PL
 |
EN
Preferencje help
Polish version English version Język
Widoczny [Schowaj] Abstrakt
Liczba wyników

Znaleziono wyników: 10

Liczba wyników na stronie
first rewind previous Strona / 1 next fast forward last
Wyniki wyszukiwania
Wyszukiwano:
w słowach kluczowych:  approximation operators
help Sortuj według:

help Ogranicz wyniki do:
first rewind previous Strona / 1 next fast forward last
1
Content available Fuzzy modal operators and their applications
Radzikowska A. M.
Journal of Automation Mobile Robotics and Intelligent Systems
|
2017
|
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”.
2
Content available remote On Four Types of Multi-Covering Rough Sets
Zhang X., Kong Q.
Fundamenta Informaticae
|
2016
|
Vol. 147, nr 4
457--476
EN
The generalization of Pawlak rough sets is one of the most important directions of rough set theory. In this paper, we propose four types of multi-covering rough set (MCRS) models by combining multi-granulation rough sets with covering rough sets. In the first place,We propose two types of optimistic MCRS models and study their corresponding properties, and then propose another two types of the pessimistic MCRS models and study their corresponding properties as well. Finally, the relationships among the four types of MCRS and the interrelationships between the proposed MCRS models and the existing ones listed in [8] are further investigated.
3
Content available remote Using One Axiom to Characterize Fuzzy Rough Approximation Operators Determined by a Fuzzy Implication Operator
Wu W.-Z., Li T-J., Gu S.-M.
Fundamenta Informaticae
|
2015
|
Vol. 142, nr 1-4
87--104
EN
Axiomatic characterizations of approximation operators are important in the study of rough set theory. In this paper, axiomatic characterizations of relation-based fuzzy rough approximation operators determined by a fuzzy implication operator I are investigated. We first review the constructive definitions and properties of lower and upper I-fuzzy rough approximation operators. We then propose an operator-oriented characterization of I-fuzzy rough sets. We show that the lower and upper I-fuzzy rough approximation operators generated by an arbitrary fuzzy relation can be described by single axioms. We further examine that I-fuzzy rough approximation operators corresponding to some special types of fuzzy relations, such as serial, reflexive, and T -transitive ones, can also be characterized by single axioms.
4
Content available remote Algebras of Definable and Rough Sets in Quasi Order-based Approximation Spaces
Kumar A., Banerjee M.
Fundamenta Informaticae
|
2015
|
Vol. 141, nr 1
37--55
EN
A pair of approximation operators, based on the notion of granules in generalized approximation spaces, was studied in an earlier work by the authors. In this article, we investigate algebraic structures formed by the definable sets and also by the rough sets determined by this pair of approximation operators. The definable sets are open sets of an Alexandrov topological space, and form a completely distributive lattice in which the set of completely join irreducible elements is join dense. The collection of rough sets also forms a similar structure. Representation results for such classes of completely distributive lattices as well as Heyting algebras in terms of definable and rough sets are obtained. Further, two unary operators on rough sets are considered, making the latter constitute a structure that is named a ‘rough lattice’. Representation results for rough lattices are proved.
5
Content available remote The Construction of Fuzzy Concept Lattices Based on (θ,σ)-Fuzzy Rough Approximation Operators
Yao Y., Li Z., Mi J., Xie B.
Fundamenta Informaticae
|
2011
|
Vol. 111, nr 1
33-45
EN
Formal concept analysis and rough set analysis are two complementary approaches for analyzing data. This paper studies approaches to constructing fuzzy concept lattices based on generalized fuzzy rough approximation operators. For a residual implicator θ satisfying θa, b) = *theta;(1 -b, 1 -a) and its dual σ, a pair of (θ,σ)-fuzzy rough approximation operators is defined. We then propose three kinds of fuzzy operators, and examine some of their basic properties. Thus, three complete fuzzy concept lattices can be produced, for which the properties are analogous to those of the classical concept lattices.
6
Content available remote Textures and Fuzzy Rough Sets
Diker M.
Fundamenta Informaticae
|
2011
|
Vol. 108, nr 3/4
305-336
EN
In this paper, we consider the Alexandroff topology for texture spaces. We prove that there exists a one-to-one correspondence between the Alexandroff ditopologies, and the reflexive and transitive direlations on a given texture. Using textural fuzzy direlations on a fuzzy lattice, we obtain a fuzzy rough set algebra where the inverse fuzzy relation and inverse fuzzy corelation are the upper approximation and lower approximation, respectively. In a special case, this gives us the fuzzy rough sets which are calculated with respect to the min-t norm introduced by S. Gottwald, or the fuzzy rough sets which are considered by D. Pei.
7
Content available remote On Some Mathematical Structures of T-Fuzzy Rough Set Algebras in Infinite Universes of Discourse
Wu W. Z.
Fundamenta Informaticae
|
2011
|
Vol. 108, nr 3/4
337-369
EN
