Words fom the father of fuzzy logic

Among my many Ph.D. students, some have forged new tools in their work. J.-S. Roger Jang and C.-T. Sun fall into this category. "Neuro-Fuzzy and Soft Computing" makes visible their mastery of the subject matter, their insightfulness and their expository skill. Their co-author, Eiji Mizutani, has made an important contribution by bringing to the writing of the text his extensive experience in dealing with real-world problems in an industrial setting. 

"Neuro-Fuzzy and Soft Computing," is one of the first texts to focus on soft computing -- a concept which has direct bearing on machine intelligence. In this connection, a bit of history is in order. 

The concept of soft computing began to crystallize during the past several years and is rooted in some of my earlier work on soft data analysis, fuzzy logic and intelligent systems. Today, close to four decades after AI was born, it can finally be said with some justification that intelligent systems are becoming a reality. Why did it take so long for the era of intelligent systems to arrive? 

In the first place, the AI community had greatly underestimated the difficulty of attaining the ambitious goals which were on its agenda. The needed technologies were not in place and the conceptual tools in AI's armamentarium -- mainly predicate logic and symbol manipulation techniques -- were not the right tools for building machines which could be called intelligent in a sense that matters in real-world applications. 

Today we have the requisite hardware, software and sensor technologies at our disposal for building intelligent systems. But, perhaps more importantly, we are also in possession of computational tools which are far more effective in the conception and design of intelligent systems than the predicate-logic-based methods which form the core of traditional AI. The tools in question derive from a collection of methodologies which fall under the rubric of what has come to be known as soft computing (SC). In large measure, it is the employment of soft computing techniques that underlies the rapid growth in the variety and visibility of consumer products and industrial systems which qualify to be assessed as possessing significantly high MIQ (Machine Intelligence Quotient). 

The essence of soft computing is that unlike the traditional, hard computing, soft computing is aimed at an accommodation with the pervasive imprecision of the real world. Thus, the guiding principle of soft computing is: Exploit the tolerance for imprecision, uncertainty and partial truth to achieve tractability, robustness, low solution cost and better rapport with reality. In the final analysis, the role model for soft computing is the human mind. 

Soft computing (SC) is not a single methodology. Rather, it is a partnership. The principal partners at this juncture are fuzzy logic (FL), neurocomputing (NC) and probabilistic reasoning (PR), with the latter subsuming genetic algorithms (GA), chaotic systems, belief networks and parts of learning theory. The pivotal contribution of FL is a methodology for computing with words; that of NC is system identification, learning and adaptation; that of PR is propagation of belief; and that of GA is systematized random search and optimization. 

In the main, FL, NC and PR are complementary rather than competitive. For this reason, it is frequently advantageous to use FL, NC and PR in combination rather than exclusively, leading to so-called hybrid intelligent systems. At this juncture, the most visible systems of this type are neuro-fuzzy systems. We are also beginning to see fuzzy-genetic, neuro-genetic and neuro-fuzzy-genetic systems. Such systems are likely to become ubiquitous in the not distant future. 

In coming years, the ubiquity of intelligent systems is certain to have a profound impact on the ways in which man-made systems are conceived, designed, manufactured, employed and interacted with. This is the perspective in which the contents of "Neuro-Fuzzy and Soft Computing" should be viewed. 

Taking a closer look at the contents of "Neuro-Fuzzy and Soft Computing," what should be noted is that, today, most of the applications of fuzzy logic involve what might be called the calculus of fuzzy rules or CFR, for short. To a considerable degree, CFR is self-contained. Furthermore, CFR is relatively easy to master because it is close to human intuition. Taking advantage of this, the authors focus their attention on CFR and minimize the time and effort that are needed to acquire sufficient expertise in fuzzy logic to be able to apply it to real-world problems. 

One of the central issues in CFR is the induction of rules from observations. In this context, neural network techniques and genetic algorithms play pivotal roles which are discussed in "Neuro-Fuzzy and Soft Computing," in considerable detail and a great deal of insight. In the application of neural network techniques, the main tool is that of gradient programming. By contrast, in the application of genetic algorithms, simulated annealing and random search methods, the existence of a gradient is not assumed. The complementarity of gradient programming and gradient-free methods provides a basis for the conception and design of neuro- genetic systems. 

A notable contribution of "Neuro-Fuzzy and Soft Computing," is the exposition of ANFIS (Adaptive-Network-based Fuzzy Inference System) -- a system developed by the authors which is finding numerous applications in a variety of fields. ANFIS and its variants and relatives in the realms of neural, neuro-fuzzy and reinforcement learning systems represent a direction of basic importance in the conception and design of intelligent systems with high MIQ. 

"Neuro-Fuzzy and Soft Computing" is a thoroughly up-to-date text with a wealth of information which is well-organized, clearly presented and illustrated by many examples. It is a must reading for anyone who is interested in acquiring a solid background in soft computing -- a partnership of methodologies which play pivotal roles in the conception, design and application of intelligent systems. 

Lotfi A. Zadeh 
July 28, 1995