Iterative rule learning is a common strategy for fuzzy rule induction using stochastic population-based algorithms (SPBAs) such as Ant Colony Optimisation and genetic algorithms. Several SPBAs are run in succession with the result of each being a rule added to an emerging final ruleset. Between SPBA runs, cases in the training set that are covered by the newly evolved rule are generally removed...

Backfitting of fuzzy rules is an Iterative Rule Learning technique for obtaining the knowledge base of a fuzzy rule-based system in regression problems. It consists in fitting one fuzzy rule to the data, and replacing the whole training set by the residual of the approximation. The obtained rule is added to the knowledge base, and the process is repeated until the residual is zero, or near zero...

Nowadays, one of the most important areas of application of fuzzy set theory are fuzzy rule-based systems. These kinds of systems constitute an extension of classical rule-based systems, because they deal with “IF-THEN” rules whose antecedents and consequents are composed of fuzzy logic statements instead of classical logic. They have been successfully applied to a wide range of problems in dif...

SLAVE is an inductive learning algorithm that uses concepts based on fuzzy logic theory. This theory has been shown to be a useful representational tool for improving the understanding of the knowledge obtained from a human point of view. Furthermore, SLAVE uses an iterative approach for learning based on the use of a genetic algorithm (GA) as a search algorithm. In this paper, we propose a mod...

" The problem of learning rules for a fuzzy inference model directly from empirical observations, without resorting to assessments from experts is considered. We develop a method that builds uncertain rules from a set of examples. These rules match the following pattern: If X is A then Y is B is [a,/3], where A and B are fuzzy sets representing fuzzy restrictions on the variables X and Y; a and...

This paper discusses the linguistic knowledge extraction from the iterative execution of a multiplayer non-cooperative repeated game. Linguistic knowledge is automatically extracted in the form of fuzzy if-then rules. Our knowledge extraction is mainly based on the on-line incremental learning of fuzzy rule-based systems. In this sense, our linguistic knowledge extraction is the learning of fuz...

In this paper, we introduce and study a mixed variational inclusion problem involving infinite family of fuzzy mappings. An iterative algorithm is constructed for solving a mixed variational inclusion problem involving infinite family of fuzzy mappings and the convergence of iterative sequences generated by the proposed algorithm is proved. Some illustrative examples are also given.

In this paper, we present Gauss-Sidel and successive over relaxation (SOR) iterative methods for finding the approximate solution system of fuzzy Sylvester equations (SFSE), AX + XB = C, where A and B are two m*m crisp matrices, C is an m*m fuzzy matrix and X is an m*m unknown matrix. Finally, the proposed iterative methods are illustrated by solving one example.

In 2006, Espinola and Kirk made a useful contribution on combining fixed point theoryand graph theory. Recently, Reich and Zaslavski studied a new inexact iterative scheme for fixed points of contractive and nonexpansive multifunctions. In this paper, by using  the main idea of their work and the idea of combining fixed point theory on intuitionistic fuzzy metric spaces and graph theory, ...

In Mixed Fuzzy Rule Formation [Int. J. Approx. Reason. 32 (2003) 67] a method to extract mixed fuzzy rules from data was introduced. The underlying algorithm’s performance is influenced by the choice of fuzzy t-norm and t-conorm, and a heuristic to avoid conflicts between patterns and rules of different classes throughout training. In the following addendum to [Int. J. Approx. Reason. 32 (2003)...