E-fuzzy groups

Budimirović, Branka; Budimirović, Vjekoslav; Šešelja, Branimir; Tepavčević, Andreja

doi:10.1016/j.fss.2015.03.011

Cited by 10 publications

(17 citation statements)

References 20 publications

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“…These have been proved in [6], in the framework of groups. E(x, x) for all x ∈ A), is an Ω-valued subalgebra of A.…”

Section: B ω-Algebra; Identitiesmentioning

confidence: 89%

“…The proof goes easily by induction on the complexity of terms ( [6]). Proposition 1: Let μ : A → Ω be an Ω-valued subalgebra of an algebra A and let t(x 1 , .…”

Section: B ω-Valued Functions and Relationsmentioning

confidence: 99%

“…An Ω-set is a pair (A, E), where A is a nonempty set, and E is a symmetric and transitive Ω-valued relation on A, fulfilling the strong separation property (6).…”

Section: B ω-Valued Functions and Relationsmentioning

confidence: 99%

“…Identities for lattice-valued structures with fuzzy equality were introduced in [20], and then developed in [3], [4], [5], [6]. In this framework, an identity holds if the corresponding lattice-theoretic formula is fulfilled.…”

Section: Introductionmentioning

confidence: 99%

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Omega-Algebras

eelja

Tepavčević

2015

2015 IEEE Symposium Series on Computational Intelligence

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In the framework of Ω-sets, where Ω is a complete lattice, we generalize the notion of a (universal) algebra, and we investigate its basic properties. Our techniques belong to the theory of lattice-valued (fuzzy) structures and we use cut-sets.An Ω-algebra is equipped with an Ω-valued equality instead of the classical one. We investigate identities and their satisfiability by these new structures. We prove that a set of identities holds on an Ω-algebra if and only if the cut-subalgebras over the corresponding cut-congruences of the Ω-valued equality satisfy the same identities in the classical setting.

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“…These have been proved in [6], in the framework of groups. E(x, x) for all x ∈ A), is an Ω-valued subalgebra of A.…”

Section: B ω-Algebra; Identitiesmentioning

confidence: 89%

“…The proof goes easily by induction on the complexity of terms ( [6]). Proposition 1: Let μ : A → Ω be an Ω-valued subalgebra of an algebra A and let t(x 1 , .…”

Section: B ω-Valued Functions and Relationsmentioning

confidence: 99%

“…An Ω-set is a pair (A, E), where A is a nonempty set, and E is a symmetric and transitive Ω-valued relation on A, fulfilling the strong separation property (6).…”

Section: B ω-Valued Functions and Relationsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Omega-Algebras

eelja

Tepavčević

2015

2015 IEEE Symposium Series on Computational Intelligence

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show abstract

“…either identity holds or it does not hold). This notion was firstly introduced in [16], and then developed in [1]. Basic properties of Ω-algebras and representation theorems for Ω-algebras in general are proved in [12].…”

Section: Introductionmentioning

confidence: 99%