International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems

We propose an extension of the Takagi-Sugeno-Kang (TSK) fuzzy inference system, using Choquet integration for aggregating the single rule outputs. In the new Choquet-TSK fuzzy inference system, the pairwise synergies between rules are encoded in a rule correlation matrix computed from the activation pattern of the rule base. The rule correlation matrix is then used to modulate the parameters of the Choquet integration scheme in order to compensate for the effect of rule synergies, which are present in most rule bases to a higher or lesser extent.

The standard TSK fuzzy inference system remains a particular instance of the proposed Choquet-TSK extension and corresponds to the ideal case of rule independence. However, when rule correlation is present, the Choquet-TSK fuzzy inference system takes it into account when computing the final output of the system. On the basis of the rule correlation matrix, the new aggregation scheme of the Choquet-TSK fuzzy inference system attenuates the effective weight of positively correlated rules and emphasizes that of negatively correlated rules. Some case studies are discussed in order to illustrate the proposed methodology.

This paper continues an earlier investigation of automorphisms of the algebra of truth values of type-2 fuzzy sets. Several significant problems left unresolved are settled, the most basic being that the automorphism group of the algebra of fuzzy truth values is isomorphic in a natural way to the product of two copies of the automorphism group of the unit interval. This theorem has several corollaries concerning characteristic subalgebras.

Recently a new type of data source came into the focus of knowledge discovery from temporal data: interval sequences. In contrast to event sequences, interval sequences contain labeled events with a temporal extension. However, existing algorithms for mining patterns from interval sequences proved to be far from satisfying our needs. In brief, we missed an approach that, at the same time, defines support as the number of pattern instances, allows input data that consists of more than one sequence, implements time constraints on a pattern instance, and counts multiple instances of a pattern within one interval sequence. In this paper we propose a new support definition which incorporates these properties. We also describe FSMSet, an algorithm that employs the new support definition, and demonstrate its performance on field data from the automotive business.

Since fuzzy linear regression was introduced by Tanaka et al., fuzzy regression analysis has been widely studied and applied in various areas. Diamond proposed the fuzzy least squares method to eliminate disadvantages in the Tanaka et al method. In this paper, we propose a modified fuzzy least squares regression analysis. When independent variables are crisp, the dependent variable is a fuzzy number and outliers are present in the data set. In the proposed method, the residuals are ranked as the comparison of fuzzy sets, and the weight matrix is defined by the membership function of the residuals. To illustrate how the proposed method is applied, two examples are discussed and compared in methods from the literature. Results from the numerical examples using the proposed method give good solutions.

This paper presents an intelligent technology based method for analyzing and interpreting sensory data provided by multiple panels in evaluation of industrial products. In order to process the uncertainty existing in these sensory data, we first transform all sensory data on an unified optimal scale. Based on these normalized data sets, we compute the dissimilarities or distances between different panels and between different evaluation terms used by them, defined according to the degree of consistency of data variation. The obtained distances are then transformed into fuzzy numbers for physical interpretation. These fuzzy distances permit to characterize the evaluation behaviour of each panel and the quality of the evaluation terms used. Also, based on a Genetic Algorithm with punishment policy and the dissimilarity between terms, we develop a procedure for interpreting terms of one panel using those of another panel. This method has been applied to the fabric hand evaluation for a number of samples of knitted cotton in order to identify consumers' preference of different populations.

In an expert system having a consistent set of linear constraints it is known that the Method of Tribus may be used to determine a probability distribution which exhibits maximised entropy. The method is extended here to include independence constraints (Accommodation).

The paper proceeds to discusses this extension, and its limitations, then goes on to advance a technique for determining a small set of independencies which can be added to the linear constraints required in a particular representation of an expert system called a causal network, so that the Maximum Entropy and Causal Networks methodologies give matching distributions (Emulation). This technique may also be applied in cases where no initial independencies are given and the linear constraints are incomplete, in order to provide an optimal ME fill-in for the missing information.

Fuzzy mathematics is a generalization in which fuzzy numbers replace real numbers and fuzzy arithmetic replaces real arithmetic. It is an excellent scope for modeling vague and uncertain aspects of the actual environments. In this important area, Dubois and Prade¹ defined a fuzzy matrix as a rectangular array of fuzzy numbers. They have also defined the LR type fuzzy numbers with some useful approximate arithmetic operators. The aim of this paper is to extend some useful aspects of linear algebra e.g. determinant, norm and eigenvalue for fuzzy matrices with LR fuzzy number entries by the use of fuzzy arithmetic. Finally, applications in fuzzy analytical hierarchy process (AHP) are investigated.

Knowledge intensive applications require an intelligent environment, which can perform deductions in response to user queries or events that occur inside or outside of the applications. For that, we propose a fuzzy active object-oriented database for modeling knowledge intensive applications. In that, we incorporate fuzziness within the event, condition and action parts of an active rule. We consider deductive rules as special cases of active rules so that deductive queries are handled using abstract kind of events. We also introduce a model for fuzzy inferencing of fuzzy active rules where we develop a model for scenario concept. We use a Fuzzy Petri Net model for fuzzy rule-based inference.

This section is maintained by Vladik Kreinovich. Please send your abstracts (or copies of papers that you want to see reviewed here) to vladik@utep.edu, or by regular mail to: V. Kreinovich, Department of Computer Science, University of Texas, El Paso, TX 79968, USA.