A fuzzy clustering-based genetic TSK system with fuzzy IF part parameters and nonlinear THEN part

Traditional TSK system employs standard membership functions with adjustable crisp parameters in the IF part and linear combinations of input variables in the THEN part, which leads to loss of data fuzziness. Moreover, linear THEN part of this system restricts the number of learning parameters. On the other hand, parameters of the system are tuned to meet a predefined error threshold, but the system does not necessarily display actual structure of data, which impairs its interpretability. This work proposes modifications to the TSK system to tackle these issues and improve its performance. Extended TSK System (ETSK) is presented by replacing crisp parameters of membership functions with fuzzy numbers and adopting arbitrary functions in THEN part of the system. In addition, a Clustering-based TSK system (CTSK) is proposed, which is established from fuzzy clustering algorithms and represents structures and patterns of the data. CTSK has no IF part parameters to tune, which makes the system much faster, but its THEN part is the same as ETSK. Finally, CETSK system is presented as a combination of CTSK and ETSK to study the possibility of further improvements of the systems. The IF parts of TSK, ETSK, and CETSK are tuned by genetic algorithms and their THEN parts are adjusted by the least-squares estimate method. Performance of the systems are studied using ۲۲ datasets in terms of accuracy and runtime. On average, CTSK is ۱۰.۸۲% and ۴.۸۴% more accurate than TSK and CETSK; and ۹۱.۵۸% and ۹۲.۲۱% faster than these systems, respectively. CETSK is ۶.۲۷% more accurate than TSK, but ۶.۹۱% slower because fuzzy clustering and genetic algorithms are jointly employed to tune its IF part whereas only genetic algorithms is used in TSK for this purpose. Keywords: Fuzzy systems, fuzzy clustering, genetic algorithms, gradient descent algorithm, particle swarm optimization, least-squares estimate method, TSK system, fuzzy numbers.

Keywords:

Fuzzy systems , Fuzzy clustering , Genetic algorithms , gradient descent algorithm , Particle Swarm Optimization , least-squares estimate method , TSK system , Fuzzy numbers