Lotfi A. Zadeh
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Index Terms
- Fuzzy logic, neural networks, and soft computing
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Yu-Wen Tung
The term “soft” computing refers to a way of solving problems similar to that of humans, which is often imprecise but more effective than precise approaches. This idea was first expressed by Zadeh himself some 20 years ago, and is shared by others, such as Papert, who tries to establish a new human epistemology and a new human education in his recent book [1]. Zadeh, on the other hand, uses this concept as a philosophical foundation for building machine intelligence with nontraditional computing, in particular with fuzzy logic. The first part of this paper advocates the concept of soft computing and summarizes its relation to machine intelligence, fuzzy logic, neural networks, and other areas. Zadeh describes the principal constituents of soft computing: fuzzy logic, neural networks, and probabilistic reasoning, which in turn subsume belief networks, generic algorithms, parts of learning theory, and chaotic systems. In the second part, Zadeh picks a subset of fuzzy logic, namely the fuzzy graph, as the central topic of discussion. He shows its full power to express any function or relation as well as fuzzy probabilities. Using the techniques of dynamic programming and gradient programming, he also shows that optimal parameters in a fuzzy logic system and weights in a neural network system can be computed in essentially the same way, which shows that fuzzy logic and neural networks are strongly related. This paper serves well as an introduction for novices. A good reference list providing pointers for further reading is a crucial part of such a paper. This paper does provide an adequate reference list, although with some errors and omissions. The transition from the general discussion of soft computing to the treatment of the fuzzy graph calculus is abrupt. Also, the difference between fuzzy logic and neural networks is not addressed. Both issues may be taken care of by explicitly pointing the reader to appropriate references. The paper is easy to read and understand. Nevertheless, its readability could have been improved if special terms and symbols had been defined at their first appearance. These include the belief network, chaotic systems, the squashing function (in Figure 14), &mgr;, and sup .
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