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29
Rough Sets: A Tutorial
, 1998
"... A rapid growth of interest in rough set theory [290] and its applications can be lately seen in the number of international workshops, conferences and seminars that are either directly dedicated to rough sets, include the subject in their programs, or simply accept papers that use this approach t ..."
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Cited by 85 (8 self)
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A rapid growth of interest in rough set theory [290] and its applications can be lately seen in the number of international workshops, conferences and seminars that are either directly dedicated to rough sets, include the subject in their programs, or simply accept papers that use this approach to solve problems at hand. A large number of high quality papers on various aspects of rough sets and their applications have been published in recent years as a result of this attention. The theory has been followed by the development of several software systems that implement rough set operations. In Section 12 we present a list of software systems based on rough sets. Some of the toolkits, provide advanced graphical environments that support the process of developing and validating rough set classifiers. Rough sets are applied in many domains, such as, for instance, medicine, finance, telecommunication, vibration analysis, conflict resolution, intelligent agents, image analysis, p...
A logic for metric and topology
 Journal of Symbolic Logic
, 2005
"... Abstract. We propose a logic for reasoning about metric spaces with the induced topologies. It combines the ‘qualitative ’ interior and closure operators with ‘quantitative’ operators ‘somewhere in the sphere of radius r, ’ including or excluding the boundary. We supply the logic with both the inten ..."
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Cited by 15 (12 self)
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Abstract. We propose a logic for reasoning about metric spaces with the induced topologies. It combines the ‘qualitative ’ interior and closure operators with ‘quantitative’ operators ‘somewhere in the sphere of radius r, ’ including or excluding the boundary. We supply the logic with both the intended metric space semantics and a natural relational semantics, and show that the latter (i) provides finite partial representations of (in general) infinite metric models and (ii) reduces the standard ‘εdefinitions ’ of closure and interior to simple constraints on relations. These features of the relational semantics suggest a finite axiomatisation of the logic and provide means to prove its EXPTIMEcompleteness (even if the rational numerical parameters are coded in binary). An extension with metric variables satisfying linear rational (in)equalities is proved to be decidable as well. Our logic can be regarded as a ‘wellbehaved ’ common denominator of logical systems constructed in temporal, spatial, and similaritybased quantitative and qualitative representation and reasoning. Interpreted on the real line (with its Euclidean metric), it is a natural fragment of decidable temporal logics for specification and verification of realtime systems. On the real plane, it is closely related to quantitative and qualitative formalisms for spatial
On approximate reasoning with graded rules
 Fuzzy Sets and Systems
"... This contribution presents a comprehensive view on problems of approximate reasoning with imprecise knowledge in the form of a collection of fuzzy IFTHEN rules formalized by approximating formulas of a special type. Two alternatives that follow from the dual character of approximating formulas are ..."
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Cited by 10 (3 self)
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This contribution presents a comprehensive view on problems of approximate reasoning with imprecise knowledge in the form of a collection of fuzzy IFTHEN rules formalized by approximating formulas of a special type. Two alternatives that follow from the dual character of approximating formulas are developed in parallel. The link to the theory of fuzzy control systems is also explained.
Fuzzy Heterogeneous Neurons for Imprecise Classification Problems
"... In the classical neuron model, inputs are continuous realvalued quantities. However, in many important domains from the real world, objects are described by a mixture of continuous and discrete variables, usually containing missing information and uncertainty. In this paper, a general class of neur ..."
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Cited by 4 (3 self)
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In the classical neuron model, inputs are continuous realvalued quantities. However, in many important domains from the real world, objects are described by a mixture of continuous and discrete variables, usually containing missing information and uncertainty. In this paper, a general class of neuron models accepting heterogeneous inputs in the form of mixtures of continuous (crisp and/or fuzzy) and discrete quantities admitting missing data is presented. From these, several particular models can be derived as instances and different neural architectures constructed with them. Such models deal in a natural way with problems for which information is imprecise or even missing. Their possibilities in classification and diagnostic problems are here illustrated by experiments with data from a realworld domain in the field of environmental studies. These experiments show that such neurons can both learn and classify complex data very effectively in the presence of uncertain information. K...
