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Content available Fuzzy relation-based approximation techniques in supporting medical diagnosis
Radzikowska A. M.
Journal of Automation Mobile Robotics and Intelligent Systems
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2017
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Vol. 11, No. 1
21--29
EN
In this paper we present an application of fuzzy approximation operators in supporting medical diagnosis. These operators are compositions of fuzzy modal operators. The underlying idea is based on the observation that approximations of fuzzy sets may be viewed as intuitionistic fuzzy sets. Reasoning scheme is determined by distances between intuitionistic fuzzy sets proposed by Szmidt and Kacprzyk.
2
Content available Fuzzy modal operators and their applications
Radzikowska A. M.
Journal of Automation Mobile Robotics and Intelligent Systems
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2017
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Vol. 11, No. 1
10--20
EN
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”.
3
Content available remote Representation Theorems for Lattice-ordered Modal Algebras and their Axiomatic Extensions
Radzikowska A. M.
Fundamenta Informaticae
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2016
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Vol. 144, nr 2
183--203
EN
In this paper we present relational representation theorems for lattice-based modal algebras and their axiomatic extensions taking into account well-known schemas of modal logics. The underlying algebraic structures are bounded, not necessarily distributive lattices. Our approach is based on the Urquhart’s result for non-distributive lattices and Allwein and Dunn developments for algebras of liner logics.
4
Content available remote Duality via Truth for Information Algebras Based on De Morgan Lattices
Radzikowska A. M.
Fundamenta Informaticae
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2016
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Vol. 144, nr 1
45--75
EN
Duality via truth is a kind of correspondence between a class of algebras and a class of relational systems (frames). These classes are viewed as two kinds of semantics for some logic: algebraic semantics and Kripke-style semantics, respectively. Having defined the notion of truth, the duality principle states that a sequent/formula is true in one semantics if and only if it is true in the other one. In consequence, the algebras and their corresponding frames express equivalent notion of truth. In this paper we develop duality via truth between modal algebras based on De Morgan lattices and their corresponding frames. Some axiomatic extensions of these algebras are considered. Basing on these results we present duality via truth between some classes of latticebased information algebras and their corresponding frames.
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