International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems

In this paper, we present some methods for constructing copulas with a given diagonal section that are not necessarily symmetric. An interesting application for the construction of copulas with given tail dependence coefficients is, hence, provided.

Different methods have been proposed for ranking fuzzy numbers. These include methods based on distances, centroid point, coefficient of variation, and weighted mean value. However, there is still no method that can always give a satisfactory result to every situation; some are counterintuitive and not discriminating. This paper presents an approach for ranking fuzzy numbers with integral value that is an extension of the index of Liou and Wang. This method, that is independent of the type of membership function used, can rank more than two fuzzy numbers simultaneously. This ranking method use an index of optimism to reflect the decision maker's optimistic attitude, but rather it also contains an index of modality that represents the neutrality of the decision maker. The approach is illustrated with numerical examples.

This paper studies a class of fuzzy random differential equations with non-Lipschitz coefficients. We first generalize the Bihari's inequality which is later applied to solving the related problem of uniqueness of the solution to fuzzy random differential equations with non-Lipschitz coefficients. The dependence of fuzzy random differential equations on initial values is also discussed. Finally, the non confluence property of the solutions to fuzzy random differential equations is investigated.

When the outliers exist in the data set, fuzzy regression gives incorrect results. A few number of researchers considered this problem and proposed linear-programming-based methods and fuzzy least-squares methods to deal with the outliers problem. In this paper, we develop a new model along with a linear-programming-based approach for computation of fuzzy regression models. The problem of outliers is modeled with this approach. Two examples are illustrated to compare the performance of proposed approach with those given in literature. Results from numerical examples show that our approach gives good solutions.

An interval-valued fuzzy logic controller (I-V FLC) is presented to control a class of nonlinear distributed parameter systems. The proposed FLC is inspired by human operators' knowledge or expert experience to control a distributed parameter process from the point of view of overall space domain. Based on spatial fuzzy set, the I-V FLC employs a centralized rule base over the space domain. Using spatial membership degree fusion operation, the I-V FLC can compress spatial input information into interval-valued fuzzy sets and then execute an interval-valued rule inference mechanism; thereby the I-V FLC has the capability to process spatial information over the space domain. Compared with traditional FLCs, the I-V FLC can improve its control performance due to its increased ability to express and process spatial information. The I-V FLC is successfully applied to a catalytic packed-bed reactor and compared with the traditional FLCs. The results demonstrate its effectiveness to control the unknown nonlinear distributed parameter process.

In some probabilistic problems, complete information about the probability model may not exist. In this article, we obtain a lower and upper probability for an arbitrary event by using rough set theory and then a measurement for inclusiveness of events is introduced.

Recently, Zhao and Liu [IJUFKS 11 (2003) 573–586] proposed a "fuzzy elementary renewal theorem" and "fuzzy renewal rewards theorem" for a renewal process in which the inter-arrival times and rewards are characterized as continuous fuzzy variables. The continuity assumption is restrictive. In this note, we prove the same results without the assumption of continuity of the inter-arrival times and rewards.

Theory of fuzzy set and theory of rough set are two useful means of describing and modeling of uncertainty in ill defined environment where precise mathematical analysis are not suitable. Classical rough set theory is based on equivalent relation. It has been indicated that it could be generated to case with a similarity relation. So far, there has been theoretical investigations on roughness measure of fuzzy set based on equivalent relation. The intention of this paper is to go further and propose a measure of roughness of a type-2 fuzzy set based on similarity relation and prove some properties of this novel measure.

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.