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Kragujevac Journal of Mathematics, 2023 Picture fuzzy subgroup of a crisp group is established here and some properties connected to it are investigated. Also, normalized restricted picture fuzzy set, conjugate picture fuzzy subgroup, picture fuzzy coset, picture fuzzy normal subgroup and the order of picture fuzzy subgroup are defined.
Dogra, Shovan, Pal, Madhumangal
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Fuzzy Subgroups and Digraphs Induced by Fuzzy Subgroups
Transactions on Fuzzy Sets and Systems, 2022 Given a fuzzy subgroup $\mu$ of a group $G$, $x\rhd_uy$ if and only if $\mu(xy) < \mu(yx)$ defines a directed relation with an associated digraph $(G, \rhd_u)$. We consider $(\mu, \nu)$-homomorphisms $\varphi: (G, \mu)\to (H, \nu)$ where $\mu$ and $\nu$ are fuzzy subgroups of $G$ and $H$ respectively and the preservation of properties of ...
Allen, Paul J. +2 more
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Nilpotent Fuzzy Subgroups [PDF]
Mathematics, 2018 In this paper, we introduce a new definition for nilpotent fuzzy subgroups, which is called the good nilpotent fuzzy subgroup or briefly g-nilpotent fuzzy subgroup. In fact, we prove that this definition is a good generalization of abstract nilpotent groups.
Elaheh Mohammadzadeh, Rajab Ali Borzooei
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Aggregation of fuzzy subgroups
Fuzzy Sets and Systems, 2021 Given an aggregation function, and two fuzzy subgroups of a group, this study investigates whether the aggregation of them is also a fuzzy subgroup. It is proven that if the cardinal of the group is a prime power, then it is always a fuzzy subgroup. For a general group, it is proven that the existence of a binary relation between the fuzzy subgroups ...
Bejines-López, Carlos +2 more
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Homomorphism of Characteristic Fuzzy Subgroup and Abelian Fuzzy Subgroup
International Journal for Research in Applied Science and Engineering Technology, 2022 Abstract: In this paper, we have established some independent proof of homomorphism on algebra of abelian and characteristic fuzzy subgroup. The characteristic of fuzzy subgroup [13] was first introduced by P. Bhattacharya and N. P. Mukharjee in 1986.
Amit Kumar Arya, Dr. M. Z. Alam
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A Study of Normal Fuzzy Subgroups and Characteristic Fuzzy Subgroups of a Fuzzy Group [PDF]
Fuzzy Information and Engineering, 2012 \textit{A. Rosenfeld} [in J. Math. Anal. Appl. 35, 512-517 (1971; Zbl 0194.05501)] initiated the study of fuzzy group theory by introducing the concepts of fuzzy subgroupoids and fuzzy subgroups. Then, several authors studied the notion of fuzzy normal subgroups.
Ajmal, Naseem, Jahan, Iffat
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Intuitionistic Fuzzy Subgroups and Level Subgroups [PDF]
International Journal of Fuzzy Logic and Intelligent Systems, 2006 We introduce the concept of level subgroups of an intuitionistic fuzzy subgroup and study some of it's properties. These level subgroups in turn play an important role in the characterization of all intuitionistic fuzzy subgroup of a prime cyclic group.
Tae-Chon Ahn, Kul Hur, Kyung-Won Jang
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Level Subgroup Homomorphism in Fuzzy Subgroup
IOP Conference Series: Earth and Environmental Science, 2020 Abstract For all arbitrary set X with characteristic functions is known as fuzzy subsets. On group X, fuzzy subgroups can be formed appropriate with some axioms. In fuzzy subgroup there is sub set with some properties that known as level subgroups of fuzzy subgroup.
Miftah Sigit Rahmawati +3 more
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Fuzzy subgroups: Some characterizations
Journal of Mathematical Analysis and Applications, 1987 The author considers fuzzy groups on a finite group and examines an equivalence relation between them: possession of the same family of level subgroups. The paper gives some refinements of results and proofs of \textit{P. S. Das} [J. Math. Anal. Appl. 84, 264--269 (1981; Zbl 0476.20002)]. This paper was continued [cf. Part II, Inf. Sci.
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FUZZY SUBGROUPS BASED ON FUZZY POINTS [PDF]
Communications of the Korean Mathematical Society, 2011 Using the "belongs to" relation and "quasi-coincident with" relation between a fuzzy point and a fuzzy subgroup, Bhakat and Das, in 1992 and 1996, initiated general types of fuzzy subgroups which are a generalization of Rosenfeld's fuzzy subgroups. In this paper, more general notions of "belongs to" and "quasi-coincident with" relation between a fuzzy ...
Young-Bae Jun +2 more
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