On Implicative Closure Operators in Approximate Reasoning
, 1999
"... This paper introduces a new definition of fuzzy closure operator called Implicative Closure Operators. The Implicative Closure Operators generalize some notions of fuzzy closure operators given by differents authors. We show that the Implicative Closure Operators capture some usual Consequence Relat ..."
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Cited by 3 (0 self)
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This paper introduces a new definition of fuzzy closure operator called Implicative Closure Operators. The Implicative Closure Operators generalize some notions of fuzzy closure operators given by differents authors. We show that the Implicative Closure Operators capture some usual Consequence Relations used in Approximate Reasoning, like the Approximation and Proximity entailments defined by Dubois et al. [5] and the Natural Inference Operator defined by Boixader and Jacas [1].
Roughness Bounds in Rough Set Operations
"... This paper presents some roughness bounds for rough set operations. The results show that a bound of the set operation can be determined from their operand’s roughnesses. We prove also that this bound is not determined under some special operations. Key words: Rough sets, Roughness 1 ..."
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Cited by 3 (0 self)
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This paper presents some roughness bounds for rough set operations. The results show that a bound of the set operation can be determined from their operand’s roughnesses. We prove also that this bound is not determined under some special operations. Key words: Rough sets, Roughness 1
Bidding Strategies for Trading Agents in AuctionBased Tournaments
 Agent Mediated Electronic Commerce. Lecture Notes in Artificial Intelligence
, 1999
"... Abstract. Auctionbased electronic commerce is an increasingly interesting domain for AI researchers. In this paper we present an attempt towards the construction of trading agents capable of competing in multiagent auction markets by introducing both a formal and a more pragmatic approach to the de ..."
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Abstract. Auctionbased electronic commerce is an increasingly interesting domain for AI researchers. In this paper we present an attempt towards the construction of trading agents capable of competing in multiagent auction markets by introducing both a formal and a more pragmatic approach to the design of bidding strategies for buyer agents in auctionbased tournaments. Our formal view relies on possibilisticbased decision theory as the means of handling possibilistic uncertainty on the consequences of actions (bids) due to the lack of knowledge about the other agents ’ behaviour. For practical reasons we propose a twofold method for decision making that does not require the evaluation of the whole set of alternative actions. This approach utilizes global (marketcentered) information in a first step to come up with an initial set of potential bids. This set is subsequently refined in a second step by means of the possibilisitic decision model using individual (rival agent centered) information induced from a memory of cases composing the history of tournaments. 1
Possibilistic Residuated Implication Logics with Applications
"... this paper, we will develop a class of logics for reasoning about qualitative and quantitative uncertainty. The semantics of the logics is uniformly based on possibility theory. Each logic in the class is parameterizedby a tnorm operation on [0,1], and we express the degree of implication between t ..."
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Cited by 1 (0 self)
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this paper, we will develop a class of logics for reasoning about qualitative and quantitative uncertainty. The semantics of the logics is uniformly based on possibility theory. Each logic in the class is parameterizedby a tnorm operation on [0,1], and we express the degree of implication between the possibilities of two formulas explicitly by using residuated implication with respect to the tnorm. The logics are then shown to be applicable to possibilistic reasoning, approximate reasoning, and nonmonotonic reasoning.
Fuzzy interpolation and level 2 gradual rules
"... Functional laws may be known only at a finite number of points, and then the function can be completed by interpolation techniques obeying some smoothness conditions. We rather propose here to specify constraints by means of gradual rules for delimiting areas where the function may lie between known ..."
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Cited by 1 (1 self)
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Functional laws may be known only at a finite number of points, and then the function can be completed by interpolation techniques obeying some smoothness conditions. We rather propose here to specify constraints by means of gradual rules for delimiting areas where the function may lie between known points. Such an approach results in an imprecise interpolation graph whose shape is controlled by tuning the fuzziness attached to the reference points. However, the graph sobuilt is still crisp, which means that different possible paths between the interpolation points cannot be distinguished according to their plausibility. The paper discusses a method for introducing membership degrees inside the interpolation graph. The developed formalism relies on the use of weighted nested graphs. It amounts to handling level 2 gradual rules for specifying a family of flexible constraints on the reference points. The proposed approach is compared with the one of extending gradual rules for dealing with type 2 fuzzy reference points.