International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems

In this paper we give a nesessary and sufficient condition for a Choquet integral model to be decomposable into an equivalent hierarchical Choquet integral model constructed by hierarchical combinations of some ordinary Choquet integral models. The condition is obtained by Inclution-Exclusion Covering (IEC). Moreover we show some properties on the set of IECs.

In this paper we will analyze some computational problems related with ordered hierarchical aggregations of OWA operators as defined by the authors in a previous paper. In particular, we will provide polynomial algorithms to maximize or minimize the degrees of dispersion and orness of the hierarchical OWA aggregation.

The solution of Meyerowitz, Richman and Walker to the problem of determining the maximum-entropy probability consistent with a belief function (an ∞-monotone capacity) is shown to remain valid in the case of a convex (i.e., 2-monotone) capacity.

In this paper we introduce a definition of consistency of the judgement matrix in the fuzzy Analytic Hierarchy Process (AHP) and give a general expression of all fuzzy weights under the condition of consistency. Finally, based on our discussion, the geometric average method is suggested for fuzzy weights calculation in the practical decision-making situation.

We discuss the aggregation problem for transitive fuzzy binary relations. An aggregation procedure assigns a group fuzzy binary relation to each finite set of individual binary relations. Individual and group binary relations are assumed to be transitive fuzzy binary relation with respect to a given continuous t-norm. We study a particular class of aggregation procedures given by quasi-arithmetic (Kolmogorov) means and show that these procedures are well defined if and only if the t-norm is Archimedean. We also give a geometric characterization of t-norms for which the arithmetic mean is a well-defined aggregation procedure.

We present an adjustment-to-user facility of a facial images database system in order to improve retrieval performance. The system uses linguistic (qualitative) descriptions, both in the data model and in the query language. These descriptions are internally represented as fuzzy sets. As the same linguistic descriptions can be used by different users to describe different values, the need of adjusting fuzzy sets, such that the user’s meaning is represented arises. We provide a method which, upon repeated queries by the same user, finds the best representation (as fuzzy set) of the linguistic descriptions given by the user in question. The method is based on an extension of the inverse problem of matching of fuzzy sets. Experiments show that when compared with the unadjusted system, significantly better results are obtained during the process of finding the best representation, and much better results after the best representation (given the whole database) is found.

The reference class problem in probability theory and the multiple inheritances (extensions) problem in non-monotonic logics are special cases of conflicting beliefs. One popular solution accepted in the two domains is the specificity principle. By analyzing an example, several factors beyond specificity are found to be relevant to the priority of a reference class. A new approach, Non-Axiomatic Reasoning System (NARS), is discussed, where these factors are all taken into account. It is argued that the solution provided by NARS is better than the solutions provided by probability theory and non-monotonic logics.

This paper investigates the problems incurred when fuzzy values and certainty factors are used in rule-based knowledge representation. It proposes several measures for evaluating the satisfaction degree of fuzzy matching, fuzzy comparison and interval inclusion occurring in the course of inference for such knowledge representation. It introduces an inference method for such knowledge representation. In addition, it suggests a strategy for flexibly using and managing both conventional rules and fuzzy production rules in rule-based systems. Finally a fuzzy expert system shell, called FOPS5, designed to accommodate fuzzy information processing, is presented in consideration of the proposed methods.