Support vector machines (SVMs) proved to be highly efficient computational tools in various classification tasks. However, the knowledge learned by an SVM is encoded in a long list of parameter values, and it is not easy to comprehend what the SVM is actually computing. We show that certain types of SVMs are mathematically equivalent to a specific fuzzy–rule base, the fuzzy all–permutations rul...

Fuzzy logic has proven to be a promising method for developing simple, robust controllers for uncertain or nonlinear systems. One problem with fuzzy controllers, however, is that they are difficult to apply to higher-order systems. The reason for this is that the number of rules required for the rule base increases geometrically with the number of states. For example, if a system was fourth-ord...

Fuzzy rule-based systems (FRBS) use the principle of fuzzy sets and fuzzy logic to describe vague and imprecise statements and provide a facility to express the behaviours of the system with a human-understandable language. Fuzzy information, once defined by a fuzzy system, is fixed regardless of the circumstances and therefore makes it very difficult to capture the effect of context on the mea...

abstract— in this paper, a new extended method of multi criteria decision making based on fuzzy-topsis theory is introduced. fuzzy mcdm algorithm for determining the best choice among all possible choices when the data are fuzzy is also presented. using a new index leads to procedure for choosing fuzzy ideal and negative ideal solutions directly from the fuzzy data observed alternatives.in this...

Constructing concise fuzzy rule bases from databases containing many features present an important yet challenging goal in the current researches of fuzzy rule-based systems. Utilization of all available attributes is not realistic due to the “curse of dimensionality” with respect to the rule number as well as the overwhelming computational costs. This paper proposes a general framework to trea...

the concept of intelligently controlling the search process of gravitational search algorithm (gsa) is introduced to develop a novel data mining technique. the proposed method is called fuzzy gsa miner (fgsa-miner). at first a fuzzy controller is designed for adaptively controlling the gravitational coefficient and the number of effective objects, as two important parameters which play major ro...

Fuzzy logic in narrow sense: A summary on t-norm-based logics In the seventies and eighties operations over [0,1] corresponding to connectives of a multi-valued logic has been studied and used to define Fuzzy Set operations. From then t-norms, t-conorms, negation and implication functions have been widely studied and applied. The nineties were the start point of the study of the kernel of fuzzy...

This paper briefly elaborates on a development in (applied) fuzzy logic that has taken place in the last couple of decades, namely, the complementation or even replacement of the traditional knowledge-based approach to fuzzy rule-based systems design by a data-driven one. It is argued that the classical rule-based modeling paradigm is actually more amenable to the knowledge-based approach, for ...

This contribution is concerned with the interpretability of fuzzy rule-based systems. While this property is widely considered to be a crucial one in fuzzy rule-based modeling, a more detailed formal investigation of what "interpretability" actually means is not available. So far, interpretability has most often been associated with rather heuristic assumptions about shape and mutual overlappin...