International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems

The representation of the degree of difference between two fuzzy subsets by means of a real number has been proposed in previous papers, and it seems to be useful in some situations. However, the requirement of assigning a precise number may lead us to the loss of essential information about this difference. Thus, (crisp) divergence measures studied in previous papers may not distinguish whether the differences between two fuzzy subsets are in low or high membership degrees. In this paper we propose a way of measuring these differences by means of a fuzzy valued function which we will call fuzzy divergence measure. We formulate a list of natural axioms that these measures should satisfy. We derive additional properties from these axioms, some of them are related to the properties required to crisp divergence measures. We finish the paper by establishing a one-to-one correspondence between families of crisp and fuzzy divergence measures. This result provides us with a method to build a fuzzy divergence measure from a crisp valued one.

The work considers the problem of solvability of a fuzzy relation equation with max-min composition. It presents the necessary and sufficient conditions for the existence of solutions, then derives a fast algorithm for finding all minimal solutions. The results are compared with those of previous publications regarding this subject.

Yield forecasting is a very important task to a semiconductor manufacturing factory. To enhance both the precision and accuracy of semiconductor yield forecasting, a fuzzy-neural system incorporating unequally important expert opinions is constructed in this study. In the proposed methodology, multiple experts construct their own fuzzy yield learning models from various viewpoints to predict the yield of a product. Besides, these expert opinions can also be considered unequally important. To aggregate these fuzzy yield forecasts, a two-step aggregation mechanism is applied. At the first step, fuzzy intersection is applied to aggregate the fuzzy yield forecasts into a polygon-shaped fuzzy yield forecast, in order to improve the precision of yield forecasting. After that, a back propagation network is constructed to defuzzify the polygon-shaped fuzzy yield forecast and to generate a representative/crisp value, so as to enhance the accuracy. For evaluating the effectiveness of the proposed methodology and to make comparison with some existing approaches, all approaches were applied to the practical data of three products in a real semiconductor manufacturing factory. According to experimental results, the proposed methodology improved both the precision and accuracy of semiconductor yield forecasting by 48% and 38%, respectively.

This paper focuses on the role that social norms play in the selection of equilibrium points seen as social conventions under unforeseen contingencies — that is, their role in the emergence of regularities of behavior which are self-enforcing and effectively adhered to by bounded rational agents due to their self-policing incentives. Differently stated, given a set of game situations imperfectly described, we want to understand how general and abstract norms provide at least the starting point for a norm-based equilibrium selection reasoning procedure which in the end will be able to determine which equilibrium point, belonging to perfectly described games, will be played as the unique solution of each imperfectly described game. In order to solve such a problem we introduce a selection process based on the reformulation of default logic in terms of possibility theory.

In this paper, a new approach is proposed to solve group decision making (GDM) problems where the preference information on alternatives provided by decision makers (DMs) is represented in incomplete fuzzy preference relations. In order to make the collective opinion close each decision maker's opinion as near as possible, an optimization model is constructed to integrate the incomplete fuzzy preference relations and to compute the collective ranking values of alternatives. The ranking of alternatives or selection of the most desirable alternative(s) is directly obtained from the derived collective ranking values. A numerical example is also used to illustrate the applicability of the proposed approach.

Fuzzy variables are functions from credibility spaces to the set of real numbers. The set of fuzzy variables is a linear space with the classic operations of addition and multiplication by numbers. Its subspace formed by fuzzy variables with finite p^th absolute moments is showed to be a complete para-normed space. The concept of para-normed space is novel, and is an extension of normed space. It is seen that most properties of normed spaces hold in para-normed spaces. Also some useful inequalities in para-normed spaces are obtained.

In this paper we define a new set of spline functions called “Fuzzy Splines” to interpolate fuzzy data. Numerical examples will be presented to illustrate the differences between of using our spline and other interpolations that have been studied before.

The main purpose of this paper is to introduce a new topological structure which is called fuzzifying topological structure determined by the method of co-tower topologies in Menger probabilistic normed spaces. We prove that the fuzzifying topological structure is compatible with the vector structure. A characterization of probabilistically bounded sets in Menger probabilistic normed spaces is obtained.

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.