Novel neural algorithms based on fuzzy δ rules for solving fuzzy relation equations: Part II

In this paper, we first design a fuzzy neuron which possesses some generality. This fuzzy neuron is founded by replacing the operators of the traditional neuron with a pair of abstract fuzzy operators as (+̂, ·̂) which we call fuzzy neuron operators. For example, it may be (⊥,·), (∧·), (∨·), or (∧,∧), etc. It is an extended fuzzy neuron, and a network composed of such neurons is an extended fuzzy neural network. Then we discuss the relationship between the fuzzy neuron operators and t-norm and t-conorm, and point out fuzzy neuron operators are based on t-norm but much wider than t-norm. In this paper we will emphatically discuss a two-layered network and its training algorithm which will have to satisfy a set of various operators. This work is very related to solving fuzzy relation equations. So it can be used to resolve fuzzy relation equations. Furthermore, the new fuzzy neural algorithm is found to be: stronger than other existing methods to some degree. Some simulation results will be reported in detail.