Yeung Yam

A new method for avoiding abnormal conclusion for /spl alpha/-cut based rule interpolation

The first published result in fuzzy rule interpolation was the /spl alpha/-cut based fuzzy rule interpolation, termed as KH-interpolation, originally devoted for complexity reduction. Some deficiencies of this method were presented, such as abnormal conclusion for a certain configuration of the involved fuzzy sets. This inspired several authors to propose various conceptually different fuzzy interpolation approaches, however, none of those algorithms has such a low computational complexity as the KH-method. In the frequent practical cases of using piecewise linear sets only with three of four characteristic points the new methods maintain their relatively high complexity. The goal of this paper is to modify properly the original /spl alpha/-cut based interpolation approach to eliminate the abnormality problem and to ensure normal conclusion in the practical case when the fuzzy sets are of a finite number of characteristic points, while at the same time maintaining the advantageous properties of the original method. A concise analysis of the proposed method is also presented.

Stability of a new interpolation method

Aims to complete the analysis of an /spl alpha/-cut based interpolation technique originating from the KH interpolation. Our goal is to investigate its stability behaviour. As it was shown in Joo et al. (1997) and Tikk et al. (1999) the original KH interpolation is stable in the sense that if inputs change slightly the output does not change much, as well. The main result of this paper shows that this significant feature of the KH interpolation can be carried over for the proposed method. A possible generalization of the proposed method is also presented.

A general extension of fuzzy SVD rule base reduction using arbitrary inference algorithm

Fuzzy rule base reduction has emerged recently as an important topic of research in fuzzy theories. Main difficulty of any generated rule bases is that the number of rules increases exponentially with the number of variables and fuzzy terms. Singular value decomposition (SVD) based method has been first published for Sugeno algorithm. It was then extended to the Takagi-Sugeno controller, to rule bases with nonsingleton consequents and to fuzzy rule interpolation algorithms. However, the application of these methods are restricted to some special inference engines and rule bases. In this paper we introduce a general SVD-based rule base reduction method for arbitrary rule base, namely arbitrary shaped antecedents, inference algorithm, and consequent sets described by arbitrary (but finite) number of parameters. We demonstrate the use of the proposed method on a control system of automatically guided vehicle.

Singular value-based fuzzy rule interpolation

In sparse fuzzy rule bases, conventional fuzzy reasoning methods cannot reach a proper conclusion. To eliminate this problem interpolative reasoning has emerged in fuzzy research as a new topic. If the number of variables or the number of fuzzy terms is growing the size of the rule base increases exponentially, hence, the inference/control time also increases considerably. Interpolative reasoning can help to reduce the number of rules, but does not eliminate the problem of exponential growth. Singular value based rule base reduction (FuzzySVD) methods have been published with various conventional methods. This paper introduces the extension of the FuzzySVD method to the specialized fuzzy rule interpolation method to achieve more significant reduction.

Singular value decomposition of linguistic symbol-array

This paper is motivated by the fact that the application of the linguistic symbol-array is popular in artificial intelligence techniques. Sometimes their use is restricted by their exponential complexity, like in fuzzy logic algorithms. The main goals of this paper are two fold: one is to define a general form of the most widely applied linguistic symbol based relations; and the second is to define a storage-space complexity reduction algorithm to the general form. The key idea of this paper is supported by the fuzzy reduction approach based on singular value decomposition.