Modal MTL-algebras

Morton, Wilmari; Alten, C. J. Van

doi:10.1016/j.fss.2012.11.008

Cited by 3 publications

(2 citation statements)

References 20 publications

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“…One may wonder about the relation of these operators to those in other systems of fuzzy modal logic (e.g [MvA13]). These approaches usually deal only with algebras where the whole carrier set coincides with the interval [0, 1].…”

Section: Modal Operatorsmentioning

confidence: 99%

Fuzzifying Modal Algebra

Desharnais

Möller

2014

Relational and Algebraic Methods in Computer Science

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Fuzzy relations are mappings from pairs of elements into the interval [0, 1]. As a replacement for the complement operation one can use the mapping that sends x to 1 − x. Together with the concepts of t-norm and t-conorm a weak form of Boolean algebra can be defined. However, to our knowledge so far no notion of domain or codomain has been investigated for fuzzy relations. These might, however, be useful, since fuzzy relations can, e.g., be used to model flow problems and many other things. We give a new axiomatisation of two variants of domain and codomain in the more general setting of idempotent left semirings that avoids complementation and hence is applicable to fuzzy relations. Some applications are sketched as well.

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Section: Modal Operatorsmentioning

confidence: 99%

Fuzzifying Modal Algebra

Desharnais

Möller

2014

Relational and Algebraic Methods in Computer Science

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“…Modal operators on Heyting algebras were firstly introduced by Macnab in [8] as an algebraic counterpart of intuitionistic propositional logics. Since then, the properties of modal operators were considered on other algebraic structures such as MV-algebras [5], MTL-algebras [10], bounded commutative residuated Rℓmonoids [13], bounded commutative residuated lattices [6], equality algebras [14] and so on.…”

Section: Introductionmentioning

confidence: 99%

EQ-algebras with Modal Operators

Gao

Cheng

2023

Preprint

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The main goal of this paper is to investigate modal operators on EQ-algebras. To begin with, we introduce the concept of modal EQ-algebras, that is, EQ-algebras equipped with modal operators. Moreover, we study some basic properties of modal EQ-algebras, and we obtain that modal operators are closure operators on EQ-algebras and vice verse. Furthermore, we introduce modal filters(prefilters) and modal congruences of modal EQ-algebras. We show that there is a one-to-one correspondence between modal filters and modal congruences on good modal EQalgebras. Finally, we give a characterization for minimal modal prime prefilters and characterize the representable good modal EQ-algebras via minimal modal prime prefilters.

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WMV-Algebra and Its Wajsberg's form

Liang

Zhao

2015

2015 10th International Conference on Intelligent Systems and Knowledge Engineering (ISKE)

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Modal MTL-algebras

Cited by 3 publications

References 20 publications

Fuzzifying Modal Algebra

Fuzzifying Modal Algebra

EQ-algebras with Modal Operators

WMV-Algebra and Its Wajsberg's form

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