Results 11  20
of
1,321
Current Approaches to Handling Imperfect Information in Data and Knowledge Bases
, 1996
"... This paper surveys methods for representing and reasoning with imperfect information. It opens with an attempt to classify the different types of imperfection that may pervade data, and a discussion of the sources of such imperfections. The classification is then used as a framework for considering ..."
Abstract

Cited by 70 (1 self)
 Add to MetaCart
(Show Context)
This paper surveys methods for representing and reasoning with imperfect information. It opens with an attempt to classify the different types of imperfection that may pervade data, and a discussion of the sources of such imperfections. The classification is then used as a framework for considering work that explicitly concerns the representation of imperfect information, and related work on how imperfect information may be used as a basis for reasoning. The work that is surveyed is drawn from both the field of databases and the field of artificial intelligence. Both of these areas have long been concerned with the problems caused by imperfect information, and this paper stresses the relationships between the approaches developed in each.
Two views of the theory of rough sets in finite universes
 International Journal of Approximate Reasoning
, 1996
"... This paper presents and compares two views of the theory of rough sets. The operatororiented view interprets rough set theory as an extension of set theory with two additional unary operators. Under such a view, lower and upper approximations are related to the interior and closure operators in top ..."
Abstract

Cited by 67 (20 self)
 Add to MetaCart
(Show Context)
This paper presents and compares two views of the theory of rough sets. The operatororiented view interprets rough set theory as an extension of set theory with two additional unary operators. Under such a view, lower and upper approximations are related to the interior and closure operators in topological spaces, the necessity and possibility operators in modal logic, and lower and upper approximations in interval structures. The setoriented view focuses on the interpretation and characterization of members of rough sets. Iwinski type rough sets are formed by pairs of definable (composed) sets, which are related to the notion of interval sets. Pawlak type rough sets are defined based on equivalence classes of an equivalence relation on the power set. The relation is defined by the lower and upper approximations. In both cases, rough sets may be interpreted, or related to, families of subsets of the universe, i.e., elements of a rough set are subsets of the universe. Alternatively, rough sets may be interpreted using elements of the universe based on the notion of rough membership functions. Both operatororiented and setoriented views are useful in the understanding and application of the theory of rough sets.
A Review of Rough Set Models
, 1997
"... Since introduction of the theory of rough set in early eighties, considerable work has been done on the development and application of this new theory. The paper provides a review of the Pawlak rough set model and its extensions, with emphasis on the formulation, characterization, and interpretation ..."
Abstract

Cited by 66 (19 self)
 Add to MetaCart
Since introduction of the theory of rough set in early eighties, considerable work has been done on the development and application of this new theory. The paper provides a review of the Pawlak rough set model and its extensions, with emphasis on the formulation, characterization, and interpretation of various rough set models. 1
A Survey Of Data Mining And Knowledge Discovery Software Tools
 SIGKDD Explorations
, 1999
"... Knowledge discovery in databases is a rapidly growing field, whose development is driven by strong research interests as well as urgent practical, social, and economical needs. While the last few years knowledge discovery tools have been used mainly in research environments, sophisticated software p ..."
Abstract

Cited by 61 (1 self)
 Add to MetaCart
(Show Context)
Knowledge discovery in databases is a rapidly growing field, whose development is driven by strong research interests as well as urgent practical, social, and economical needs. While the last few years knowledge discovery tools have been used mainly in research environments, sophisticated software products are now rapidly emerging. In this paper, we provide an overview of common knowledge discovery tasks and approaches to solve these tasks. We propose a feature classification scheme that can be used to study knowledge and data mining software. This scheme is based on the software's general characteristics, database connectivity, and data mining characteristics. We then apply our feature classification scheme to investigate 43 software products, which are either research prototypes or commercially available. Finally, we specify features that we consider important for knowledge discovery software to possess in order to accommodate its users effectively, as well as issues that are either ...
Fuzzy sets and probability : Misunderstandings, bridges and gaps
 In Proceedings of the Second IEEE Conference on Fuzzy Systems
, 1993
"... This paper is meant to survey the literature pertaining to this debate, and to try to overcome misunderstandings and to supply access to many basic references that have addressed the "probability versus fuzzy set" challenge. This problem has not a single facet, as will be claimed here. Mor ..."
Abstract

