FUZZY THINKING - BART KOSKO

(THE NEW SCIENCE OF FUZZY LOGIC)
This book was first published in 1993. It must have been reviewed then and may be several times. I would like to write here a review of the book recording my own impressions about this book
I remember reading about Fuzzy Sets as an article by Lofti A. Zadeh in the Information and Control magazine. It was during a Final Year seminar during our Engineering Course that we had presented a glimpse of this concept. After that I must admit we all but forgot about Fuzzy Logic. We had, as one of the papers in Bachelor of Engineering (Electronics and Communications Engg) course, a lesson on Threshold Logic as part of our Paper on Logic Design. Neural Networks was a nascent field then, perhaps.
After I joined a manufacturing company as an engineering professional, I nurtured an interest in Artificial Intelligence, as a personal passion as all my efforts to make it a part of my professional practice came to a naught. In the field of AI I was fascinated by Automated Theorem Proving based on Aristotelian Logic, studied by Logicians as Formal Logic – the so called Statement Calculus and First Order Predicate Calculus. This I think was a carryover of my interest from my college days in Pure Math and Logic. Even though I was a student of Engineering, and if at all natural, an interest in Applied Math would have been most appropriate, I had this interest in Logic and Pure Math.
Even as I studied Logic way beyond the requirements of my scholastic curriculum, there was always one gnawing doubt that was never answered sufficiently by any book on Logic. Books on Logic separated meaning from structure and the Calculus was all about tautological structures and formal constituents of Valid Inferential schema. Central to Classical Logics as they are now called was their binary or bivalent nature. As I progressed through the study, I was even thrilled about successful implementations of Theorem Proving programs based on the Null Horn Clause idea. Though the program itself was ‘creative’ enough to offer, for instance, in respect of one theorem, a proof different from the ones in Euclid’s Elements for a theorem of Elementary High School Geometry, there were reasons that turned me off Formal Logic, as time passed. Godel’s Theorem of Undecidability about the completeness of an Axiomatic System created in my mind a dichotomy about the utility of Logic as a means for implementing Intelligence in Machines. The next to captivate my attention was the concept of Expert Systems and by that time AI as a field, even if considered Inter-disciplinary was losing its sheen. Many thought it was just a sophisticated way of Programming. It was about 1989, I shifted from Logic to Intuition as a means to discovery. Thus, to me Intuition was the source of creative thinking. I was now looking for working on Machine Intelligence by mimicking the workings of the human brain. This is when I came across, a news paper article on what was then called as neo-connectionism or what is presently known by the name Neural Networks. Thus over a decade I had started with memberships to the Journal of Symbolic Logic and shifted to the AI Magazine and last to the Journal of the International Society of Neural Networks. After a time the subscriptions became unaffordable and I had to discontinue.
One more idea that troubled me all those years when I was consumed by a passion for Classical Logic was how it is possible that statements have only a binary truth value! Though I needed a discussion on this topic, I had no one to look up to as no one seemed to be interested in Logic in the first place. My professional company was still less interested as they were people from mainstream manufacturing of proven technological products. Thus there were hardly any who were even interested in these at an intellectual level too as there was no apparent use for these ideas in our day to day professional life. So sad, I did not chance to see the present book in our own library shelf. I vaguely remember a book on Neuro-fuzzy algorithms for Control Strategy implementation, but right now I am not able to locate it. But two years back I thought I must renew my interest in Neural Networks and bought two good graduate level texts on these.
In this book the author laments the lack-luster treatment that the subject of Fuzzy Logic/Fuzzy Systems received in the US. The field according to him has come up to where it is today mainly due to efforts in Japan. He attributes this Japanese preference for this field to their Zen Buddhist background and the comparative lack of interest in the Western countries, to the Aristotelian orientation of all Western Science and Technology.
The author begins with Set Theory where set membership is an all or none phenomenon and makes out the case for membership by “degrees”. Similarly, about statement Truth Values in Logic. The concept of Fuzzy sets and Fuzzy Logic is developed progressively, leading to some computationally important results like the FAT (Fuzzy Approximation Theorem): simply put the statement of the FAT is: A curve (even quite a kinky one at that) could be covered by finite number of fuzzy patches. FAT also says that one could approximate a continuous system (on a closed bounded set) as closely as possible. This leads to an idea of Math Model free estimation. The whole idea of Math Modeling of Real Time systems is to afford design of robust and finely tuned control systems. But then in all but the simplest of, partitioned parts of complex control systems only Math Modeling is possible, or has been useful.
The author laments ad nauseum the scant regard given to Fuzzy System Design. Mainstream S&T tend to pooh- pooh or belittle the development of the idea. This may not be so today as in Japan significant commercial results have been achieved esp. in the intelligent control of home appliances and some industrial processes and in aerospace. Thus if the scientific community refuses to admit the utility of Fuzzy System design on the plea that it lacks sufficient rigor, or the administrators refuse funding for Fuzzy systems research being influenced by the scientific community, then the best route is through the industrial applications generated and/or the commercially successful products released to the market. A part of the profits gained could be siphoned off for research into mainstream control and computational application of Fuzzy system concepts. The author again repeats too often the, funding availability for Neural Network systems as the concepts have been furthered by some rigorous Math! He recounts how he had even obtained funding for Neural Network research which he had combined with Fuzzy System research.
It is felt that if the repetitions were avoided the volume of the book could be brought to about 250 pages, without loss of clarity or intuitive appeal. I have procured a copy of the author’s standard text Neural Networks and Fuzzy Systems. It is hoped that this being a University curriculum text would not contain avoidable repetitions. The book also extends the idea to Adaptive Fuzzy systems where the set of Fuzzy rules developed evolve over a period of time to improve the closeness of the process image to reality.
The author gives an impression that Fuzzy Systems and Neural Networks play a complementary role and would be a power Decision Making and/or Control Strategy taken together. If rigorous Math Modeling could be successfully replaced leaving it as only an academic curiosity then one could say a revolution of sorts would have been achieved.
The influence of an Eastern Philosophical bent is clearly seen by the author, who elaborates on this by using Buddha and Aristotle references, for picking the concept of Fuzzy Systems, taken together with the Neural Network Research, in Japan. We know from recent history of the development of Science that Japan had picked up on the Logic Programming approach in the early seventies, only to abandon that in favor of Fuzzy Systems gives some hope for finding new applications to concepts from Classical Philosophical Systems of India like Nyaya and Navy-Nayaya etc. It is worthwhile to pursue these ideas in the light of the successes in Japan. Even otherwise a modern re-evaluation of the same to develop a holistic logic system would not be out of place. The author of this review subscribes to this opinion. It is time we(in India) take an independent approach if necessary different and divergent form western thinking using creation of working products and systems as a measure of the success of the approach.