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Prime $L$-fuzzy filters of a semilattice
Ch. Santhi Sundar Raj,B. Subrahmanyam,U. M. Swamy 원광대학교 기초자연과학연구소 2020 ANNALS OF FUZZY MATHEMATICS AND INFORMATICS Vol.20 No.1
In this paper, we study the notion of prime $L$-fuzzy filter of a bounded distributive semilattice S with truth values in a frame $L$. A characterization theorem of prime (maximal) $L$-fuzzy filters of $S$ is established and, the set of all prime $L$-fuzzy filters of $S$ is topologized and the resulting space is discussed.
Ch. Santhi Sundar Raj,K. Rama Prasad,K. Ramanuja Rao,Natnael Teshale A. 원광대학교 기초자연과학연구소 2019 ANNALS OF FUZZY MATHEMATICS AND INFORMATICS Vol.18 No.2
In this paper, we introduce the notion of $L$-fuzzy sublattice of a bounded lattice with truth values in a complete lattice satisfying the infinite meet distributive law and prove certain general properties of these, by observing that these form an algebraic fuzzy set system.
Fuzzy ideals of almost distributive lattices
U. M. Swamy,Ch. Santhi Sundar Raj,Natnael Teshale A. 원광대학교 기초자연과학연구소 2017 ANNALS OF FUZZY MATHEMATICS AND INFORMATICS Vol.14 No.4
The notion of an Almost Distributive Lattice (ADL) is a common abstraction of several lattice theoretic and ring theoretic generalization of Boolean algebra and Boolean rings. In this paper, we introduce the notion of $L$-fuzzy ideal of an ADL with truth values in a complete lattice $L$ satisfying the infinite meet distributive law and prove certain properties of these. Mainly, it is proved that the class of $L$-fuzzy ideals of an ADL forms a complete distributive lattice.
G. Srikanya,G. Prakasam Babu,Ch. Santhi Sundar Raj,Natnaeal Teshale 한국전산응용수학회 2024 Journal of applied mathematics & informatics Vol.42 No.4
The set of all prime $L$-fuzzy ideals of an ADL $A$ with truth values in a frame $L$ is topologized and the resulting space is denoted by $\mathcal{F}_{L}~Spec~(A)$, called fuzzy Stone space of $A$. Certain properties of the space $\mathcal{F}_{L}~Spec~(A)$ are discussed, and it is proved that $\mathcal{F}_{L}~Spec~(A)$ is homeomorphic with the product space $Spec~(A)\times Spec~(L)$.