Cited by 59 (6 self)
 Add to MetaCart
(Show Context)
This paper is meant to survey the literature pertaining to this debate, and to try to overcome misunderstandings and to supply access to many basic references that have addressed the "probability versus fuzzy set" challenge. This problem has not a single facet, as will be claimed here. Moreover it seems that a lot of controversies might have been avoided if protagonists had been patient enough to build a common language and to share their scientific backgrounds. The main points made here are as follows. i) Fuzzy set theory is a consistent body of mathematical tools. ii) Although fuzzy sets and probability measures are distinct, several bridges relating them have been proposed that should reconcile opposite points of view ; especially possibility theory stands at the crossroads between fuzzy sets and probability theory. iii) Mathematical objects that behave like fuzzy sets exist in probability theory. It does not mean that fuzziness is reducible to randomness. Indeed iv) there are ways of approaching fuzzy sets and possibility theory that owe nothing to probability theory. Interpretations of probability theory are multiple especially frequentist versus subjectivist views (Fine [31]) ; several interpretations of fuzzy sets also exist. Some interpretations of fuzzy sets are in agreement with probability calculus and some are not. The paper is structured as follows : first we address some classical misunderstandings between fuzzy sets and probabilities. They must be solved before any discussion can take place. Then we consider probabilistic interpretations of membership functions, that may help in membership function assessment. We also point out nonprobabilistic interpretations of fuzzy sets. The next section examines the literature on possibilityprobability transformati...
Similarity Relation as a Basis for Rough Approximations
, 1995
"... The indiscernibility relation originally used for the definition of the rough set concept is extended to a similarity relation subject to a minimal set of conditions. It is shown that in order to meet these conditions, the similarity relation needs only to be reflexive. The lower and upper approxima ..."
Abstract

Cited by 57 (3 self)
 Add to MetaCart
The indiscernibility relation originally used for the definition of the rough set concept is extended to a similarity relation subject to a minimal set of conditions. It is shown that in order to meet these conditions, the similarity relation needs only to be reflexive. The lower and upper approximations are defined according to a new more general definition using the similarity relation. Comparison between approximations based on indiscernibility relation and similarity relation is established. Then, a general framework for defining similarity relations on objects described by a set of attributes is given. The proposed construction of a similarity measure takes into account both positive and negative contributions to the credibility of the similarity (concordance and discordance). Induction of decision rules from similaritybased approximations is discussed and an illustrative example is given. 1 Introduction Suppose we are given a finite non empty set U of objects, called universe. ...
Conjunto: Constraint Logic Programming with Finite Set Domains
 Logic Programming  Proceedings of the 1994 International Symposium, pages 339358, Massachusetts Institute of Technology
, 1994
"... Combinatorial problems involving sets and relations are currently tackled by integer programming and expressed with vectors or matrices of 01 variables. This is efficient but not flexible and unnatural in problem formulation. Toward a natural programming of combinatorial problems based on sets, gra ..."
Abstract

