semigroups through their fuzzy generalized $m$-bi-ideals
Mohammad Munir,Nasreen Kausar,Rukhshanda Anjum,Asghar Ali,Rashida Hussain 강원경기수학회 2020 한국수학논문집 Vol.28 No.3
In this article, we initially present the concept of the fuzzy generalized $m$-bi-ideals in semigroups, then making use of their important types like prime, semiprime and strongly fuzzy generalized $m$-bi-ideals, we give the important characterizations of the semigroups. We also characterize the $m$-regular and $m$-intraregular semigroups using the properties of the irreducible and strongly irreducible fuzyy generalized $m$-bi-ideals.
Hypergroupoids as Tools for Studying Blood Group Genetics
Mohammad Munir,Nasreen Kausar,Salahuddin,Rukhshanda Anjum,Qingbing Xu,Waqas Ahmad 한국지능시스템학회 2021 INTERNATIONAL JOURNAL of FUZZY LOGIC and INTELLIGE Vol.21 No.2
We initially introduce the concepts of an m-right (m-left) hyperideal and an m-hyperideal in a hypergroupoid. The ideas behind an m-factor and a generalized m-factor are then introduced. Next, we demonstrate the existence and important properties of these sub-hyperstructures through theorems and examples. We then define the m-right (m-left) consistent, m-consistent, m-intra-consistent, and m-simple hypergroupoids. Finally, we demonstrate that practical problems in biology, such as ABO blood group genetics, can be studied by defining these hypergroupoid substructures.