A new type of fuzzy systems using pyramid membership functions (PMFs) and approximation properties

This paper focuses on improving the precision and simplifying the structure of fuzzy systems. A new type of fuzzy systems that using a proposed pyramid membership function (PMF) is constructed. The original compound of fuzzy rule antecedents is replaced by PMF. Specifically, the commonly used one-dimensional triangular membership functions are generalized to three kinds of two-dimensional PMFs. Cone fuzzy systems (CFSs) with the proposed rectangular pyramid, circular cone and triangular mesh pyramid membership functions are, respectively, given. Approximation properties of CFS, including universal approximation property and approximation accuracy, are proved theoretically. It is shown that, rectangular pyramid fuzzy system and triangular mesh pyramid fuzzy system are capable of achieving first-order and second-order accuracy, respectively. Two experimental examples are presented to demonstrate the effectiveness of CFS. Both theoretical and numerical results illustrate that CFS is capable of obtaining good accuracy.