International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems

In this paper we study a generalization of a submeasure notion which is related to a probabilistic concept, especially to Menger spaces where triangular norms play a crucial role. The resulting notion of a τ_T-submeasure is suitable for modeling those situations in which we have only probabilistic information about the measure of the set. We characterize a class of universal τ_T-submeasures (i.e., τ_T-submeasures for an arbitrary t-norm T) and give explicit formulas for τ_T-submeasures for some classes of t-norms. Also, transformations and aggregations of τ_T-submeasures are discussed.

Intuitionistic fuzzy set, was introduced by Atanassov, has been applied to many different fields, such as logic programming, pattern recognition, and decision making, etc. However, so far there has been few investigation on how to transform attribute tested values of alternative into a intuitionistic fuzzy number, and then complete decision making by intuitionistic fuzzy information. In this paper, the original attribute value (objective information) are characterized by crisp number which are given by decision maker. We define the concepts of supporting, opposing and neutral set of alternative respectively, develop an approach for transform attribute values into intuitionistic fuzzy number, and determine the order of alternatives based on the score and the degree of accuracy of the intuitionistic fuzzy number. Finally, a practical example is provided to illustrate the developed method.

Perhaps more than ever in the European Union many groups and associations of companies and institutions are trying, in different ways, to play an active role in the economic scene of the Union.

We verified, on the basis of information obtained, that the studies which precede the decision of a Financial Corporation to initiate the launching of a public offering on a certain economic unit/company or to acquire the shares of a Public Limited Company to take over control, are based on numerical mathematics, adapted mainly to the study of the future hypothetical profitability of the group resulting from the merging process or fusion.

We present a proposal based on combinatorial pretopology that leads to an algorithm capable of solving our objective adequately.

The theory of cooperative games with vague cooperation is based on modelling fuzzy coalitions as fuzzy subsets of the set of all players who participate in the coalitions with some part of their "power". Here, we suggest an alternative approach assuming that coalitions are formed by relatively compact groups of individual players each of which represents a specific common interest. Each individual player may participate in several such groups and, as their member, in several coalitions. Our aim is to show that such an alternative model of fuzzy coalitions, in spite of its seemingly higher complexity, offers an interesting more sophisticated reflection of the structure of vague cooperation and of relations being in its background.

This study proposes fuzzy multiple objective programming to determine the measure of fitness and the number of change-points in an interval piecewise regression model. To increase the measure of fitness, Tanaka and Lee proposed a conceptual procedure, which is a heuristic approach and becomes complicated for determining the proper polynomial. Therefore, a multiple objective approach is adopted to obtain a compromise solution among three objectives — maximizing the measure of fitness, minimizing the number of change-points and minimizing the width to obtain the interval regression models. By using the proposed method, a better measure of fitness can be obtained. Two numerical examples are used as demonstrations to illustrate our approach in more detail.

Beta distributions have been applied in a variety of fields in part due to its similarity to the normal distribution while allowing for a larger flexibility of skewness and kurtosis coverage when compared to the normal distribution. In spite of these advantages, the two-sided power (TSP) distribution was presented as an alternative to the beta distribution to address some of its short-comings, such as not possessing a cumulative density function (cdf) in a closed form and a difficulty with the interpretation of its parameters. The introduction of the biparabolic distribution and its generalization in this paper may be thought of in the same vein. Similar to the TSP distribution, the generalized biparabolic (GBP) distribution also possesses a closed form cdf, but contrary to the TSP distribution its density function is smooth at the mode. We shall demonstrate, using a moment ratio diagram comparison, that the GBP distribution provides for a larger flexibility in skewness and kurtosis coverage than the beta distribution when restricted to the unimodal domain. A detailed mean-variance comparison of GBP, beta and TSP distributions is presented in a Project Evaluation and Review Technique (PERT) context. Finally, we shall fit a GBP distribution to an example of financial European stock data and demonstrate a favorable fit of the GBP distribution compared to other distributions that have traditionally been used in that field, including the beta distribution.

A fuzzy-neural fluctuation smoothing rule is proposed in this study to improve the performance of scheduling jobs with various priorities in a semiconductor manufacturing factory. The fuzzy-neural fluctuation smoothing rule is modified from the well-known fluctuation smoothing rule by improving the accuracy of estimating the remaining cycle time of a job, which is done by applying Chen's fuzzy-neural approach with multiple buckets. To evaluate the effectiveness of the proposed methodology, production simulation is also applied in this study. According to experimental results, incorporating a more accurate remaining cycle time estimation mechanism did improve the scheduling performance especially in reducing the average cycle times. Besides, the fuzzy-neural fluctuation smoothing rule was also shown to be a Pareto optimal solution for scheduling jobs with various priorities in a semiconductor manufacturing factory.

In this paper, we discuss some properties in uncertainty theory when uncertain measure is continuous. Firstly, the judgement conditions of continuous uncertain measure are proposed. Secondly, basic properties of uncertainty distribution and critical values of uncertain variable are proved. Finally, the convergence theorems for expected value are discussed.

In this paper, we generalize Ying's model of linguistic quantifiers [M.S. Ying, Linguistic quantifiers modeled by Sugeno integrals, Artificial Intelligence, 170 (2006) 581-606] to intuitionistic linguistic quantifiers. An intuitionistic linguistic quantifier is represented by a family of intuitionistic fuzzy-valued fuzzy measures and the intuitionistic truth value (the degrees of satisfaction and non-satisfaction) of a quantified proposition is calculated by using intuitionistic fuzzy-valued fuzzy integral. Description of a quantifier by intuitionistic fuzzy-valued fuzzy measures allows us to take into account differences in understanding the meaning of the quantifier by different persons. If the intuitionistic fuzzy linguistic quantifiers are taken to be linguistic fuzzy quantifiers, then our model reduces to Ying's model. Some excellent logical properties of intuitionistic linguistic quantifiers are obtained including a prenex norm form theorem. A simple example is presented to illustrate the use of intuitionistic linguistic quantifiers.

Based on the geometrical representation of generalized Atanassov's intuitionistic fuzzy sets (GA-IFSs), we take into account all three parameters describing GA-IFSs, propose a method to calculate the correlation coefficient for GA-IFSs in a finite set and a probability space, respectively, and discuss some properties of correlation and correlation coefficient of GA-IFSs.

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: Vladik Kreinovich, Department of Computer Science, University of Texas at El Paso, El Paso, TX 79968, USA.