Anti Q-Fuzzy Hx Group and Its Lower Level Sub Hx Groups

2019

In this research, we introduce a hyper Q-fuzzy HX subgroup of a HX group ν notion also we discuss a few of its properties. Also we define a hyper Qfuzzy normal HX subgroup, normal level subgroup HX of hyper Q-fuzzy normal HX subgroup of a HX group also self conjugate and we discussed some of their important properties.

International journal of physical sciences

In this paper, we define the concept of an intuitionistic Q-fuzzy normal HX group and some related properties are investigated. We also define the level subsets of an intuitionistic Q-fuzzy normal HX group and discussed some of its properties. A few equivalent propositions of fuzzy HX group constituting an intuitionistic Q-fuzzy normal HX group are given. Keywords: Intuitionistic fuzzy set, intuitionistic Q-fuzzy set, intuitionistic fuzzy subgroup , intuitionistic Q-fuzzy subgroup, intuitionistic Q-fuzzy HX subgroup and level sub HX groups, intuitionistic normal Q-fuzzy HX subgroup.

In this paper, we define the concept of pseudo fuzzy cosets of a fuzzy HX subgroup of a HX group and pseudo fuzzy cosets of an anti fuzzy HX subgroup of a HX group with suitable examples. Also We discussed some of their properties.

Applied Mathematical Sciences, 2013

In this paper, we define the concept of pseudo fuzzy cosets of a fuzzy HX subgroup of a HX group and pseudo fuzzy cosets of an anti fuzzy HX subgroup of a HX group with suitable examples. Also We discussed some of their properties.

Annals of Pure and Applied Mathematics, 2017

In this paper, we discussed some properties of bipolar anti L-fuzzy sub ℓ-HX group of aℓ-HX group. The purpose of this study is to implement the fuzzy set theory and graph theory in bipolar anti L-fuzzy sub ℓ-HX group. Characterizations of lower level subsets of a bipolar anti L-fuzzy sub ℓ-HX group are given. We also discussed the relation between a bipolar anti L-fuzzy sub ℓ-HX group and its lower level subℓ-HX groups and investigate the conditions under which a given sub ℓ-HX group has a properly inclusive chain of sub ℓ-HX groups. In particular, we formulate how to structure a bipolar anti L-fuzzy sub ℓ-HX group by a given chain of sub ℓ-HX groups. We also establish the relation between bipolar L-fuzzy sub ℓ-HX group and bipolar anti L-fuzzy sub ℓ-HX group.

2017

In this paper, the notion of the normal level sub HX group is introduced. We discuss the properties of normal level sub HX groups of a bipolar fuzzy normal HX subgroup of a HX group under homomorphism and anti-homomorphism. AMS Subject Classification (2000): 20N25, 03E72, 03F055, 06F35, 03G25. Keywordsfuzzy set, bipolar fuzzy set, bipolar fuzzy HX subgroup, bipolar fuzzy normal HX subgroup, level sub HX group, normal level sub HX group

International Journal of Algebra and Statistics, 2016

More general form of "quasi-coincident with" relation (q) is introduced, and related properties are investigated. The notions of (∈, ∈ ∨ q δ 0)-fuzzy subgroups, q δ 0-level sets and ∈ ∨ q δ 0-level sets are introduced, and related results are investigated. Relations between an (∈, ∈)-fuzzy subgroup and an (∈, ∈ ∨ q δ 0)-fuzzy subgroup are discussed, and characterizations of (∈, ∈ ∨ q δ 0)-fuzzy subgroups are displayed by using level sets and ∈ ∨ q δ 0-level sets. The concepts of ∈ ∨ q δ 0-admissible fuzzy sets, admissible (∈, ∈ ∨ q δ 0)-fuzzy subgroups and δ-characteristic fuzzy sets are introduced. Using these notions, characterizations of admissible (∈, ∈ ∨ q δ 0)-fuzzy subgroups and admissible subgroups are considered. 2010 Mathematics Subject Classification. 20N25, 03E72. Keywords. (∈, ∈ ∨ q δ 0)-fuzzy subgroup, q δ 0-level set, ∈ ∨ q δ 0-admissible fuzzy set.

