Permutable indistinguishability operators, perfect vague groups and fuzzy subgroups

Recasens, J.

doi:10.1016/j.ins.2012.02.005

Cited by 10 publications

(3 citation statements)

References 17 publications

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“…Then T is generated by the pair (µ, ν). Indeed, for all x, y ∈ [0, 1], The results of this section are adapted from [16] where normality of the fuzzy subsets was assumed and they provide an important application of local indistinguishability operators to fuzzy algebraic structures. T (E (µ) (x, y), E µ (y, z)) = T (µ(x • y −1 ), µ(y…”

Section: T-normsmentioning

confidence: 99%

On the representation of local indistinguishability operators

Calvo

Recasens

2021

Fuzzy Sets and Systems

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Section: T-normsmentioning

confidence: 99%

On the representation of local indistinguishability operators

Calvo

Recasens

2021

Fuzzy Sets and Systems

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“…It was proved in [28] that two fuzzy * -indistinguishability relations defined on a finite set X permute if and only if E • F is an * -indistinguishability relation. In this case, E • F = max (E, F ).…”

Section: Permutability Of Fuzzy Preoders and Fuzzy Indistinguishabilimentioning

confidence: 99%

Permutable fuzzy consequence and interior operators and their connection with fuzzy relations

Carmona

Elorza

Recasens

et al. 2015

Information Sciences

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Fuzzy operators are an essential tool in many fields and the operation of composition is often needed. In general, composition is not a commutative operation. However, it is very useful to have operators for which the order of composition does not affect the result. In this paper, we analyze when permutability appears. That is, when the order of application of the operators does not change the outcome. We characterize permutability in the case of the composition of fuzzy consequence operators and the dual case of fuzzy interior operators. We prove that for these cases, permutability is completely connected to the preservation of the operator type.We also study the particular case of fuzzy operators induced by fuzzy relations through Zadeh's compositional rule and the inf-→ composition. For this cases, we connect permutability of the fuzzy relations (using the sup- * composition) with permutability of the induced operators. Special attention is paid to the cases of operators induced by fuzzy preorders and similarities. Finally, we use these results to relate the operator induced by the transitive closure of the composition of two reflexive fuzzy relations with the closure of the operator this composition induces.

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“…13 [12]. If E µ and ν E are the right and left invariant indistinguishability operators associated to two fuzzy subgroups µ and ν of a group (G, •) respectively, then they commute.…”

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confidence: 99%

On the relationship between fuzzy subgroups and indistinguishability operators

Boixader

Recasens

2019

Fuzzy Sets and Systems

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Fuzzy subgroups are revisited considering their close relationship with indistinguishability operators (fuzzy equivalences) invariant under translations. Different ways to obtain new fuzzy subgroups from a given one are provided and different ways to characterize normal fuzzy subgroups are obtained. The idea of double coset of two (crisp) subgroups allow us to relate them via their equivalence classes. This is generalized to the fuzzy framework. The conditions in which a fuzzy relation R on a group G can be considered a fuzzy subgroup of G × G are obtained.

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Permutable indistinguishability operators, perfect vague groups and fuzzy subgroups

Cited by 10 publications

References 17 publications

On the representation of local indistinguishability operators

On the representation of local indistinguishability operators

Permutable fuzzy consequence and interior operators and their connection with fuzzy relations

On the relationship between fuzzy subgroups and indistinguishability operators

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