# Neural Net Applications in Fuzzy Systems

• Hiroshi Kawamura
• Akinori Tani
Part of the International Series on Microprocessor-Based and Intelligent Systems Engineering book series (ISCA, volume 11)

## Conclusions

The concepts of fuzzy sets and fuzzy systems proposed by Zadeh xc18 xc19 have many possibilities of being applied to the description and analysis of this real fuzzy world. In the application of these conepts to knowledge engineering, there are two problems, i.e., learning of fuzzy knowledge and automatic inference of unknown variables. On the, other hand, one can identify any complex complex functions by means or perceptron-type neural networks xc12 and the back-propagation error method.

The purpose of this chapter is to propose some methods of neural network applications to fuzzy systems (and not of fuzzy system applications to neural networks (xc10). As mentioned above, the concept of neural networks is very useful for learning knowledge and automatic inference. In this chapter, besides usual neural networks, a couple of quasi-neural network methods are proposed.

In the field of engineering planning and design, evaluation and optimization are performed by using many kinds of variables (e.g., load, size, weight, strength, intensity, deformation, cost and so on) and constraints (e.g., design formula, mathematical equation, function, code, criterion and so on). Due to inevitable uncertainties, in general, these variables and constraints can be described with fuzzy sets and fuzzy relations cx17 xc18, respectively, which can include rationally usual crisp, deterministic and probabilistic expressions as special states.

As conditioned probabilities are used in probability systems, so conditioned fuzzy sets xc1 are used as states in fuzzy systems composed of inputs, states and outputs xc19. In engineering problems, such conditioned fuzzy sets which belong to fuzzy relations are very useful enough to discriminate uncertainties in variables from ones in constraints (or functions) xc3.

The final purpose of this paper is to propose a paradig, of intelligent and neural fuzzy networks in which learning, identification, evaluation and optimization can be performed for engineering planning and design by expanding fuzzy systems and employing a couple of models similar to neural networks xc10 .

## Keywords

Membership Function Fuzzy System Structural Safety Engineering Planning Fuzzy Relational Equation
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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