A New Type of  Interval Valued Fuzzy Normal Subgroups of Groups

Saleem Abdullah; Muhammad Naeem

Article Details

A New Type of Interval Valued Fuzzy Normal Subgroups of Groups

Authors:

Saleem Abdullah | Muhammad Naeem

Publisher:

Biska Bilişim

Journal:

New Trends in Mathematical Sciences 2015 Vol.3 Issue 3, pp.62-77

Document Type:

Article

Publication Date:

6/2015

Document Language:

English

Document ID (Org No.):

2000830076

Frequency:

Quarterly

eISSN:

2147-5520

pISSN:

2147-5520

Abstract:

 

In this paper we are using the notions of not belonging (∈) and non quasi-k-coincidenceqk ( ) of an interval valued fuzzypoint with an interval valued fuzzy set, we define the concepts of interval valued (∈,∈ ∨ qk)-fuzzy normal subgroups and interval valued(∈,∈ ∨ qk)-fuzzy cosets which is a generalization of fuzzy normal subgroups, fuzzy coset, interval valued fuzzy normal subgroups,interval valued fuzzy coset, interval valued (∈,∈ ∨ q)-fuzzy normal subgroups and interval valued (∈,∈ ∨ q)-fuzzy cosets. We givesome characterizations of an interval valued (∈,∈ ∨ qk)-fuzzy normal subgroup and interval valued (∈,∈ ∨ qk)-fuzzy coset, and dealwith several related properties. The important achievement of the study with an interval valued (∈,∈ ∨ qk)-fuzzy normal subgroupand interval valued (∈,∈ ∨ qk)-fuzzy cosets is the generalization of that the notions of fuzzy normal subgroups, fuzzy coset, intervalvalued fuzzy normal subgroups, interval valued fuzzy coset, interval valued (∈,∈ ∨ q)-fuzzy normal subgroups and interval valued(∈,∈ ∨ q)-fuzzy cosets. We prove that the set of all interval valued (∈,∈ ∨ qk)-fuzzy cosets of G is a group, where the multiplicationis defined byλx·λy=λxyfor all x, y∈ G. Ifµ : F → D[0,1] is defined by µ←−←−(←−)λx =λ (x) for all x ∈ G. Then µ is an interval valued( )-fuzzy normal subgroup of F.

Article Details

A New Type of Interval Valued Fuzzy Normal Subgroups of Groups

Authors: Saleem Abdullah | Muhammad Naeem

Publisher: Biska Bilişim

Journal: New Trends in Mathematical Sciences 2015 Vol.3 Issue 3, pp.62-77

Document Type: Article

Publication Date: 6/2015

Document Language: English

Document ID (Org No.): 2000830076

Frequency: Quarterly

eISSN: 2147-5520

pISSN: 2147-5520

Issues

Authors:

Saleem Abdullah | Muhammad Naeem

Publisher:

Biska Bilişim

Journal:

New Trends in Mathematical Sciences 2015 Vol.3 Issue 3, pp.62-77

Document Type:

Article

Publication Date:

6/2015

Document Language:

English

Document ID (Org No.):

2000830076

Frequency:

Quarterly

eISSN:

2147-5520

pISSN:

2147-5520