Investigating the logical structure of FUZZY IF-THEN rule bases using concepts of mathematical logic and of functional analysis

In developing a semantics for a Fuzzy If-Then Rule Base we in principle distinguish the following two approaches. Firstly, a Fuzzy If-Then Rule Base is considered as a Fuzzy Knowledge Base describing (time independent) situations by means of fuzzy logic. Secondly, a Fuzzy If-Then Rule Base describes the 'inner part' of a fuzzy controller, therefore the conclusions of If-Then rules must be interpreted as assignments. In the paper presented we discuss only the first approach. To this end following TARSKI we define a suitable concept of model and semantic entailment for Fuzzy If-Then Rule Basis. Furthermore, we adopt the concept of fact from logic programming. (orig.)Available from TIB Hannover: RR 8071(98-33) / FIZ - Fachinformationszzentrum Karlsruhe / TIB - Technische InformationsbibliothekSIGLEDEGerman

Methods for the analysis of evolutionary algorithms on pseudo-boolean functions

SIGLEAvailable from TIB Hannover: RR 8071(2000,99)+a / FIZ - Fachinformationszzentrum Karlsruhe / TIB - Technische InformationsbibliothekDeutsche Forschungsgemeinschaft (DFG), Bonn (Germany)DEGerman

On the mutual definability of classes of generalized fuzzy implications and of classes of generalized negations and S-norms

SIGLEAvailable from TIB Hannover: RR 8071(98-28) / FIZ - Fachinformationszzentrum Karlsruhe / TIB - Technische InformationsbibliothekDEGerman

Towards axiomatic foundations for defuzzification theory

The starting point of the paper presented are the well-known defuzzification procedures on the one hand and approaches to axiomatize the concept of defuzzification, on the other hand. We present a new attempt to build up an axiomatic foundation for defuzzification theory using the theory of groups and the theory of partially ordered sets, and in particular, the theory of Galois connections. (orig.)SIGLEAvailable from TIB Hannover: RR 8071(98-31) / FIZ - Fachinformationszzentrum Karlsruhe / TIB - Technische InformationsbibliothekDEGerman

On classification of fitness functions

It is well-known that evolutionary algorithms succeed to optimize some functions efficiently and fail for others. Therefore, one would like to classify fitness functions as more or less hard to optimize for evolutionary algorithms. The aim of this paper is to clarify limitations and possibilities for classifications of fitness functions from a theoretical point of view. We distinguish two different types of classifications, descriptive and analytical ones. We shortly discuss three widely known approaches, namely the NK-model, epistasis variance, and fitness distance correlation. Furthermore, we consider another recent measure, bit-wide epistasis introduced by Fonlupt, Robilliard, and Preux (1998). We discuss shortcomings and counter-examples for all four measures and use this to motivate a discussion of possibilities and limitations of classifications of fitness functions in a broader context and find out its shortcomings. (orig.)SIGLEAvailable from TIB Hannover: RR 8071(99-76)+a / FIZ - Fachinformationszzentrum Karlsruhe / TIB - Technische InformationsbibliothekDEGerman

Ease - Evolutionary algorithms scripting environment

SIGLEAvailable from TIB Hannover: RR 8071(98-54)+a / FIZ - Fachinformationszzentrum Karlsruhe / TIB - Technische InformationsbibliothekDEGerman

On median quantifiers

SIGLEAvailable from TIB Hannover: RR 8071(98-27) / FIZ - Fachinformationszzentrum Karlsruhe / TIB - Technische InformationsbibliothekDEGerman

A unified model of non-panmictic population structures in evolutionary algorithms

SIGLEAvailable from TIB Hannover: RR 8071(99-55)+a / FIZ - Fachinformationszzentrum Karlsruhe / TIB - Technische InformationsbibliothekDEGerman

Takeover times of noisy non-generational selection rules that undo extinction

SIGLEAvailable from TIB Hannover: RR 8071(2000,95)+a / FIZ - Fachinformationszzentrum Karlsruhe / TIB - Technische InformationsbibliothekDEGerman

On the expected runtime and the success probability of evolutionary algorithms

SIGLEAvailable from TIB Hannover: RR 8071(2000,98)+a / FIZ - Fachinformationszzentrum Karlsruhe / TIB - Technische InformationsbibliothekDEGerman