This paper gives some known theoretical results about fuzzy rule-based classifiers and offers a few new ones. The ability of Takagi-Sugeno-Kang (TSK) fuzzy classifiers to match exactly and to approximate classification boundaries is discussed. The lemma by Klawonn and Klement about the exact match of a classification boundary in R (2) is extended from monotonous to arbitrary functions. Equivale...

For the last decade, fuzzy controllers have been applied with great success to a variety of domains. Nevertheless the underlying theoretical framework still remains unsatisfactory. One of the key questions still open is concerned with approximate reasoning. How should we determine the eeect of applying the fuzzy rule IF x is ~ A THEN y is ~ B] to ~ A 0 with ~ A 0 , ~ A, and ~ B being fuzzy sets...

Over the last years, a number of methods have been proposed to automatically learn and optimize fuzzy rule bases from data. The obtained rule bases are usually robust and allow an interpretation even for data sets that contains imprecise or uncertain information. However, most of the proposed methods are still restricted to learn and/or optimize single layer feed-forward rule bases. The main di...

Systems which use a fuzzy rule base and an inference mechanisms are quite frequently used in many applications. Fuzzy rules and inference mechanisms can be described by a system of fuzzy relation equations. A solution to a given system of fuzzy relation equations can serve us a proper model of fuzzy rules (fuzzy model for short). But only two particular solutions, let us call them disjunctive a...

Systems of fuzzy relation equations are considered as models of fuzzy inference systems. A proper use of an inference mechanism connected to a fuzzy relation modelling a fuzzy rule base is certified by keeping the fundamental interpolation condition. The paper aims at new solutions of systems of fuzzy relation equations and introduces new solvability criteria.

The prediction of product acceptability is often an additive effect of individual fuzzy impressions developed by a consumer on certain underlying attributes characteristic of the product. In this paper, we present the development of a data-driven fuzzy-rule-based approach for predicting the overall sensory acceptability of pistachio green hull’s marmalade. The model was formulated using the Tak...

Sensor nodes are easily compromised to malicious attackers due to an open environment. A false injected attack which takes place on application layer is elected by the compromised node. If the false report arrives in a base station, a false alarm is occurred, and the energy of the nodes is consumed. To detect the false report, statistical en-route filtering method is proposed. In this paper, we...

In complex multidimensional problems with a highly nonlinear input-output relation, inconsistent or redundant rules can be found in the fuzzy model rule base, which can result in a loss of accuracy and interpretability. Moreover, the rules could not cooperate in the best possible way. It is known that the use of rule weights as a local tuning of linguistic rules, enables the linguistic fuzzy mo...