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

Scale and move transformation-based fuzzy interpolative reasoning:A revisit

This paper generalises the previously proposed interpolative reasoning method 151 to cover interpolations involving complex polygon, Gaussian or other bell-shaped fuzzy membership functions. This can be achieved by the generality of the proposed scale and move transformations. 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 generalised method has two advantages thanks to the elegantly proposed transformations: I) It can easily handle interpolation of multiple antecedent variables with simple computation; and 2) It guarantees the uniqueness as well as normality and convexity of the resulting interpolated fuzzy sets. Numerical examples are provided to demonstrate the use of this method