Left almost semigroups characterized by their interval valued fuzzy ideals

Yaqoob, Naveed; Chinram, Ronnason; Ghareeb, A.; Aslam, Muhammad

doi:10.1007/s13370-011-0055-5

Cited by 21 publications

(10 citation statements)

References 9 publications

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“…The study of LA-semigroups has wide applications in the locally associative LA-semigroups, abelian groups, the theory of fuzzy LA-semigroups, ternary semihypergroups,

-semihypergroups, neutrosophic LA-semigroups, soft sets and the theory of non-commutative groupoids [ 42 , 43 , 44 , 45 , 46 , 47 , 48 , 49 ]. Here, we propose a new scheme for the encryption of images based on an inverse LA-semigroup and a modified nonlinear chaotic map, which has better confusion and diffusion characteristics that are necessary for a modern substitution-permutation network.…”

Section: Introductionmentioning

confidence: 99%

A New Efficient Digital Image Encryption Based on Inverse Left Almost Semi Group and Lorenz Chaotic System

Younas

Khan

2018

Entropy

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In this research article, we propose a new structure namely inverse left almost semigroup (LA-semigroup) by adding confusion in our proposed image encryption scheme along with discrete and continuous chaotic systems in order to complement the diffusion characteristics. The performance analysis was conducted in terms of the correlation analysis, the pixels uniformity analysis, the sensitivity analysis, the information entropy analysis, and pixels difference based measurements. The results show that the proposed algorithm has better information security properties, which can provide strong security and a high performance.

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“…The study of LA-semigroups has wide applications in the locally associative LA-semigroups, abelian groups, the theory of fuzzy LA-semigroups, ternary semihypergroups,

Section: Introductionmentioning

confidence: 99%

A New Efficient Digital Image Encryption Based on Inverse Left Almost Semi Group and Lorenz Chaotic System

Younas

Khan

2018

Entropy

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“…They proved that for a locally associative Γ -LA-semigroup S with a left identity, S/ρ is a maximal weakly separative homomorphic image of S, where ρ is a relation on S defined by: aρb if and only if aγ b n = b n+1 and bγ a n = a n+1 for some positive integer n and for all γ ∈ Γ , where a, b ∈ S. In 2014, Abdullah et al [3] introduced the concept of interval-valued (∈, ∈ ∨q)-fuzzy ideals, interval-valued (∈, ∈ ∨q)-fuzzy bi-ideals and interval-valued (∈, ∈ ∨q)-fuzzy quasi-ideals of an LA-semigroup. Nowadays many scholars have studied different aspects of fuzzy subsets on LA-semigroups and Γ -LA-semigroups see [9,11,12,15,20,30,31,36,38,41,45,50]. In 2015, Abbasi and Basar [1] studied quasi-ideals and bi-ideals of locally associative Γ -LA-semigroups, (m, n) simple Γ -LA-semigroups, minimal bi-Γ -ideal, semiprime Γ -ideal and quasi-regular Γ -LA-semigroups.…”

Section: Introductionmentioning

confidence: 99%

On generalizations of quasi-prime ideals of an ordered left almost semigroups

Yiarayong

2021

Afr. Mat.

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The purposes of this paper are to introduce generalizations of quasi-prime ideals to the context of $$\phi $$ ϕ -quasi-prime ideals. Let $$\phi : {\mathcal {I}}(S) \rightarrow {\mathcal {I}}(S) \cup \left\{ \emptyset \right\} $$ ϕ : I ( S ) → I ( S ) ∪ ∅ be a function where $$ {\mathcal {I}}(S)$$ I ( S ) is the set of all left ideals of an ordered $${{\mathcal {L}}}{{\mathcal {A}}}$$ L A -semigroup S. A proper left ideal A of an ordered $${{\mathcal {L}}}{{\mathcal {A}}}$$ L A -semigroup S is called a $$\phi $$ ϕ -quasi-prime ideal, if for each $$a, b\in S$$ a , b ∈ S with $$ab \in A - \phi (A)$$ a b ∈ A - ϕ ( A ) , then $$a \in A$$ a ∈ A or $$b\in A$$ b ∈ A . Some characterizations of quasi-prime and $$\phi $$ ϕ -quasi-prime ideals are obtained. Moreover, we investigate relationships between weakly quasi-prime, almost quasi-prime, $$\omega $$ ω -quasi-prime, m-quasi-prime and $$\phi $$ ϕ -quasi-prime ideals of ordered $${{\mathcal {L}}}{{\mathcal {A}}}$$ L A -semigroups. Finally, we obtain necessary and sufficient conditions of $$\phi $$ ϕ -quasi-prime ideal in order to be a quasi-prime ideal.

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“…Yaqoob et al [42] studied intuitionistic fuzzy soft sets and groups. Yaqoob et al [43] introduced interval valued fuzzy L A-subsemigroups and ideals in L A-semigroups. Akram et al [4] initiated the study of interval valued (θ, δ)-fuzzy KU-ideals of KU-algebras.…”

Section: Introductionmentioning

confidence: 99%

Interval valued L-fuzzy cosets of nearrings and isomorphism theorems

2015

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In this paper, we study homomorphic images of interval valued L-fuzzy ideals of a nearring. If f : N 1 → N 2 is an onto nearring homomorphism andμ is an interval valued L-fuzzy ideal of N 2 then we prove that f −1 (μ) is an interval valued L-fuzzy ideal of N 1 . If μ is an interval valued L-fuzzy ideal of N 1 then we show that f (μ) is an interval valued Lfuzzy ideal of N 2 wheneverμ is invariant under f and interval valued t-norm is idempotent. Finally, we define interval valued L-fuzzy cosets and prove isomorphism theorems.

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Left almost semigroups characterized by their interval valued fuzzy ideals

Cited by 21 publications

References 9 publications

A New Efficient Digital Image Encryption Based on Inverse Left Almost Semi Group and Lorenz Chaotic System

A New Efficient Digital Image Encryption Based on Inverse Left Almost Semi Group and Lorenz Chaotic System

On generalizations of quasi-prime ideals of an ordered left almost semigroups

Interval valued L-fuzzy cosets of nearrings and isomorphism theorems

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