Applying bacterial algorithm to optimise trapezoidal membership functions in a fuzzy rule base J. Botzheim, B. Hámori, L. T. Kóczy Department of Telecommunication and Telematics, Budapest University of Technology and Economics, H-1117 Budapest, Pázmány P. sétány 1/d, Hungary koczy@ttt.bme.hu Abstract. This paper presents a method of using the so-called „bacterial algo- rithm” [4, 5] for extracting the fuzzy rule base from a training set. The class of membership functions is restricted to trapezoidal, as it is general enough and widely used. The pseudobacterial genetic algorithm (PBGA) is show. The PBGA optimises the trapezoidal membership functions in the rules by the bac- terial mutation operator. This allows the change of more than one membership function at one time, and fine-tuning as well. Besides, it is important to deter- mine the optimal rule number in the rule base. For this, further operators are used, which eliminates the ineffective rules and contract groups of two or more similar rules into single ones.The evaluation criteria of these operators for trapezoidal membership functions is proposed. … 1 Introduction In the applications of fuzzy systems [1] one of the most important tasks is to find the optimal rule base. This might be given by a human expert or might be given a priori by the linguistic description of the modelled system. If however neither an expert, nor linguistic descriptions are available, the system has to be designed by other methods based on numerical data [5]. Nature inspired some evolutionary optimisation algo- rithms suitable for global optimisation of even non-linear, high-dimensional, multimo- dal, and discontinuous problems. The original genetic algorithm (GA) was developed by Holland [2] and was based on the process of evolution of biological organisms. GA-s use three well-known operators: reproduction, crossover, and mutation. Closely related evolutionary programming (EP) was proposed by Fogel [3]. EP uses selection and mutation operators. A more recent approach is the bacterial algorithm. This in- cludes a modified mutation operator called bacterial mutation, emulating a biological phenomenon of microbial evolution. This gives an alternative by other algorithms, because it is simpler, and it is possible to reach lower error within a short time. In Section 2 the basics of fuzzy systems and evolutionary algorithms are introduced. In Section 3 the bacterial algorithm for trapezoidal fuzzy systems is described. Simula- tion results can be found in Section 4. Section 5 concludes the paper.