International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems

The problem of normalisation of non-normalised fuzzy sets/possibility distributions is considered. A definition of a valid normalised possibility distribution is given at the mass assignment level and a characterisation of this definition at the distribution level is proposed. A number of possible normalisations are considered these being related to certain epistemic principles. Finally an interval approach to reasoning with partially inconsistent knowledge is introduced.

A hierarchical clustering approach is proposed for reducing the number of focal elements in a crisp or fuzzy belief function, yielding strong inner and outer approximations. At each step of the proposed algorithm, two focal elements are merged, and the mass is transfered to their intersection or their union. The resulting approximations allow the calculation of lower and upper bounds on the belief and plausibility degrees induced by the conjunctive or disjunctive sum of any number of belief structures. Numerical experiments demonstrate the effectiveness of this approach.

Abductive inference in Bayesian belief networks is intended as the process of generating the K most probable configurations given an observed evidence. These configurations are called explanations and in most of the approaches found in the literature, all the explanations have the same number of literals. In this paper we propose some criteria to simplify the explanations in such a way that the resulting configurations are still accounting for the observed facts. Computational methods to perform the simplification task are also presented. Finally the algorithms are experimentally tested using a set of experiments which involves three different Bayesian belief networks.

This paper presents a characterization of a new family of operators. Namely, all non-decreasing, associative binary operators U: [0, 1]² → [0, 1] with a left (or right) neutral element e ∈ [0, 1], and such that they satisfy an additional hypothesis on continuity which is called here left (or right) pseudocontinuity.

In this paper, we propose a method to calculate the correlation coefficient of intuitionistic fuzzy sets by means of mathematical statistics. This value obtained from our formula tell us not only the strength of relationship between the intuitionistic fuzzy sets, but also whether the intuitionistic fuzzy sets are positively or negatively related. This approach looks better than previous methods which only evaluate the strength of the relation. Furthermore, we extend the proposed method to interval-valued intuitionistic fuzzy sets. The value of the correlation coefficient between interval-valued intuitionistic fuzzy sets lies in the interval [-1, 1], as computed from our formula.

In this paper, we propose a method to calculate the correlation coefficient of fuzzy numbers by means of "expected interval" (see [8], [9]). This value obtained from our formula tell us not only the strength of relationship between the fuzzy numbers, but also whether the fuzzy numbers are positively or negatively related. This approach looks better than previous methods which only evaluate the strength of the relation. Furthermore, we extend the "expected interval" method to interval-valued fuzzy numbers. The value of the correlation coefficient between interval-valued fuzzy numbers lies in the interval [-1,1], as computed from our formula.

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