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A note on fuzzy subgroups and fuzzy homomorphism

1988
*
Journal of Mathematical Analysis and Applications
*

of a

doi:10.1016/0022-247x(88)90224-7
fatcat:s27ryfa6sngpdollfmci6pbcfu
*fuzzy**subgroup*of G, is a*fuzzy**subgroup*of G*I*. ... A*fuzzy*subset (G, , u) is called a t-level f-*fuzzy*sub- group of G, if there exists a*fuzzy**subgroup*(G,, 6) of G, such that (*i*) C(x) d*v*(x), Vx E G, (ii)*v*(xIxJ~*v*(xI)~~(xZ) Vx,, x2 EGO, and*v*(x,x2)>/ ... Then By the definition of supremum, V6 >O, there exists Z0 E G, with*I**,-(&, JJJ = 1 such that @o) 2*v*u,(cq -6. Therefore (G,, f;'(rs)) E&. N ow W;'(G,, Y~H=~,~;'G, Y/S)= (G,, ys), asfi is onto (cf. ...##
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The Intuitionistic Fuzzy Normal Subgroup

2010
*
International Journal of Fuzzy Logic and Intelligent Systems
*

In this paper we continue the study of intuitionistic

doi:10.5391/ijfis.2010.10.1.082
fatcat:lshfkytiw5afllsut2ik4nqk7a
*fuzzy*groups by introducing the notion of intuitionistic*fuzzy*normal*subgroup*based*on*intuitionistic*fuzzy*space as a generalization of*fuzzy*normal ... Key Word :*Fuzzy*space, intuitionistic*fuzzy*space, intuitionistic*fuzzy*group, normal intuitionistic*fuzzy**subgroup*. ... and then we define the intuitionistic*fuzzy*normal*subgroup*. where , α β and γ are some intuitionistic*fuzzy*elements of U or ( , , ) G*I**I*such that*one*or two of these intuitionistic*fuzzy*elements ...##
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Algebraic Structure Of Union Of Fuzzy Subgroups And Fuzzy Sub-Bigroups

2017
*
Zenodo
*

In this Paper, we discuss the definitions of union of

doi:10.5281/zenodo.844068
fatcat:ttdds7j4ljgkjnhv6iycnfnbea
*Fuzzy*subsets,*Fuzzy**subgroup*, properties, union of*Fuzzy**subgroups*and related theorems and proofs. ... Proof: If {μ*i*} is a set of*fuzzy**subgroups*. then, ∩ μ*i*(xy)≥min (∩ μ*i*(x), ∩ μ*i*(y)).*i**i**i*( ∩ μ*i*) x¯¹ =inf μ*i*(x¯¹) ≥ inf μ*i*(x)= ( ∩ μ*i*) (x) .*i**i**i**i*Theorem 5: Let μ be a*fuzzy**subgroup*... Main Theorem 1: The union of two*fuzzy**subgroups*of a group G is a*fuzzy**subgroup*If and only if*one*is contained in the other. ...##
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MEASURES OF FUZZY SUBGROUPS

2010
*
Proyecciones
*

A

doi:10.4067/s0716-09172010000100005
fatcat:sk25ddxbdbb73f2neirnq77vtu
*fuzzy*subset µ in a group G is a*fuzzy**subgroup*if and only if its*subgroup*degree m g (µ) = 1. Some properties of*subgroup*degrees are investigated. ... In this paper, we introduce the notion of degree to which a*fuzzy*subset is a*fuzzy**subgroup*by means of the implication operator of [0, 1]. ... Preliminaries Throughout this paper, [0, 1] X (or*I*X ) denotes the set of all*fuzzy*sets*on*X. a denotes the constant*fuzzy*sets*on*X taking the value a. ...##
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On Fuzzy Internal Direct Product

