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### A note on fuzzy subgroups and fuzzy homomorphism

F.P. Choudhury, A.B. Chakraborty, S.S. Khare
1988 Journal of Mathematical Analysis and Applications
of a 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.  ...

### The Intuitionistic Fuzzy Normal Subgroup

Mohammed F. Marashdeh, Abdul Razak Salleh
2010 International Journal of Fuzzy Logic and Intelligent Systems
In this paper we continue the study of intuitionistic 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  ...

### Algebraic Structure Of Union Of Fuzzy Subgroups And Fuzzy Sub-Bigroups

N. Duraimanickam, N. Deepica
2017 Zenodo
In this Paper, we discuss the definitions of union of 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.  ...

### MEASURES OF FUZZY SUBGROUPS

Shu Rui Shi
2010 Proyecciones
A 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.  ...

### On Fuzzy Internal Direct Product

N. M. Nama
2017 Ibn AL- Haitham Journal For Pure and Applied Science
The main aim of this paper is to introduce the concept of a 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  ...

### A Study on Fuzzy Ideals ofN-Groups

B. Davvaz, O. Ratnabala Devi
2013 Algebra
Using the idea of the new sort of 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)  ...

### Correspondence Theorem For Anti L-Fuzzy Normal Subgroups

Jian Tang, Yunfei Yao
2012 Zenodo
Finally, we prove that if f : G1 -→ G2 is an epimorphism of groups, then there is a 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.  ...  ; iI}) ∨ (∧{b j ; j ∈ J}) = ∧{a i ∨ b j ; iI, j ∈ J} for any a i , b j ∈ L (iI, j ∈ J).  ...

### Algebraic Nature of Fuzzy Subgroups Under Homomorphism

2018 International Journal of Innovative Research in Engineering & Management
Algebraic Nature of 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     ...

### Anti L-Fuzzy Normal M-Subgroups

P. Pandiammal, R. Natarajan, N. Palaniappan
2010 International Journal of Computer Applications
This paper contains some definitions and results of anti L-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.  ...

### Generalized Complex Fuzzy and Anti-Fuzzy H_v-Subgroups

2018 International Journal of Analysis and Applications
We investigate their properties and their relations with the generalized traditional 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.  ...

### Fuzzy groups

Azriel Rosenfeld
1971 Journal of Mathematical Analysis and Applications
Let CL, 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)) = &).  ...

### On the number of fuzzy subgroups of symmetric group S_5 [article]

M.E. Ogiugo, M. EniOluwafe
2020 arXiv   pre-print
First, an equivalence relation 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  ...

### Connections between fuzzy multi-groups and fuzzy multi-graphs

Saeed Mirvakili, Hossein Naraghi, Maryam Shirvani
2021 Journal of Algebraic Hyperstructures and Logical Algebras
In this paper, we introduce the concept of 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 .  ...

### The Commutator of Two Fuzzy Subsets

L. N. M. Tawfiq, R. H. Shihab
2017 Ibn AL- Haitham Journal For Pure and Applied Science
In this paper we introduce the idea of the commutator of two 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.  ...   ,  A fuzzy subgroup m of G is said to be normal fuzzy subgroup if ( ) ( ) x* y y* x , x, y G m m = " Î .  ...

### 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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