International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems

The turbulent flow consists of coherent time- and space-organized vortical structures with a particular formation and instability cycle. Research has already shown that some dynamic systems and experimental models still cannot provide a good nonlinear analysis of turbulent time series because in the real turbulent flow there exist very complicated nonlinear behaviors affected by many vague factors. An approach of fuzzy piecewise regression analysis has been proposed to predict the nonlinear time series of turbulent flows. In this paper, we propose kernel interval regression machine for nonlinear time series analysis of turbulent flows. The proposed method applies the kernel trick to interval regression analysis in terms of the inner products of input vectors. In order to indicate the performance of this method, we present an example of predicting the near-wall turbulence time series as a verifiable model. Furthermore, we compare this method with fuzzy piecewise regression model. Experimental results show that the proposed method is very attractive for the turbulence time series in nonlinear analysis and in fuzzy environments.

In this study, we deal with the optimization methodology in fuzzy decision-making systems. The issue of convergence for sequences of integrable fuzzy variables is discussed. Based on credibility theory, a new class of fuzzy programming—two-stage fuzzy programming or fuzzy programming with recourse problem is introduced, and a discussion about basic properties of the recourse problems is included. To solve the two-stage fuzzy programming problems, a heuristic solution method, which combines fuzzy simulations, genetic algorithm and neural network, is proposed, and the convergence of approximating a recourse functions is proved. We provide three numerical examples to illustrate the feasibility and effectiveness of the designed algorithm.

In this work we define a generalization of the twofold integral (generalization of the Choquet and Sugeno integrals) that operates in an arbitrary universal set. A graphical representation of this integral is also introduced.

Tandem queueing models play an important role in many real world systems such as computer systems, production lines, and service systems. This paper proposes a procedure to construct the membership functions of the performance measures in tandem queueing systems, in that the arrival rate and service rates are fuzzy numbers. The basic idea is to transform a fuzzy tandem queue to a family of crisp tandem queues by applying the α -cut approach. Then on the basis of α -cut representation and the extension principle, a pair of mathematical programs is formulated to describe this family of crisp tandem queues, via which the membership functions of the performance measures are derived. Two numerical examples are solved successfully to demonstrate the validity of the proposed approach. Since the performance measures are expressed by membership functions rather than by crisp values, the fuzziness of input information is completely conserved. Thus the proposed approach for fuzzy systems can represent the system more accurately, and more information is provided for designing queueing systems. The successful extension of tandem queues to fuzzy environments permits tandem queueing models to have wider applications.

Traditionally the beta distribution has been used due to its ease for computing the mean of tasks, times, cash-flows, etc. because, in this case, the expected value is a weighted average of optimistic, most likely and pessimistic values. One of the critiques of PERT has been the difficulty of introducing the level of confidence that the expert has in his own estimate of the modal value. The Belief in Fuzzy Probability Estimations of Time (BIFPET) model uses human judgement instead of stochastic assumptions to determine the duration of a project. Thus, each supervisor responsible of an activity specifies the three values with their respective probabilities. The manager accepts these probabilities or may extend them within a certain range, according to his belief in these likelihoods or the degree of control exercised by himself in achieving the lower bound of the expected value. However, this approach can be implemented in the PERT methodology. Thus, in this paper, we introduce the confidence that the manager has in the most likely value supplied by the supervisor in order to determine the specific beta distribution to model the variable, showing the advantages of this intuitive procedure which moreover can be easily implemented.

Interval-valued fuzzy sets constitute an extension of fuzzy sets which give an interval approximating the "real" (but unknown) membership degree. Interval-valued fuzzy sets are equivalent to intuitionistic fuzzy sets in the sense of Atanassov which give both a membership degree and a non-membership degree, whose sum must be smaller than or equal to 1. Both are equivalent to L-fuzzy sets w.r.t. a special lattice L*. In fuzzy set theory, an important class of triangular norms is the class of those that satisfy the residuation principle. In a previous paper⁵ we gave a construction for t-norms on L* satisfying the residuation principle which are not t-representable. In this paper we investigate the Smets-Magrez axioms and some other properties for the residual implicator generated by such t-norms.

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.