2017
*
Ibn AL- Haitham Journal For Pure and Applied Science
*

The main aim of this paper is to introduce the concept of a

doaj:9ac864ad066d4303aef33a962ec204e8
fatcat:vyikfr3uzferpikhw6mu2n66du
*Fuzzy*Internal Direct Product of*fuzzy**subgroups*of group . ... in*fuzzy*groups. ... Definition 1.2: Let*v*, be*fuzzy*subsets of G, if (*i*) ) ( ), ( max ) ( x*v*x x*v* (ii) ) ( ), ( min ) ( x*v*x x*v* , for all G x Then*v*and*v* are called ...##
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A Study on Fuzzy Ideals ofN-Groups

2013
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Algebra
*

Using the idea of the new sort of

doi:10.1155/2013/594636
fatcat:5ujns6hvlrg77m3pghke6zl6sq
*fuzzy*subnear-ring of a near-ring,*fuzzy**subgroups*, and their generalizations defined by various researchers, we try to introduce the notion of (ϵ,ϵ∨q)-*fuzzy*ideals ofN-groups ... These*fuzzy*ideals are characterized by their level ideals, and some other related properties are investigated. ... Definition 28 . 28 A*fuzzy*subset of is called an ( , ∨ )-*fuzzy**subgroup*of if for all , ∈ (0, 1] and for all , ∈ , ∈ , (*i*) (a) ( + ) min( , ) ∈ implies ∈*V*or ∈*V*,(b) (− ) ∈ implies ∈*V*,Algebra 5 (ii) ...##
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Correspondence Theorem For Anti L-Fuzzy Normal Subgroups

2012
*
Zenodo
*

Finally, we prove that if f : G1 -→ G2 is an epimorphism of groups, then there is a

doi:10.5281/zenodo.1061284
fatcat:gti6tcruxjeqjpshksxaurndku
*one*-to-*one*order-preserving correspondence between the anti L-*fuzzy*normal*subgroups*of G2 and those of G1 which are ... Furthermore, the group G/A of cosets of an anti L-*fuzzy*normal*subgroup*A of a group G is shown to be isomorphic to a factor group of G in a natural way. ... ;*i*∈*I*}) ∨ (∧{b j ; j ∈ J}) = ∧{a*i*∨ b j ;*i*∈*I*, j ∈ J} for any a*i*, b j ∈ L (*i*∈*I*, j ∈ J). ...##
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Algebraic Nature of Fuzzy Subgroups Under Homomorphism

2018
*
International Journal of Innovative Research in Engineering & Management
*

Algebraic Nature of

doi:10.21276/ijirem.2018.5.4.4
fatcat:qisklex6fvhnzlnietpzrbwkr4
*Fuzzy**Subgroups*Under Homomorphism ... Keywords*Fuzzy*homomorphism,*fuzzy*anti-homomorphism,*fuzzy*level*subgroups*, homomorphic image, anti homomorphic image Then g is called image of f under . ... set and pre-image of a*fuzzy*set Suppose S is a groupoid and : f S*I* is a*fuzzy*set and : S S is a mapping and : g S*I* is a*fuzzy*set defined by 1 max x y g y f x ...##
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Anti L-Fuzzy Normal M-Subgroups

2010
*
International Journal of Computer Applications
*

This paper contains some definitions and results of anti L-

doi:10.5120/1620-2178
fatcat:kv6nunw4kvhd3izxvkqzjvgnya
*fuzzy*normal M-*subgroup*is being given. Using homomorphism and anti-homomorphism, anti L-*fuzzy*normal M-*subgroups*is studied. ... Some properties of anti L-*fuzzy*normal M-*subgroups*are also established. ... Proof: Let {A*i*}*i**I*be a family of anti L-*fuzzy*normal Msubgroups of a M-group G and let A = A*i*.Then for x and y in G. ...##
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Generalized Complex Fuzzy and Anti-Fuzzy H_v-Subgroups

2018
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International Journal of Analysis and Applications
*

We investigate their properties and their relations with the generalized traditional

doi:10.28924/2291-8639-16-2018-628
fatcat:gkgcpnkbgnefndbzoypkil3yda
*fuzzy*(anti-*fuzzy*) subhypergroup (Hv-*subgroup*). ... In this paper, we introduce the concept of generalized complex*fuzzy*subhypergroup (Hvsubgroup) as well as the generalized concept of complex anti-*fuzzy*subhypergroup (Hv-*subgroup*). ... Then µ is an (∈, ∈ ∨q) complex*fuzzy*H*v*-*subgroup*of H but it is not a complex*fuzzy*H*v*-*subgroup*of H. ...##
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Fuzzy groups

