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...

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 ‘ε-definitions ’ 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 EXPTIME-completeness (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 ‘well-behaved ’ common denominator of logical systems constructed in temporal, spatial, and similarity-based 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 real-time systems. On the real plane, it is closely related to quantitative and qualitative formalisms for spatial

In the classical neuron model, inputs are continuous real-valued 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 real-world 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...

This contribution presents a comprehensive view on problems of approximate reasoning with imprecise knowledge in the form of a collection of fuzzy IF-THEN 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.

Abstract. Auction-based 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 auction-based tournaments. Our formal view relies on possibilistic-based 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 two-fold 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

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

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 t-norm 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 t-norm. The logics are then shown to be applicable to possibilistic reasoning, approximate reasoning, and nonmonotonic reasoning.

. Fuzzy heterogeneous networks are recently introduced neural network models composed of neurons of a general class whose inputs and weights are mixtures of continuous variables (crisp and/or fuzzy) with discrete quantities, also admitting missing data. These networks have net input functions based on similarity relations between the inputs and the weights of a neuron. They thus accept heterogeneous --possibly missing-- inputs, and can be coupled with classical neurons in hybrid network architectures, trained by means of genetic algorithms or other evolutionary methods. This paper compares the effectiveness of the fuzzy heterogeneous model based on similarity with the classical feed-forward one, in the context of an investigation in the field of environmental sciences, namely, the geochemical study of natural waters in the Arctic (Spitzbergen). Classification performance, the effect of working with crisp or fuzzy inputs, the use of traditional scalar product vs. similarity-ba...

This paper deals with fuzzy similaritybased models of the basic principle of casebased reasoning (CBR) stating that "similar problems lead (or may lead) to similar outcomes ". A stronger form of this principle stating that "outcome attributes are at least as similar as problem description attributes " has been studied in some previous works. In this paper another form of the basic principle stating that "the more similar are the problem description attributes, the more similar are the outcome attributes " is studied. These two forms of the CBR principle are used to infer possible

This research introduces a general class of functions serving as generalized neuron models to be used in artificial neural networks. They are cast in the common framework of computing a similarity function, a flexible definition of a neuron as a pattern recognizer. The similarity endows the model with a clear conceptual view and leads naturally to handle heterogeneous information, in the form of mixtures of continuous numbers (crisp or fuzzy), linguistic information and discrete quantities (ordinal, nominal and finite sets). Missing data are also explicitly considered. The absence of coding schemes and the precise computation attributed to the neurons makes the networks highly interpretable. The resulting heterogeneous neural networks are trained by means of a special-purpose genetic algorithm. The cooperative integration of different soft computing techniques (neural networks, evolutionary algorithms and fuzzy sets) makes these networks capable of learning from non-trivial data sets with a remarkable effectiveness, comparable or superior to that of classical models. This claim is demonstrated by a set of experiments on benchmarking realworld data sets.