International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems

This paper deals with an important probabilistic knowledge integration problem: revising a Bayesian network (BN) to satisfy a set of probability constraints representing new or more specific knowledge. We propose to solve this problem by adopting IPFP (iterative proportional fitting procedure) to BN. The resulting algorithm E-IPFP integrates the constraints by only changing the conditional probability tables (CPT) of the given BN while preserving the network structure; and the probability distribution of the revised BN is as close as possible to that of the original BN. Two variations of E-IPFP are also proposed: 1) E-IPFP-SMOOTH which deals with the situation where the probabilistic constraints are inconsistent with each other or with the network structure of the given BN; and 2) D-IPFP which reduces the computational cost by decomposing a global E-IPFP into a set of smaller local E-IPFP problems.

In this paper, an adaptive fuzzy tracking control is presented for a class of SISO nonlinear strict feedback systems with unknown time delays. The proposed algorithm does not use the backstepping scheme rather it converts the strict-feedback time-delayed system to the normal form. The Mamdani-type fuzzy system is employed to approximate on-line the lumped uncertain system nonlinearity. The developed controller guarantees uniform ultimate boundedness of all signals in the closed-loop system. The designed control law is independent of the time delays and has a simple form with only one adaptive parameter vector needed to be updated on-line. As a result, the proposed control algorithm is considerably simpler than the previous ones based on backstepping. The Lyapunov stability of the fuzzy system parameters and the filtered tracking error is employed to guarantee semiglobal uniform boundedness for the closed loop system. Simulation results are presented to verify the effectiveness of the proposed approach.

In order to solve group decision making (GDM) problems where the preference relations are provided by decision makers with incomplete fuzzy and interval numbers, this paper develops a GDM approach on the basis of multiple objective optimization and goal programming methods. The proposed approach first analyzes the two types of preference relations and then builds their respective optimization models. Subsequently, an integrated programming model combining the two preference relations is developed to minimize the inconsistency among the decision makers' opinions. By solving the programming model, the ranking of alternatives or selection of the most desirable alternative can be obtained using the intermediate priority vector. Two numerical examples including incomplete fuzzy and interval preference relations are examined to illustrate and show the applicability of the proposed approach.

This paper proposes a Genetic Algorithm for jointly performing a feature selection and granularity learning for Fuzzy Rule-Based Classification Systems in the scenario of highly imbalanced data-sets. We refer to imbalanced data-sets when the class distribution is not uniform, a situation that it is present in many real application areas. The aim of this work is to get more compact models by selecting the adequate variables and adapting the number of fuzzy labels for each problem, improving the interpretability of the model. The experimental analysis is carried out over a wide range of highly imbalanced data-sets and uses the statistical tests suggested in the specialized literature.

The neighborhood system based rough set is a generalization of Pawlak's rough set model since the former uses the neighborhood system instead of the partition for constructing target approximation. In this paper, the neighborhood system based rough set approach is employed to deal with the incomplete information system. By the coverings induced by the maximal consistent blocks and the support sets of the descriptors, respectively, two neighborhood systems based rough sets are explored. By comparing with the original maximal consistent block and descriptor based rough sets, the neighborhood system based rough sets hold the same lower approximations and the smaller upper approximations. Furthermore, the concept of attribute reduction is introduced into the neighborhood systems and the corresponding rough sets. The judgement theorems and discernibility functions to compute reducts are also presented. Some numerical examples are employed to substantiate the conceptual arguments.

Uncertain differential equation with jumps is a type of differential equation driven by two classes of uncertain processes, namely canonical process and renewal process. Based on uncertain differential equation with jumps, this paper proposes a stock model with jumps for uncertain financial markets. Furthermore, the European call and put option pricing formulas for the stock model are formulated and some mathematical properties of them are studied. Finally, some generalized uncertain stock models with jumps are discussed.

In this paper, new similarity, inclusion measure and entropy between type-2 fuzzy sets corresponding to grades of memberships are proposed. We also create the relationships among these measures between type-2 fuzzy sets. Several examples are used to present the calculation of these similarity, inclusion measure and entropy between type-2 fuzzy sets. The comparison results show that the proposed similarity measure presents better than those of Hung and Yang (2004) and Yang and Lin (2009). Moreover, measuring the similarity between type-2 fuzzy sets is important in clustering. We also use the proposed similarity measure as a clustering method for type-2 fuzzy sets.

Multiple Criteria Decision Making (MCDM) aims at giving people a knowledge recommendation concerning a set of objects evaluated from multiple preference-ordered attributes. The Superiority and Inferiority Ranking (SIR) is a generation of the well-known outranking approach-PROMETHEE, which is an efficient approach for MCDM. As the traditional MCDM approach, however, it faces the obstacle in handling uncertainties of real world. We are concerned about the issue on how to extend the traditional MCDM approach for applications in uncertain environments. This paper proposes a new Intuitionistic Fuzzy SIR (IF-SIR for short) approach and focuses on its application to supplier selection which is the important activity in supply chain management. Toward practical applications, two factors are considered here: (1) multiple decision makers and (2) decision information in the form of linguistic terms. We firstly identify these terms via Intuitionistic Fuzzy Set (IFS) which is proven to be a powerful mathematical tool in modeling uncertain information. Then, we provide the IF-SIR approach for group aggregation and decision analysis. Hereinto, a rule-based method is developed for ranking and selection of suppliers. Finally, an illustrative example is used for illustration of the proposed approach.

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.