The maximization of the performance of the most if not all the fuzzy identification techniques is usually expressed in terms of the generalization performance of the derived neuro-fuzzy construction. Support Vector algorithms are adapted for the identification of a Support Vector Fuzzy Inference (SVFI) system that obtains robust generalization performance. However, these SVFI rules usually lack...

The present paper proposes a new cluster validity measure as an additional criterion to help the decision making process in fuzzy cluster analysis. This measure, named Fuzzy Silhouette, is a generalization to the fuzzy case of the Average Silhouette Width Criterion, originally conceived to assess crisp (non-fuzzy) data partitions. The Fuzzy Silhouette is more appealing than its crisp counterpar...

This paper proposes a Reinforcement Self-Organizing Fuzzy Control method using Ant Colony Optimization (RSOFCACO). Only reinforcement signals are required when using the RSOFC-ACO for fuzzy controller design. There are no fuzzy rules initially in RSOFC-ACO. An online fuzzy clustering method is used to generate fuzzy rules automatically during control process. The fuzzy clustering method flexibl...

In this contribution, we will analyse the importance of the fuzzy partition granularity for the linguistic variables in the design of fuzzy rule-based systems (FRBSs). In order to put this into e€ect, we will study the FRBS behaviour considering uniform fuzzy partitions with the same number of labels for all the linguistic variables, and considering uniform fuzzy partitions with any number of l...

Shannon entropy was defined for probability distributions and then its using was expanded to measure the uncertainty of knowledge for systems with complete information. In this article, it is proposed to extend the using of Shannon entropy to under-defined or over-defined information systems. To be able to use Shannon entropy, the information is normalized by an affine transformation. The const...

This paper presents a hybrid unsupervised clustering algorithm, referred to as the Rough Fuzzy C-Means (RFCM) algorithm and Particle Swarm Optimization (PSO). The PSO algorithm features high quality of searching in the nearoptimum. At the same time, in RFCM, the concept of lower and upper approximation can deal with uncertainty, vagueness and indiscernibility in cluster relations while the memb...

Images of fuzzy sets under fuzzy relations have been investigated mainly in two contexts: on the one hand, mostly under the term “full image” (Gottwald, 1993), they can be regarded as very general tools for fuzzy inference, leading to the so-called “compositional rule of inference” (Gottwald, 1993; Bauer et al., 1995). The theory of fuzzy relational equations makes direct use of this fundamenta...

A hybrid control system is proposed for regulating an unknown nonlinear plant. The interface between the continuous-state plant and the discrete-event supervisor is designed using a fuzzy logic approach. The fuzzy logic interface partitions the continuous-state space into a finite number of regions. In each region, the original unknown nonlinear plant is approximated by a fuzzy logic-based line...