Papers by Anna Radzikowska
John Wiley & Sons, Ltd eBooks, Jul 16, 2008
Fuzzy sets and rough sets address two important, and mutually orthogonal, characteristics of impe... more Fuzzy sets and rough sets address two important, and mutually orthogonal, characteristics of imperfect data and knowledge: while the former allow that objects belong to a set or relation to a given degree, the latter provide approximations of concepts in the presence of incomplete information. In this chapter, we demonstrate how these notions can be combined into a hybrid theory that is able to capture the best of different worlds. In particular, we review various alternatives for defining lower and upper approximations of a fuzzy set under a fuzzy relation, and also explore their application in query refinement. Rough set analysis makes statements about the membership of some element y of X to the concept of which A is a set of examples, based on the indistinguishability between y and
Springer eBooks, 2007
The hybridization of rough sets and fuzzy sets has focused on creating an end product that extend... more The hybridization of rough sets and fuzzy sets has focused on creating an end product that extends both contributing computing paradigms in a conservative way. As a result, the hybrid theory inherits their respective strengths, but also exhibits some weaknesses. In particular, although they allow for gradual membership, fuzzy rough sets are still abrupt in a sense that adding or omitting a single element may drastically alter the outcome of the approximations. In this paper, we revisit the hybridization process by introducing vague quantifiers like "some" or "most" into the definition of upper and lower approximation. The resulting vaguely quantified rough set (VQRS) model is closely related to Ziarko's variable precision rough set (VPRS) model.
Journal of Automation, Mobile Robotics & Intelligent Systems, Mar 23, 2017
In this paper we present an applica on of fuzzy approxima on operators in suppor ng medical diagn... more In this paper we present an applica on of fuzzy approxima on operators in suppor ng medical diagnosis. These operators are composi ons of fuzzy modal operators. The underlying idea is based on the observa on that approxima ons of fuzzy sets may be viewed as intui onis c fuzzy sets. Reasoning scheme is determined by distances between intui onis c fuzzy sets proposed by Szmidt and Kacprzyk.
Algebraic Techniques and Their Use in Describing and Processing Uncertainty, 2020
Duality via truth is a kind of correspondence between a class of algebras and a class of relation... more Duality via truth is a kind of correspondence between a class of algebras and a class of relational systems (frames, following terminology well-known in nonclassical logies). The first class is viewed as an algebraic semantics of some logic, whereas the other class constitutes Kripke-style semantics of this logic. The duality principle underlying the duality via truth States that algebras and their corresponding frames provide equivalent semantics for this logic in the sense that a formula is true with respect to one semantics if and only if it is true with respect to the other semantics. Consequently, the algebras and the frames express the equivalent notions of truth and in this sense they are viewed as dual structures. In this paper we develop duality via truth for a fuzzy modal logic. The MTL logic, introduced by Esteva and Godo, is taken as a basis. Several axiomatic extensions, motivated by well-known schemas of modal logic, are also considered.
A fuzzy generalization of information relations
Algebraic characterisations of some fuzzy information relations
Fuzzy rough sets revisited
An algebraic approach to fuzzy modalities
Lattice-based Fuzzy Information Relations and Operators
Journal of Automation, Mobile Robotics & Intelligent Systems, 2017
In this paper we present an applica on of fuzzy approxima on operators in suppor ng medical diagn... more In this paper we present an applica on of fuzzy approxima on operators in suppor ng medical diagnosis. These operators are composi ons of fuzzy modal operators. The underlying idea is based on the observa on that approxima ons of fuzzy sets may be viewed as intui onis c fuzzy sets. Reasoning scheme is determined by distances between intui onis c fuzzy sets proposed by Szmidt and Kacprzyk.
Journal of Automation, Mobile Robotics and Intelligent Systems, 2017
In this paper we present some fuzzy modal operators and show their two possible applica ons. Thes... more In this paper we present some fuzzy modal operators and show their two possible applica ons. These operators are fuzzy generaliza ons of modal operators well-known in modal logics. We present an applica on of some composi ons of these operators in approxima ons of fuzzy sets. In par cular, it is shown how skills of candidates can be matched for selec ng research projects. The underlying idea is based on the observa on that fuzzy sets approxima ons can be viewed as intui onis c fuzzy sets introduced by Atanassov. Distances between intui onis c fuzzy sets, proposed by Szmidt and Kacprzyk, support the reasoning process. Also, we point out how modal operators are useful for represen ng linguis c hedges, that is terms like "very", "definitely", "rather", or "more or less".
Relational representation theorems for some
In many applications we have a set of objects together with their properties. Since the available... more In many applications we have a set of objects together with their properties. Since the available information is often incomplete and/or imprecise, the true knowledge about subsets of objects can be determined approximately only. In this paper we present a fuzzy generalisation of two relation-based operations suitable for fuzzy set approximations. Main properties of these operations are presented. We show that under specific assumptions these operations coincide with the fuzzy rough approximation operators.
Double Residuated Lattices and Their Applications
Lecture Notes in Computer Science, 2002
Abstract. In this paper we introduce a new class of double residuated lattices. Basic properties ... more Abstract. In this paper we introduce a new class of double residuated lattices. Basic properties of these algebras are given. Taking double residuated lattices as a basis, we propose a fuzzy generalisation of information relations. We also define several fuzzy information operators ...
Knowledge Algebras and Their Discrete Duality
Intelligent Systems Reference Library, 2013
A class of knowledge algebras inspired by a logic with the knowledge operator presented in [17] i... more A class of knowledge algebras inspired by a logic with the knowledge operator presented in [17] is introduced . Knowledge algebras provide a formalization of the Hintikka knowledge operator [8] and reflect its rough set semantics. A discrete duality is proved for the class of knowledge algebras and a corresponding class of knowledge frames.
On Some Classes of Fuzzy Information Systems
Fuzzy Sets and Systems, 2008
In this paper we present the representation theorems for three classes of algebras based on resid... more In this paper we present the representation theorems for three classes of algebras based on residuated, not necessarily distributive lattices. These structures are algebras of weak fuzzy logics, which are the bottom part of the hierarchy of fuzzy logics proposed by Esteva and Godo. Our results are based on the methodology proposed by Urquhart and Allwein and Dunn. The representation algebras provide a Kripke-style semantics for the respective fuzzy logics.
Modelling linguistic modifiers using fuzzy-rough structures
Modelling Nondeterminstic Actions with Typical Effects
Discrete duality for some axiomatic extensions of MTL algebras
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Papers by Anna Radzikowska