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Multigranulation rough set is a new and interesting topic in the theory of rough set. In this paper, the multigranulation rough sets approach is introduced into the incomplete information system. The tolerance relation, the simila...
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Multigranulation rough set is a new and interesting topic in the theory of rough set. In this paper, the multigranulation rough sets approach is introduced into the incomplete information system. The tolerance relation, the similarity relation and the limited tolerance relations are employed to construct the optimistic and the pessimistic multigranulation rough sets, respectively. Not only the properties about these multigranulation rough sets are discussed, but also the relationships among these multigranulation rough sets models are explored. It is shown that by the multigranulation rough sets theory, the limited tolerance relations based multigranulation lower approximations fall between the tolerance and the similarity relations based multigranulation lower approximations, the limited tolerance relations based multigranulation upper approximations fall between the similarity and the tolerance relations based multigranulation upper approximations. Such results are consistent to those in single-granulation based rough sets models.
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In this paper, cluster analysis based on fuzzy relations is investigated. Tamura's max-min n-step procedure is extended to all types of max-t compositions. A max-t similarity-relation matrix is obtained by beginning with a proximi...
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In this paper, cluster analysis based on fuzzy relations is investigated. Tamura's max-min n-step procedure is extended to all types of max-t compositions. A max-t similarity-relation matrix is obtained by beginning with a proximity-relation matrix based on the proposed max-t n-step procedure. Then a clustering algorithm is created for the max-t similarity- relation matrix. Three critical max-t compositions of max-min, max-prod and max-Δ are compared. The max-Δ compo- sition is recommended as the first choice among them. Several examples give more perspectives for different choices of max-t compositions. Finally, the topic of incomplete data via max-t compositions is discussed. Max-t compositions can be effectively used to treat the t-connected incomplete data.
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In a recent paper, De Baets et al. have characterized the fuzzy tolerance and fuzzy equivalence relations that a given strict order relation is compatible with. In this paper, we generalize this characterization by considering an ...
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In a recent paper, De Baets et al. have characterized the fuzzy tolerance and fuzzy equivalence relations that a given strict order relation is compatible with. In this paper, we generalize this characterization by considering an arbitrary (crisp) relation instead of a strict order relation, while paying attention to the particular cases of a reflexive or irreflexive relation. The reasoning largely draws upon the notion of the clone relation of a (crisp) relation, introduced recently by Bouremel et al., and the partition of this clone relation in terms of three different types of pairs of clones. More specifically, reflexive related clones and irreflexive unrelated clones turn out to play a key role in the characterization of the fuzzy tolerance and fuzzy equivalence relations that a given (crisp) relation is compatible with.
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We show that although there exists no non-trivial (fuzzy) tolerance relation a partial order relation is compatible with (in the sense of Bclohlavck), the situation is quite different when considering its strict part. More specifi...
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We show that although there exists no non-trivial (fuzzy) tolerance relation a partial order relation is compatible with (in the sense of Bclohlavck), the situation is quite different when considering its strict part. More specifically, we provide a representation of all fuzzy tolerance (and, in particular, all fuzzy equivalence) relations a strict order relation is compatible with. To that end, we introduce the notion of clone relation associated with a partially ordered set and discuss its basic properties. The mentioned representation is intimately connected with this clone relation. (C) 2015 Elsevier B.V. All rights reserved.
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In a recent paper, De Baets et al. introduced the clone relation of a strict order relation. Two elements of a poset are said to be a pair of clones (or to be clones) if every other element that is greater (resp. smaller) than one...
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In a recent paper, De Baets et al. introduced the clone relation of a strict order relation. Two elements of a poset are said to be a pair of clones (or to be clones) if every other element that is greater (resp. smaller) than one of them is also greater (resp. smaller) than the other one. This clone relation played a key role in the characterization of the L-fuzzy tolerance relations and the L-fuzzy equivalence relations that a strict order relation is compatible with. In this paper, we extend the notion of clone relation to any binary relation. Although the definition of such extension is trivial, the corresponding properties significantly differ from those of the clone relation of a strict order relation. We analyse the most important ones among these properties, paying particular attention to a partition of the clone relation in terms of three different types of pairs of clones. (C) 2016 Elsevier Inc. All rights reserved.
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Rough set models based on the tolerance and similarity relations, have been widely used to deal with incomplete information systems. However, tolerance and similarity relations have their own limitations because the former is too ...
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Rough set models based on the tolerance and similarity relations, have been widely used to deal with incomplete information systems. However, tolerance and similarity relations have their own limitations because the former is too loose while the latter is too strict in classification analysis. To make a reasonable and flexible classification in incomplete information system, a new binary relation is proposed in this paper'. Such binary relation is only reflexive and it is a generalisation of tolerance and similarity relations. Furthermore, rough set models based on the above three different binary relations are compared. Finally, the direct approach to rules induction is investigated by using the proposed rough set, some illustrative examples are analysed to substantiate the conceptual arguments.
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The paper studies tolerance relations from the point of view of fuzzy logic and fuzzy set theory. Particularly, we focus on the study of natural groupings induced by a fuzzy tolerance, relations induced by fuzzy tolerances, repres...
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The paper studies tolerance relations from the point of view of fuzzy logic and fuzzy set theory. Particularly, we focus on the study of natural groupings induced by a fuzzy tolerance, relations induced by fuzzy tolerances, representational issues, and an algorithm for generating all fuzzy tolerance classes.
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While a large body of social psychological research has shed light on the nature of prejudice and how to reduce it, we argue that such work does not address situations of cultural or religious outgroup beliefs and practices that a...
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While a large body of social psychological research has shed light on the nature of prejudice and how to reduce it, we argue that such work does not address situations of cultural or religious outgroup beliefs and practices that are considered incompatible with one's own. The present theoretical article contrasts a prejudice-reduction approach with a toleration-based approach to consider the differences each have with regard to the attitude object they focus upon, the perceived reasonableness of the attitude, and the behavioral consequences each may lead to. In doing so, we consider the psychological processes involved in whether the negative attitude leads to negative actions. We conclude by arguing that a toleration-based approach forms an important addition to the psychological thinking about cultural diversity and intergroup relations. Collectively, the present work makes a novel contribution to the social psychological literature by stimulating theory development and raising novel questions for empirical research.
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Rough set approach for knowledge discovery in incomplete information systems has been extensively studied. This paper conduct a further study of valued tolerance relation based rough approximations. We make an analysis of the exis...
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Rough set approach for knowledge discovery in incomplete information systems has been extensively studied. This paper conduct a further study of valued tolerance relation based rough approximations. We make an analysis of the existing rough approximabilities and propose a new approach for lower (upper) approximability, which is a generalization of Pawlak approximation operators for complete information system. The approach has also been generalized to fuzzy cases. Some basic properties of the approximation operators are examined.
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There are well-known isomorphisms between the complete lattice of all partitions of a given set A and the lattice of all equivalence relations on A. In the paper the notion of partition is generalized in order to work correctly fo...
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There are well-known isomorphisms between the complete lattice of all partitions of a given set A and the lattice of all equivalence relations on A. In the paper the notion of partition is generalized in order to work correctly for wider classes of binary relations than equivalence ones such as quasiorders or tolerance relations. Some others classes of binary relations and corresponding counterparts of partitions are considered.
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