A New Fuzzy Interpolative Reasoning Method Based on Center of Gravity

Interpolative reasoning methods do not only help reduce the complexity of fuzzy models hut also make inference in sparse-rule based systems possible. This paper presents an interpolative reasoning method by exploiting the center of gravity (COG) property of the fuzzy sets concerned. The method works by first constructing a new inference rule via manipulating two given adjacent rules, and then by using similarity information to convert the intermediate inference results into the final derived conclusion. Two transformation operations are introduced to support such reasoning, which allow the COG of a fuzzy set to remain unaltered before and after the transformation, Results of experimental comparisons are provided to reflect the success of this work

Fuzzy interpolative reasoning via scale and move transformation

Interpolative reasoning does not only help reduce the complexity of fuzzy models but also makes inference in sparse rule-based systems possible. This paper presents an interpolative reasoning method by means of scale and move transformations. It can be used to interpolate fuzzy rules involving complex polygon, Gaussian or other bell-shaped fuzzy membership functions. The method works by first constructing a new inference rule via manipulating two given adjacent rules, and then by using scale and move transformations to convert the intermediate inference results into the final derived conclusions. This method has three advantages thanks to the proposed transformations: 1) it can handle interpolation of multiple antecedent variables with simple computation; 2) it guarantees the uniqueness as well as normality and convexity of the resulting interpolated fuzzy sets; and 3) it suggests a variety of definitions for representative values, providing a degree of freedom to meet different requirements. Comparative experimental studies are provided to demonstrate the potential of this method

Transformation Based Interpolation with Generalized Representative Values

Fuzzy interpolation offers the potential to model problems with sparse rule bases, as opposed to dense rule bases deployed in traditional fuzzy systems. It thus supports the simplification of complex fuzzy models and facilitates inferences when only limited knowledge is available. This paper first introduces the general concept of representative values (RVs), and then uses it to present an interpolative reasoning method which can be used to interpolate fuzzy rules involving arbitrary polygonal fuzzy sets, by means of scale and move transformations. Various interpolation results over different RV implementations are illustrated to show the flexibility and diversity of this method. A realistic application shows that the interpolation-based inference can outperform the conventional inferences

Fuzzy interpolation with generalized representative values

Fuzzy interpolative reasoning offers the potential to model problems using sparse rule bases, as opposed to dense rule bases deployed in traditional fuzzy systems. It thus supports the simplification of complex fuzzy models in terms of rule number and facilitates inferences when limited knowledge is available. This paper presents an interpolative reasoning method by means of scale and move transformations