Cited by 52 (3 self)
 Add to MetaCart
(Show Context)
Combinatorial problems involving sets and relations are currently tackled by integer programming and expressed with vectors or matrices of 01 variables. This is efficient but not flexible and unnatural in problem formulation. Toward a natural programming of combinatorial problems based on sets, graphs or relations, we define a new CLP language with set constraints. This language Conjunto 1 aims at combining the declarative aspect of Prolog with the efficiency of constraint solving techniques. We propose to constrain a set variable to range over finite set domains specified by lower and upper bounds for set inclusion. Conjunto is based on the inclusion and disjointness constraints applied to set expressions which comprise the union, intersection and difference symbols. The main contribution herein is the constraint handler which performs constraint propagation by applying consistency techniques over set constraints. 1 Introduction Various systems of set constraints have been define...
Information granulation and rough set approximation
 International Journal of Intelligent Systems
, 2001
"... Information granulation and concept approximation are some of the fundamental issues of granular computing. Granulation of a universe involves grouping of similar elements into granules to form coarsegrained views of the universe. Approximation of concepts, represented by subsets of the universe, d ..."
Abstract

Cited by 52 (19 self)
 Add to MetaCart
(Show Context)
Information granulation and concept approximation are some of the fundamental issues of granular computing. Granulation of a universe involves grouping of similar elements into granules to form coarsegrained views of the universe. Approximation of concepts, represented by subsets of the universe, deals with the descriptions of concepts using granules. In the context of rough set theory, this paper examines the two related issues. The granulation structures used by standard rough set theory and the corresponding approximation structures are reviewed. Hierarchical granulation and approximation structures are studied, which results in stratified rough set approximations. A nested sequence of granulations induced by a set of nested equivalence relations leads to a nested sequence of rough set approximations. A multilevel granulation, characterized by a special class of equivalence relations, leads to a more general approximation structure. The notion of neighborhood systems is also explored. 1
Rough Set Approach To KnowledgeBased Decision Support
 European Journal of Operational Research
, 1995
"... . The rough set concept is a new mathematical approach to imprecision, vagueness and uncertainty. To some extend it overlaps with fuzzy set theory and evidence theory  nevertheless the rough set theory can be viewed in its own rights, as an independent discipline. Many reallife applications of th ..."
Abstract

Cited by 50 (0 self)
 Add to MetaCart
(Show Context)
. The rough set concept is a new mathematical approach to imprecision, vagueness and uncertainty. To some extend it overlaps with fuzzy set theory and evidence theory  nevertheless the rough set theory can be viewed in its own rights, as an independent discipline. Many reallife applications of the theory have proved its practical usefulness. The paper presents the basic assumptions underlying the rough sets philosophy, gives its fundamental concepts and discusses briefly some areas of applications, in particular in decision support. Finally further problems are shortly outlined. 1 Introduction 1.1 Basic Philosophy The rough set concept proposed by the author in [5] is a new mathematical approach to imprecision, vagueness and uncertainty. The rough set philosophy is founded on the assumption that with every objects of the universe of discourse we associate some information (data, knowledge). E.g. if objects are patients suffering from a certain disease, symptoms of the disease form...
Towards Adaptive Calculus of Granules
 Proceedings of 1998 IEEE International Conference on Fuzzy Systems
, 1998
"... An importance of the idea of granularity of knowledge for approximate reasoning has been recently stressed in [6,910]. We address here the problem of synthesis of adaptive decision algorithms and we propose an approach to this problem based on the notion of a granule which we develop in the framewo ..."
Abstract

Cited by 50 (14 self)
 Add to MetaCart
(Show Context)
An importance of the idea of granularity of knowledge for approximate reasoning has been recently stressed in [6,910]. We address here the problem of synthesis of adaptive decision algorithms and we propose an approach to this problem based on the notion of a granule which we develop in the framework of rough mereology. This framework does encompass both rough and fuzzy set theories. Our approach may be applied in the problems of approximate synthesis of complex objects (solutions) in distributed systems of intelligent agents. Keywords rough sets, apporoximate reasoning, rough mereology, granules of knowledge I. Introduction: a notion of a granule In this introduction, we first present the rough set approach, then we outline the fuzzy set approach and finally we introduce elements of rough mereological theory [2], [7,8] by means of which we will define in the sequel the notion of a granule of knowledge in a unified way. We begin with rough set approach [5]. In this approach, kn...