1971
*
Journal of Mathematical Analysis and Applications
*

Let CL,

doi:10.1016/0022-247x(71)90199-5
fatcat:37bbp4slp5effhbtmupcyv6v2q
*v*be proper*fuzzy**subgroups*of S such that p(x) = 1 or*V*(X) = 1 for all x E S. Let u,*v*in S be such that P(U) = 1, ,u(*v*) < 1,*V*(U) < 1,*V*(*V*) = 1, and consider uw. ... A homomorphic image or preimage of a*fuzzy**subgroup*is a*fuzzy**subgroup*(in the former case, provided the sup property holds). Proof. For preimages, j&-l) =*v*(f (x-l)) =*v*(f (x)-l) 2 Q(x)) = &). ...##
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On the number of fuzzy subgroups of symmetric group S_5
[article]

2020
*
arXiv
*
pre-print

First, an equivalence relation

arXiv:1706.08419v2
fatcat:vdkbt34flfgndjsc3r2ch4gaqq
*on*the set of all*fuzzy**subgroups*of a group G is defined.Without any equivalence relation*on**fuzzy**subgroups*of group G, the number of*fuzzy**subgroups*is infinite, even ... This article computes the number of*fuzzy**subgroups*of symmetric group S_5. ... Also, two*fuzzy**subgroups*λ, γ of G and said to be distinct if λ ×*v*. λ ∼ γ iff (λ(a) > λ(b) ⇐⇒*v*(a) >*v*(b), As a result of this development, let G be a finite group and suppose that λ : G −→ [0, 1] is ...##
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Connections between fuzzy multi-groups and fuzzy multi-graphs

2021
*
Journal of Algebraic Hyperstructures and Logical Algebras
*

In this paper, we introduce the concept of

doi:10.52547/hatef.jahla.2.2.47
fatcat:23smwtsap5fqhhggl6rro6twym
*fuzzy*multigraphs and a type of isomorphism*on**fuzzy*multi-graphs and study their properties. ... We show that how to assign a*fuzzy*multi-graph to the appropriate*fuzzy*multi-groups. ... Now,(*i*) If σ is a*fuzzy**subgroup*of*V*, then σ is a*fuzzy**subgroup*of*V*. (ii) If µ*i*is a*fuzzy**subgroup*of*V*×*V*respect to h, then µ*i*is a*fuzzy**subgroup*of*V*×*V*.Proof. (*i*) Let x , y ∈*V*. ...##
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The Commutator of Two Fuzzy Subsets

2017
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Ibn AL- Haitham Journal For Pure and Applied Science
*

In this paper we introduce the idea of the commutator of two

doaj:18bb5422ab81412990d20646674f84d9
fatcat:mzgcca2mqjb6bbnmhctghvriua
*fuzzy*subsets of a group and study the concept of the commutator of two*fuzzy*subsets of a group .We introduce and study some of its properties ... W.J., (1982) "*Fuzzy*invariant*subgroups*and*fuzzy*ideals",*fuzzy*sets and systems . l.8. 133-139,. 6.Abou-Zaid. (1988)"*On*normal*fuzzy**subgroups*" , J.Facu.Edu.,.13, . 7. ... [8] , [9] A*fuzzy**subgroup*m of G is said to be normal*fuzzy**subgroup*if ( ) ( ) x* y y* x , x, y G m m = "*Î*. ...##
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Page 5503 of Mathematical Reviews Vol. , Issue 86m
[page]

1986
*
Mathematical Reviews
*

We prove that if o is a

*fuzzy*subset of S and pz is the strongest*fuzzy*relation*on*S that is a*fuzzy*relation*on*o, then pg is a*fuzzy**subgroup*if and only if a is a*fuzzy**subgroup*. ... Of particular interest is the investigation of conditions under which the*fuzzy*relation becomes a*fuzzy**subgroup**on*S x S. ...
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