nd (universal child.Human 7 . is given in terms of an the domain (a non-empty set) an interpretation function that maps: (class) a (property) a an element of Interpretation extended to concept expressions: = = = = = \ = {x = {x 8 and . mapping to FOL: introduce unary an atomic binary a . Translate follows x) = x) = false t(A, x) ## A(x) x) = x) x) ## x) t(C, x) = t(#R.C, x) = y) t(#R.C, x) = 9 Knowledge . DL Knowledge Base is a A#, a TBox containing general inclusion axioms of the ("concept C"), i# definitions are of the (equiv A) concept definitions are of the Sometimes, a TBox can contain primitive and concept definitions only, where no atom can be defined more than once and no recursion is allowed complexity changes dramatically a ABox containing assertions of the

This paper develops a fuzzy constraint based model for bilateral multi-issue negotiation in trading environments. In particular, we are concerned with the principled negotiation approach in which agents seek to strike a fair deal for both parties, but which, nevertheless, maximises their own payoff. Thus, there are elements of both competition and cooperation in the negotiation (hence semi-competitive environments) . One of the key intuitions of the approach is that there is often more than one option that can satisfy the interests of both parties. So, if the opponent cannot accept an offer then the proponent should endeavour to find an alternative that is equally acceptable to it, but more acceptable to the opponent. That is, the agent should make a trade-off. Only if such a trade-off is not possible should the agent make a concession. Against this background, our model ensures the agents reach a deal that is fair (Pareto-optimal) for both parties if such a solution exists. Moreover, this is achieved by minimising the amount of private information that is revealed. The model uses prioritised fuzzy constraints to represent trade-offs between the different possible values of the negotiation issues and to indicate how concessions should be made when they are necessary. Also by using constraints to express negotiation proposals, the model can cover the negotiation space more ef- ficiently since each exchange covers a region rather than a single point (which is what most existing models deal with). In addition, by incorporating the notion of a reward into our negotiation model, the agents can sometimes reach agreements that would not otherwise be possible.

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

In the Semantic Web context information would be retrieved, processed, shared, reused and aligned in the maximum automatic way possible. Our experience with such applications in the Semantic Web has shown that these are rarely a matter of true or false but rather procedures that require degrees of relatedness, similarity, or ranking. Apart from the wealth of applications that are inherently imprecise, information itself is many times imprecise or vague. For example, the concepts of a “hot” place, an “expensive” item, a “fast” car, a “near” city, are examples of such concepts. Dealing with such type of information would yield more realistic, intelligent and effective applications. In the current paper we extend the OWL web ontology language, with fuzzy set theory, in order to be able to capture, represent and reason with such type of information.

It is widely recognized today that the management of imprecision and vagueness will yield more intelligent and realistic knowledge-based applications. Description Logics (DLs) are a family of knowledge representation languages that have gained considerable attention the last decade, mainly due to their decidability and the existence of empirically high performance of reasoning algorithms. In this paper, we extend the well known fuzzy ALC DL to the fuzzy SHIN DL, which extends the fuzzy ALC DL with transitive role axioms (S), inverse roles (I), role hierarchies (H) and number restrictions (N). We illustrate why transitive role axioms are difficult to handle in the presence of fuzzy interpretations and how to handle them properly. Then we extend these results by adding role hierarchies and finally number restrictions. The main contributions of the paper are the decidability proof of the fuzzy DL languages fuzzy-SI and fuzzy-SHIN, as well as decision procedures for the knowledge base satisfiability problem of the fuzzy-SI and fuzzy-SHIN. 1.

One of the important issues in data mining is the interestingness problem. This problem is described as finding the interesting patterns from a large number of discovered patterns. Typically, in a data mining application, it is all too easy to discover a huge number of patterns. Most of these patterns are actually useless or uninteresting to the user. But due to the huge number of patterns, it is difficult for a user to comprehend all the patterns and to identify those interesting to him/her. To prevent the user from being overwhelmed by the large number of patterns, techniques are needed to analyze and to rank the patterns according to their interestingness. This paper proposes such a technique. It performs post-analysis of the discovered patterns to help the user identify those interesting ones. The technique is based on fuzzy matching of the discovered patterns with a set of user-specified patterns. The degrees of match are then used to rank the discovered patterns according to vari...

Abstract. In the Semantic Web information would be retrieved, processed, combined, shared and reused in the maximum automatic way possible. Obviously, such procedures involve a high degree of uncertainty and imprecision. For example ontology alignment or information retrieval are rarely true or false procedures but usually involve confidence degrees or provide rankings. Furthermore, it is often the case that information itself is imprecise and vague like the concept of a “tall ” person, a “hot” place and many more. In order to be able to represent and reason with such type of information in the Semantic Web (SW), as well as, enhance SW applications we present an extension of the Description Logic SHIN with fuzzy set theory. We present the semantics as well as detailed reasoning algorithms for the extended language. 1

In many real-life situations, it is very difficult or even impossible to directly measure the quantity y in which we are interested: e.g., we cannot directly measure a distance to a distant galaxy or the amount of oil in a given well. Since we cannot measure such quantities directly, we can measure them indirectly: by first measuring some relating quantities x1 ; : : : ; xn , and then by using the known relation between x i and y to reconstruct the value of the desired quantity y. In practice, it is often very important to estimate the error of the resulting indirect measurement. In this paper, we describe and compare different deterministic and randomized algorithms for solving this problem in the situation when a program for transforming the estimates e x1 ; : : : ; e xn for x i into an estimate for y is only available as a black box (with no source code at hand). We consider this problem in two settings: statistical, when measurements errors \Deltax i = e x i \Gamma x i are inde...

Granular computing (GrC) may be regarded as a label of theories, methodologies, techniques, and tools that make use of granules, i.e., groups, classes, or clusters of a universe, in the process of problem solving. The main objective of this paper is to discuss basic issues of GrC, with emphasis on the construction of granules and computation with granules. After a brief review of existing studies, a set-theoretic model of GrC is proposed based on the notion of power algebras.

Ontologies play a crucial role in the development of the Semantic Web as a means for defining shared terms in web resources. They are formulated in web ontology languages, which are based on expressive description logics. Significant research efforts in the semantic web community are recently directed towards representing and reasoning with uncertainty and vagueness in ontologies for the Semantic Web. In this paper, we give an overview of approaches in this context to managing probabilistic uncertainty, possibilistic uncertainty, and vagueness in expressive description logics for the Semantic Web.