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”.
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We present a framework of L-fuzzy modifiers for L being a complete lattice. They are used to model linguistic hedges that act on linguistic terms represented by L-fuzzy sets. In the modelling process the context is taken into account by means of L-fuzzy relations, endowing the L-fuzzy modifiers with a clear inherent semantics. To our knowledge, these L-fuzzy modifiers are the first ones proposed that are suitable to perform this representation task for a lattice L different from the unit interval. In the latter case they undoubtedly outperform the traditional representations, such as powering and shifting hedges, from the semantical point of view.
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