This paper presents a study on inference in a Fuzzy Logic Controller (FLC). Inference is made up of interpretation, implication, combination and defuzzification. These last two steps can be performed in two sequences. An explanation, through approximate reasoning, on how to implement other than the welìknown Mamdani and Larsen implications is given. (Dis)advantages of several combinations of im...

We introduce a new redistancing method for level set functions. This method applies in a finite element setting and uses a gradient recovery technique. Based on the recovered gradient a quasi-normal field on the zero level of the finite element level set function is defined and from this an approximate signed distance function is determined. For this redistancing method rigorous error bounds ar...

In this paper, we concentrate on linear programming problems in which both the right-hand side and the technological coefficients are fuzzy numbers.We consider here only the case of fuzzy numbers with linear membership function. The determination of a crisp maximizing decision [2] is used for a defuzzification of these problems. The crisp problems obtained after the defuzzification are non-line...

This paper presents circular polar coordinates transformation of periodic fuzzy membership function. The purpose is identification of domain of periodic membership functions in consequent part of IF-THEN rules. Proposed methods in this paper remove complicatedness concerning domain of periodic membership function from defuzzification in fuzzy approximate reasoning. Defuzzification on circular p...

We extend the resistance distance kernel to the domain of signed dissimilarity values, and show how it can be applied to collaborative rating prediction. The resistance distance is a graph kernel inspired by electrical network models where edges of a graph are interpreted as electrical resistances. We model the similarity between users of a large collaborative rating database using this signed ...

This paper presents a new learning algorithm for the design of Mamdani-type or fully-linguistic fuzzy controllers based on available input-output data. It relies on the use of a previously introduced parametrized defuzzification strategy. The learning scheme is supported by an investigated property of the defuzzification method. In addition, the algorithm is tested by considering a typical non-...

Many applications of fuzzy set theory require defuzzification and ranking approaches based on alpha level sets because exact membership functions may not always be available. In this article, we have assumed that exact membership functions can be approximated using piecewise linear functions based on alpha level sets and derived two analytical formulas to meet such a requirement. The two formul...

This paper presents a study on inference in a Fuzzy Logic Controller (FLC). Inference is made up of interpretation, implication, combination and defuzzification. These last two steps can be performed in two sequences. An explanation, through approximate reasoning, on how to implement other than the welìknown Mamdani and Larsen implications is given. (Dis)advantages of several combinations of im...

This chapter presents a new optimization method for clustering fuzzy data to generate Type-2 fuzzy system models. For this purpose, first, a new distance measure for calculating the (dis)similarity between fuzzy data is proposed. Then, based on the proposed distance measure, Fuzzy c-Mean (FCM) clustering algorithm is modified. Next, Xie-Beni cluster validity index is modified to be able to valu...