A class of fuzzy multisets with a fixed number of memberships

Bedregal, Benjamín R. C.; Beliakov, Gleb; Bustince, Humberto; Calvo, Tomasa; Mesiar, Radko; Paternain, Daniel

doi:10.1016/j.ins.2011.11.040

Cited by 85 publications

(63 citation statements)

References 33 publications

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“…. , u n ), an n-dimensional fuzzy set is obtained [13], [131]. Nevertheless, it is worth to point out the relation of these families of fuzzy sets with the classification model proposed in [3], and the particular model proposed in [107], where fuzzy preference intensity was arranged according to the basic preference attitudes.…”

Section: Fuzzy Multisets and N-dimensional Fuzzy Setsmentioning

confidence: 99%

A Historical Account of Types of Fuzzy Sets and Their Relationships

Bustince

Barrenechea

Pagola

et al. 2016

IEEE Trans. Fuzzy Syst.

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413

159

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Section: Fuzzy Multisets and N-dimensional Fuzzy Setsmentioning

confidence: 99%

A Historical Account of Types of Fuzzy Sets and Their Relationships

Bustince

Barrenechea

Pagola

et al. 2016

IEEE Trans. Fuzzy Syst.

Self Cite

413

159

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show abstract

“…We also intend to consider the study correlation (with respect to automorphism, negations and t-(co)norms) of others extensions of fuzzy sets, such as typical hesitant fuzzy sets and n-dimensional fuzzy sets. 6,7,11,34 To sum up, the description of an application exemplifying the advantages of using formal constructions presented here is a future challenge.…”

Section: Resultsmentioning

confidence: 99%

“…(34a) follows from Proposition 3.3 in Ref. 6 related to n-dimensional functions, by considering in this case n = 4 once L 4 ∼ =Ũ. Analogous construction can be developed in order to prove Eq.…”

Section: Interval-valued Atanassov's Intuitionistic Automorphismsmentioning

confidence: 96%

“…Other extensions are the Hesitant Fuzzy Logic 7,11,32 and n-Dimensional Fuzzy Logic. 6,34 Historical and hierarchical analysis of these and others types of FL can be found in Bustince et al 15 The action of an automorphism on the unitary interval U = [0, 1] by preserving axiomatic definitions related to fuzzy connectives can be considered in such logical approaches. According to Bustince, Burillo and Soria, 17 the conjugate of an n-ary fuzzy connective f : U n → U , obtained by action of an automorphism on fuzzy connective (i.e., t-(co)norm, (strong) negation, (co)implication and bi(co)implication) result in another fuzzy connective f φ : U n → U , which preserve the algebraic properties of corresponding class.…”

Section: Introductionmentioning

confidence: 99%

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Correlation in Interval-Valued Atanassov’s Intuitionistic Fuzzy Sets — Conjugate and Negation Operators

Reiser

Bedregal

2017

Int. J. Unc. Fuzz. Knowl. Based Syst.

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This paper studies the conjugate functions related to main connectives of the Intervalvalued Atanassov's Intuitionistic Fuzzy Logic. The relationships among automorphism classes are formalized by the φ-representability theorem, passing from automorphisms to interval-valued intuitionistic automorphisms, also visiting other two ones, intuitionistic automorphisms and interval-valued automorphisms. Additionally, the φ-conjugate of an interval-valued Atanassov's intuitionistic fuzzy negation can be obtained either from an interval-valued fuzzy negation or from an Atanassov's intuitionistic fuzzy negation, including a discussion presenting such reverse constructions. The φ-conjugate of an interval-valued Atanassov's intuitionistic fuzzy negation not only preserves the main properties of its corresponding fuzzy negation but also of two other ones, the intuitionistic fuzzy negation and interval-valued fuzzy negation. Moreover, an extension of the intuitionistic fuzzy index as well as the correlation coefficient is discussed in terms of fuzzy negations, by considering the Atanassov's Intuitionistic Fuzzy Logic.

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“…By means of them, interval-valued fuzzy functions can be transformed into the corresponding fuzzy functions. A recent study of these operators can be found in [2] in the case of dimension two and in [3] in higher dimensions than two.…”

Section: Introductionmentioning

confidence: 99%

Information retrieval from interval-valued fuzzy automata through K operators

Lizasoain

Gómez

Moreno

2015

Proceedings of the 2015 Conference of the International Fuzzy Systems Association and the European Society for Fuzzy Logic and

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Here we study the notions of lattice-valued finite state machine and lattice-valued fuzzy transformation semigroup when the lattice consists of all the closed subintervals contained in [0,1].So, we can apply techniques of interval-valued fuzzy sets to fuzzy automata. In particular, we prove that Atanassov's K α operators allow us to retrieve the information given by the transition functions of the interval-valued automata. Moreover, we analyze the functorial nature of these operators and characterize those K α operators that provide a fuzzy transformation semigroup from an intervalvalued one.

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A class of fuzzy multisets with a fixed number of memberships

Cited by 85 publications

References 33 publications

A Historical Account of Types of Fuzzy Sets and Their Relationships

A Historical Account of Types of Fuzzy Sets and Their Relationships

Correlation in Interval-Valued Atanassov’s Intuitionistic Fuzzy Sets — Conjugate and Negation Operators

Information retrieval from interval-valued fuzzy automata through K operators

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