International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems

A solution of n-person games is proposed, based on the minimum deviation from statistical equilibrium subject to the constraints imposed by the group rationality and individual rationality. The new solution is compared with the Shapley value and von Neumann-Morgenstern's core of the game in the context of the 15-person game of passing and defeating resolutions in the UN Security Council involving five permanent members and ten nonpermanent members. A coalition classification, based on the minimum ramification cost induced by the characteristic function of the game, is also presented.

This paper proposes a recurrent neural network of fuzzy units, which may be used for approximating a hetero-associative mapping and also for pattern classification. Since classification is concerned with set membership, and objects generally belong to sets to various degrees, a fuzzy network seems a natural for doing classification. In the network proposed here each fuzzy unit defines a fuzzy set. The fuzzy unit in the network determines the degree to which the input vector to the unit lies in that fuzzy set. The fuzzy unit may be compared to a perceptron in which case the input vector is compared to the weighting vector associated with the unit by taking the dot product. The resulting membership value in case of the fuzzy unit is compared to a threshold. Training of a fuzzy unit is based on an algorithm for solving linear inequalities similar to the method used for Ho-Kashyap recording. Training of the whole network is done by training each unit separately. The training algorithm is tested by trying the algorithm out on representations of letters of the alphabet with their noisy versions. The results obtained by the simulation are very promising.

In this paper we shall develop a procedure for combining numerical and linguistic information without loss of information in the transformation processes between numerical and linguistic information, taking as base for representing the information the 2-tuple fuzzy linguistic representation model. We shall analyze the conditions to impose the linguistic term set in order to ensure that the combination procedure does not produce any loss of information. Afterwards the aggregation process will be applied to a decision procedure over a multi-attribute decision-making problem dealing with numerical and linguistic information, that is, with qualitative and quantitative attributes.

Preselection of rules is an algorithm which chooses one rule from linguistic description of some process. This rule is then used for inference instead of the whole description. This article studies properties of preselection and proposes use of measures of resemblance for choosing the rule which best fits the observation.

We studied here on some simple examples the interaction between valuation family, parameters and ranking result. The ranking method studied is based upon the idea of associating with a fuzzy number a scalar value, its valuation, and using this valuation to compare and order fuzzy numbers. The valuation method considered was introduced initially by the Yager and Filev. This valuation consists in the integration over α-levels, of the average of each α-cut weighted by a weight distribution function. We finish by introducing a new weight distribution function.

Equivalence relations and orderings are key concepts of mathematics. For both types of relations, formulations within the framework of fuzzy relations have been proposed already in the early days of fuzzy set theory. While similarity (indistinguishability) relations have turned out to be very useful tools, e.g. for the interpretation of fuzzy partitions and fuzzy controllers, the utilization of fuzzy orderings is still lagging far behind, although there are a lot of possible applications, for instance, in fuzzy preference modeling and fuzzy control. The present paper is devoted to this missing link. After a brief motivation, we will critically analyze the existing approach to fuzzy orderings. In the main part, an alternative approach to fuzzy orderings, which also takes the strong connection to gradual similarity into account, is proposed and studied in detail, including several constructions and representation results.

It is often necessary to divide a certain amount of money between n participants, i.e., to assign, to each participant, a certain portionw_i≥0 of the whole sum (so that w₁+⋯+ w_n=1). In some situations, from the fairness requirements, we can uniquely determine these "weights" w_i. However, in some other situations, general considerations do not allow us to uniquely determine these weights, we only know the intervals of possible fair weights. We show that natural fairness requirements enable us to choose unique weights from these intervals; as a result, we present an algorithm for fair division under interval uncertainty.

This section is maintained by Vladik Kreinovich. Please send your abstracts (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.