International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems

This paper proposes a new definition of uncertain time-varying network to capture the uncertain and dynamic characteristics of the network with discrete uncertain link travel times. To find the a priori non-dominated paths in this type of network, three comparison criteria based on the uncertain measure, namely, deterministic dominance rule, first-order uncertain dominance rule and uncertain expected value dominance rule, are proposed to generate non-dominated paths in a single time interval and a time period, as more than one path may exist between an origin and destination for a given departure time. The proposed comparison methods are then applied to solving a simple uncertain time-varying network. The computational results verify the efficiency of three dominance rules for finding non-dominated paths.

In this article, a new human face recognition scheme is proposed. The proposed system is based on the sparsity and fuzziness, and utilizes independent component analysis (ICA). The scheme includes four parts: a fuzzy comprehensive judgment model for estimating whether the information carried by training samples is enough or not, a proper edge extraction operator to discover more hidden information for single image, ICA feature extractor, and a sparse representation model for correlation coefficient calculation to classify testing samples. In view of the intrinsic patterns of gray information distribution of face images, a weighted fuzzy distance for judgement model and cluster analysis is proposed. The new proposed method is tested on ORL, FERET and UMIST databases. The experiment results demonstrate and illustrate the feasibility of the proposed method and the effective performances on recognition rate.

Research in optimization under uncertainty is alive. It assumes different shapes and forms, all concurring to the general goal of designing effective and efficient tools for handling imprecision in an Optimization setting. In this paper we present a new approach for dealing with multiobjective programming problems with fuzzy objective functions. Similar to many approaches in the literature, our approach relies on the deffuzification of involved fuzzy quantities. Our improvement stem from the choice of a deffuzification operator that captures essential features of fuzzy parameters at hand rather than those that yield single values, leading to a loss of many useful information. Two oracles play a pivotal role in the proposed method. The first one returns a near interval approximation to a given fuzzy number. The other one delivers a Pareto Optimal solution of the resulting multiobjective program with interval coefficient. A numerical example is also provided for the sake of illustration.

Frequent itemsets are useful for discovering interesting associations hidden in large databases. Many mining algorithms use data with binary attributes to represent the occurrence of items and find frequent itemsets. However, many real-world applications provide a richer source of transactions with quantitative values. The fuzzy frequent pattern tree algorithm was thus proposed for extracting fuzzy frequent itemsets from the quantitative transactions. In this paper, a tree structure called the upper-bound multiple fuzzy frequent-pattern (UBMFFP)-tree is designed for improving the pruning effect in the mining process. A two-phase fuzzy mining approach based on the tree structure is also proposed to obtain the complete fuzzy frequent itemsets from a quantitative database. The proposed fuzzy mining approach recursively and efficiently finds the upper-bound fuzzy counts of itemsets with the aid of the tree structure. It prunes unpromising itemsets in the first phase, and then finds the actual fuzzy frequent itemsets in the second phase. Experimental results indicate that the proposed UBMFFP-tree algorithm has good performance in terms of execution time and number of tree nodes.

This paper presents a new method for fuzzy c-regression models clustering algorithm. The main motivation for this work is to develop an identification procedure for nonlinear systems using weighted recursive least squares and particle swarm optimization. The fuzzy c-regression models algorithm is sensitive to initialization which leads to the convergence to a local minimum of the objective function. In order to overcome this problem, particle swarm optimization is employed to achieve global optimization of FCRM and to finally tune parameters of obtained fuzzy model. The weighted recursive least squares is used to identify the unknown parameters of the local linear model. Finally, validation results involving simulation of two examples have demonstrated the effectiveness and practicality of the proposed algorithm.

Rough set is mainly concerned with the approximations of objects through an equivalence relation on a universe. Matroid is a generalization of linear algebra and graph theory. Recently, a matroidal structure of rough sets is established and applied to the problem of attribute reduction which is an important application of rough set theory. In this paper, we propose a new matroidal structure of rough sets and call it a parametric matroid. On the one hand, for an equivalence relation on a universe, a parametric set family, with any subset of the universe as its parameter, is defined through the lower approximation operator. This parametric set family is proved to satisfy the independent set axiom of matroids, therefore a matroid is generated, and we call it a parametric matroid of the rough set. Through the lower approximation operator, three equivalent representations of the parametric set family are obtained. Moreover, the parametric matroid of the rough set is proved to be the direct sum of a partition-circuit matroid and a free matroid. On the other hand, partition-circuit matroids are well studied through the lower approximation number, and then we use it to investigate the parametric matroid of the rough set. Several characteristics of the parametric matroid of the rough set, such as independent sets, bases, circuits, the rank function and the closure operator, are expressed by the lower approximation number.

In this paper we develop a new graphical representation of fuzzy numbers, which we then employ to propose a geometrical approach to their defuzzification. The calculations involved in the proposed method and the resultant representation use Moore's semiplane for intervals and therefore are far simpler than those involved in other approaches.

We start by representing triangular and trapezoidal fuzzy numbers in Moore's semiplane. Then we extend this work to any fuzzy number. Although this extension has to be undertaken in ${ℝ}^3$, it preserves all the properties we study for trapezoidal and triangular fuzzy numbers in Moore's semiplane.

In this paper, we firstly introduce two new classes of fuzzy implications generated from one-variable functions, called $\text{(f, g,}\wedge \text{)}$- and $\text{(f, g,}\vee \text{)}$-implications, respectively. Then we give a series of necessary and sufficient conditions that these implications satisfy: left neutrality property, identity principle, ordering principle, law of contraposition, modus ponens and modus tollens, respectively. We also discuss the relations between $\text{(f, g,}\wedge \text{)}$- implication ($\text{(f, g,}\vee \text{)}$-implications, respectively) and other known classes of fuzzy implications.

The article proposes an adaptive, noise-exclusive and assessment-based fuzzy switching median filter for high intensity impulse noise. The filter adaptively changes the size of sliding window in accordance with noise intensity and noise-exclusive operation is performed only on noise-free pixels. These steps thus preserve the image details effectively. Judicious assessment of the previously restored pixels is made in order to use them in replacing the noisy pixels and further improve the efficiency of filter. With these possibilities, fuzzy switching median filter-based approach is also incorporated for improving the performance. Experimental results justified the efficacy of the proposed fuzzy-based filtering method qualitatively and quantitatively for twelve different highly corrupted noisy images, and showed significant improvement to existing algorithms.

In the last 30 years, several distinguished researchers have proposed and discussed different fuzzy versions of well-known Saaty's Analytic Hierarchy Process (AHP). The paper recently published by K. Zhü in the European Journal of Operational Research heavily criticizes the fuzzy approaches to AHP, claiming the fallacy of all of them. Therefore, it seems to be necessary to clarify whether the criticisms are well-founded or not. The present paper aims to rebut Zhü's claims by showing that the evidences and the reasonings in his paper are very poor and far from proving the fallacy of fuzzy AHP.