In this paper, a general framework for the study of fuzzy rough approximation operators determined by a triangular norm in infinite universes of discourse is investigated. Lower and upper approximations of fuzzy sets with respect to a fuzzy approximation space in infinite universes of discourse are first introduced. Essential properties of various types of T -fuzzy rough approximation operators are then examined. An operator-oriented characterization of fuzzy rough sets is also proposed, that is, T -fuzzy rough approximation operators are defined by axioms. Different axiom sets of upper and lower fuzzy set-theoretic operators guarantee the existence of different types of fuzzy relations which produce the same operators. A comparative study of T -fuzzy rough set algebras with some other mathematical structures are presented. It is proved that there exists a one-to-one correspondence between the set of all reflexive and T -transitive fuzzy approximation spaces and the set of all fuzzy Alexandrov spaces such that the lower and upper T -fuzzy rough approximation operators are, respectively, the fuzzy interior and closure operators. It is also shown that a reflexive fuzzy approximation space induces a measurable space such that the family of definable fuzzy sets in the fuzzy approximation space forms the fuzzy -algebra of the measurable space. Finally, it is explored that the fuzzy belief functions in the Dempster-Shafer of evidence can be interpreted by the T -fuzzy rough approximation operators in the rough set theory, that is, for any fuzzy belief structure there must exist a probability fuzzy approximation space such that the derived probabilities of the lower and upper approximations of a fuzzy set are, respectively, the T -fuzzy belief and plausibility degrees of the fuzzy set in the given fuzzy belief structure.
8
Content available remote Approximation Operators, Binary Relation and Basis Algebra in L-fuzzy Rough Sets
Wu Z., Li T., Qin K., Ruan D.
Fundamenta Informaticae
|
2011
|
Vol. 111, nr 1
47-63
EN
Approximation operators play a vital role in rough set theory. Their three elements, namely, binary relation in the universe, basis algebra and properties, are fundamental in the study of approximation operators. In this paper, the interrelations among the three elements of approximation operators in L-fuzzy rough sets are discussed under the constructive approach, the axiomatic approach and the basis algebra choosing approach respectively. In the constructive approach, the properties of the approximation operators depend on the basis algebra and the binary relation. In the axiomatic approach, the induced binary relation is influenced by the axiom set and the basis algebra. In the basis algebra choosing approach, the basis algebra is constructed by properties of approximation operators and specific binary relations.
9
Content available remote Distance Measures Induced by Finite Approximation Spaces and Approximation Operators
Wolski M.
Fundamenta Informaticae
|
2008
|
Vol. 85, nr 1-4
497-512
EN
In this paper we study metric properties of finite approximation spaces and approximation operators from Rough Set Theory. In the first part of the article we examine finite approximation spaces and finite approximation topological spaces regarded as particular instances of two basic types of information structures from the framework of Information Quanta: information quantum relational systems and property systems, respectively. In the second part of the paper is the Marczewski-Steinhaus metric discussed as a certain distance of sets defined with respect to the approximation operators. We propose two types of á la Marczewski-Steinhaus distance functions: the first type is based on the lower approximation operator; the second one is based on the upper approximation operator. These types can be defined with respect to both finite approximation spaces (information quantum relational systems) and finite approximation topological spaces (property systems), giving us four distance measure functions. In order to define a distance of sets which preserves their lower and upper approximations, one can take the sum of two respective functions.
10
Content available remote The Axiomatization of the Rough Set Upper Approximation Operations
Liu G-L.
Fundamenta Informaticae
|
2006
|
Vol. 69, nr 3
331-342
EN
The theory of rough sets deals with the approximation of an arbitrary subset of a universe by two definable or observable subsets called, respectively, the lower and the upper approximation. There are at least two methods for the development of this theory, the constructive and the axiomatic approaches. The rough set axiomatic system is the foundation of rough sets theory. This paper proposes a new matrix view of the theory of rough sets, we start with a binary relation and we redefine a pair of lower and upper approximation operators using the matrix representation. Different classes of rough set algebras are obtained from different types of binary relations. Various classes of rough set algebras are characterized by different sets of axioms. Axioms of upper approximation operations guarantee the existence of certain types of binary relations(or matrices) producing the same operators. The upper approximation of the Pawlak rough sets, rough fuzzy sets and rough sets of vectors over an arbitrary fuzzy lattice are characterized by the same independent axiomatic system.
first rewind previous Strona / 1 next fast forward last
JavaScript jest wyłączony w Twojej przeglądarce internetowej. Włącz go, a następnie odśwież stronę, aby móc w pełni z niej korzystać.