Abstract
We first introduce layered, feedforward, neural nets in the next section and go through all the details on how they compute their output given inputs. Our applications of these neural nets is to: (1) approximate solutions (the α-cut and interval arithmetic solution of Section 5.2.3 in Chapter 5) to fuzzy equations, and (2) approximate the values (the α-cut and interval arithmetic value of Section 8.3 in Chapter 8) of fuzzy functions. In both cases the neural net requires sign constraints on its weights (some weights must be positive and the rest must be negative). Then in the third section of this chapter we fuzzify to get a fuzzy neural net. Our applications of fuzzy neural nets is to construct hybrid fuzzy neural nets for fuzzy functions. There is now no approximation, the output from the hybrid fuzzy neural nets will exactly equal the values of the fuzzy function.
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