Journal of Mathematical and Computational Science, 2016

In this paper, we introduce some definitions and results of L – fuzzy M – cosets of M – HX groups. Some properties of L – fuzzy M – cosets and its types are also established.

arXiv: General Mathematics, 2019

the notation of intuitionistic Q-fuzzy semi-prime ideal in a semigroup. Solairaju and Nagarajan, in 2009, defined the notation of Q-fuzzy subgroup. Further, in 2013, Sharma [4] introduced new algebraic structure of α-fuzzy subgroup. Palaniappan and Muthuraj, in 2004, proved many results in homomorphism and anti-homomorphism in fuzzy subgroups. The purpose of this work is to define notations of α-Qfuzzy subset and α-Q-fuzzy subgroup, and we prove some elementary algebraic properties related to these two notations. Furthermore, the concept of anti-homomorphism in α-Q-fuzzy subgroup between two groups is defined and some properties related to an α-Q-fuzzy abelian and cyclic α-Q-fuzzy subgroups are studied. 2. PRELIMINARY Definition 2.1. Zadeh (1965)-Let X be a non-empty set. A fuzzy subset θ of the set X is a mapping θ: X→[0, 1]. Definition 2.2. Rosenfeld (1971)-Let (G, *) be a group. A fuzzy subset θ of G said to be a fuzzy subgroup of G, if the following conditions hold: i. θ(xy) ≥ min {θ(x), θ(y)} and ii. θ(x −1) ≥ θ(x), for all x and y in G. Definition 2.3. Solairaju and Nagarajan (2006)-Let X and Q be non-empty sets. A Q-fuzzy subset θ of the set X is a mapping. i. θ: X×Q→[0, 1]. Definition 2.4. Solairaju and Nagarajan (2006)-Let (G, *) be a group and Q be a non-empty set. A Q-fuzzy subset θ of G is said to be a Q-fuzzy subgroup of G if the following conditions are satisfied: i. θ(xy, q) ≥ min {θ(x, q), θ(y, q)} and ii. θ(x −1 , q) ≥ θ(x, q), for all x and y in G and q in Q. Proposition 2.5. Solairaju and Nagarajan (2006)-Let θ and σ be any two Q-fuzzy subsets of a non-empty set X. Then, for all x∈X and q∈Q, the followings are true: i. θ⊆σ ⇔ θ(x, q) ≤ σ(x, q), ii. θ=σ ⇔ θ(x, q) = σ(x, q), iii. (θ∪σ)(x, q) = max {θ(x, q), σ(x, q)}, iv. (θ∩σ)(x, q) = min {θ(x, q), σ(x, q)}. Definition 2.6. Solairaju and Nagarajan (2006)-If θ is a Q-fuzzy subgroup of a group G, then C[θ] is the complement of Q-fuzzy subgroup θ, and is defined by C[θ(x, q)] = 1-θ (x, q), for all x in G and q in Q. Definition 2.7. Palaniappan and Muthuraj (2004)-If (G, *) and (G′,ο) are any two groups, then the function f: G→G′ is called a homomorphism if f (x * y) = f(x) ο f(y), for all x and y in G. Definition 2.8. Palaniappan and Muthuraj (2004) If (G, *) and (G′,ο) are any two groups, then the function f: G→G′ is called an anti-homomorphism if f(x*y) = f(y) ο f(x), for all x and y in G. Definition 2.9. Palaniappan and Muthuraj (2004) Let f: X→X′ be any mapping from a non-empty set X into a non

The definition of a fuzzy HX group and define a new bialgebraic structure of fuzzy sub-bi HX group of a bi-hx group and some related properties are investigated and redefined in this paper.