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Fuzzy modal operators and their applications

Radzikowska A. M.

Journal of Automation Mobile Robotics and Intelligent Systems

2017

Vol. 11, No. 1

10--20

In this paper we present some fuzzy modal operators and show their two possible applications. These operators are fuzzy generalizations of modal operators well-known in modal logics. We present an application of some compositions of these operators in approximations of fuzzy sets. In particular, it is shown how skills of candidates can be matched for selecting research projects. The underlying idea is based on the observation that fuzzy sets approximations can be viewed as intuitionistic fuzzy sets introduced by Atanassov. Distances between intuitionistic fuzzy sets, proposed by Szmidt and Kacprzyk, support the reasoning process. Also, we point out how modal operators are useful for representing linguistic hedges, that is terms like “very”, “definitely”, “rather”, or “more or less”.

Hilbert algebras with a necessity modal operator

Celani S.A., Montangie D.

Reports on Mathematical Logic

2014

Vol. 49

47--77

We introduce the variety of Hilbert algebras with a modal operator , called H-algebras. The variety of H-algebras is the algebraic counterpart of the {→;]}fragment of the intuitionitic modal logic IntK. We will study the theory of representation and we will give a topological duality for the variety of H-algebras. We are going to use these results to prove that the basic implicative modal logic IntK→ and some axiomatic extensions are canonical. We shall also to determine the simple and subdirectly irreducible algebras in some subvarieties of H-algebras.

Discrete Dualities for Heyting Algebras with Operators

Orłowska E., Rewitzky I.

Fundamenta Informaticae

2007

Vol. 81, nr 1-3

275-295

Discrete dualities are presented for Heyting algebras with various modal operators, for Heyting algebras with an external negation, for symmetric Heyting algebras, and for Heyting-Brouwer algebras.