Similarity reasoning-driven evolutionary fuzzy system for monotonic-preserving models

Fuzzy Inference System (FIS) is a popular computing paradigm which has been identified as a solution for various application domains, e.g. control, assessment, decision making, and approximation. However, it suffers from two major shortcomings, i.e., the "curse of dimensionality" and the "tomato classification" problem. The former suggests that the number of fuzzy rules increases in an exponential manner while the number of input increases. The later is an important fuzzy reasoning problem while a fuzzy rule base is incomplete. The focus of this thesis is on fuzzy rule base reduction techniques, fuzzy rule selection techniques, Approximate Analogical Reasoning Schema (AARS), evolutionary computation techniques and monotonicity property of an FIS, in order to overcome these two shortcomings. The main contribution of this thesis is to formulate the fuzzy rule selection problems to facilitate the AARS and FIS modeling as an optimization problem. An optimization tool, i.e., genetic algorithm (GA), is further implemented. The applicability of the proposed framework is demonstrated and evaluated wi,th two real problems, i.e., education assessment problem and failure analysis problem. The empirical results show the effectiveness of the proposed framework in selecting fuzzy rules and reconstruct a complete rule base with the selected fuzzy rules. However, it is observed that the results obtained do not always fulfill the monotonicity property. Hence, the proposed framework is further extended, and a set of mathematical conditions are adopt~d as governing equation. Again, the applicability of the extended framework is demonstrated and evaluated with an education assessment problem and a failure analysis problem