International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems

Song et al.[3] proposed a new fuzzy time series model by means of defining some new operations on fuzzy numbers. They presented the new model in the form of two theorems, which indicate that the value of F(t) at t+1 can be related to its previous ones by means of forward and backward linguistic difference, as a necessary condition for the homogeneous fuzzy time series. In this note, we prove that it is also a sufficient condition for the homogeneous fuzzy time series.

The contents and meanings of mapping relationships between physical domain and function domain in different design stages, such as conceptual design, detail design and enhancement design, were analyzed. According to the analysis results, the fuzzy mapping between physical domain and function domain in different design stages was established by integrating objective information and subjective information in the design process, such as expert's knowledge, designer's preferences and customer's requirements, where the fuzzy sets, fuzzy mapping and fuzzy transition were used. The property table of structure behavior parameters was established based on the fuzzy mapping relationships. The fuzzy mapping is very important to optimize product structure, perfect product function, meet the diversified and individual requirements of customers. Finally, an example was used to illustrate the fuzzy mapping relationships between physical domain and function domain in different design stages.

A method to assign fuzzy labels to unlabeled hypertext documents based on hyperlink structure information is first proposed. Then, the construction of the fuzzy transductive support vector machines is described. Also, an algorithm to train the fuzzy transductive support vector machines is presented. While in the transductive support vector machines all the test examples are treated equally, in the fuzzy transductive support vector machines, test examples are treated discriminatively according to their fuzzy labels, hence a more reliable decision function. Experimental results on the WebKB corpus show that, by fusing the plain text information and the hyperlink structure information, much better classification performance can be achieved.

Rough set theory is a relatively new mathematical tool for use in computer applications in circumstances which are characterized by vagueness and uncertainty. In this paper, we introduce the concepts of information entropy, rough entropy and knowledge granulation in rough set theory, and establish the relationships among those concepts. These results will be very helpful for understanding the essence of concept approximation and establishing granular computing in rough set theory.

Theories of fuzzy sets and rough sets have emerged as two major mathematical approaches for managing uncertainty that arises from inexact, noisy, or incomplete information. They are generalizations of classical set theory for modelling vagueness and uncertainty. Some integrations of them are expected to develop a model of uncertainty stronger than either. The present work may be considered as an attempt in this line, where we would like to study fuzziness in probabilistic rough set model, to portray probabilistic rough sets by fuzzy sets. First, we show how the concept of variable precision lower and upper approximation of a probabilistic rough set can be generalized from the vantage point of the cuts and strong cuts of a fuzzy set which is determined by the rough membership function. As a result, the characters of the (strong) cut of fuzzy set can be used conveniently to describe the feature of variable precision rough set. Moreover we give a measure of fuzziness, fuzzy entropy, induced by roughness in a probabilistic rough set and make some characterizations of this measure. For three well-known entropy functions, including the Shannon function, we show that the finer the information granulation is, the less the fuzziness (fuzzy entropy) in a rough set is. The superiority of fuzzy entropy to Pawlak's accuracy measure is illustrated with examples. Finally, the fuzzy entropy of a rough classification is defined by the fuzzy entropy of corresponding rough sets. and it is shown that one possible application of it is lies in measuring the inconsistency in a decision table.

In this paper, the well-known Egoroff's theorem in classical measure theory is established on monotone non-additive measure spaces. Taylor's theorem, which concerns almost everywhere convergence of measurable function sequence in classical measure theory, is also generalized. The converse problem of the theorems are discussed, and a necessary and sufficient condition for the Egoroff's theorem is obtained on semicontinuous fuzzy measure space with S-compactness.

We discuss the OWA and Choquet integral aggregation operators and point out the central role the ordering operation plays in these operators. We extend the capabilities of the Choquet integral aggregation by allowing the ordering to be induced by some values other then those being aggregated. This allows us to consider an induced Choquet Choquet integral aggregation operator. We look at the properties of this operator. We then look at its applications. Among the applications considered are aggregations guided by linguistic and other ordinal structures. We look at the use of induced aggregation in nearest neighbor methods. We also consider the Choquet aggregation of complex objects such as matrices and vectors.

–fuzzy acceptors in relationship with formal –fuzzy languages and –fuzzy grammars are studied, where is a bounded chain. Applications of fuzzy linguistic methods in syntactic pattern recognition are described.

In this paper we are interested in determining the fuzzy ordering, from smallest to largest, of any finite set of fuzzy numbers. We investigate two methods: (1) using a weak fuzzy ordering; and (2) using a strong fuzzy ordering. Employing a strong fuzzy ordering we show that any finite set of fuzzy numbers has a unique ranking from smallest to largest.

In this paper, the concepts of countable presemi-compactness and presemi-Lindelof property in L-topological spaces are introduced. They are defined for arbitrary L-subsets, and some of their characteristic properties and fundamental properties are studied.

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.