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Session 1532

The Obstacles to Teaching Fuzzy Set Theory and Its Applications

Dr. Henry L. Welch. P.E. Milwaukee School of Engineering

Abstract One goal of an engineering curriculum is to produce graduates who are knowledgeable in current technology and practices. One of the better ways to do this is to provide a variety of senior-level technical electives in new and popular technology areas. The danger inherent in this is that many undergraduates are unprepared for exposure to these topics due either to a lack of prerequisite material or technical maturity. Further, inappropriately scoped technical electives can leave an undergraduate too specialized for their potential career path. This paper will address the issues of prerequisite material and specialization in the area of fuzzy set theory and its applications. It will be shown that there is little or no significant prerequisite material problems for most engineering majors and that an appropriate breadth-based approach to application areas can address the specialization issue. The results of teaching a quarter-long course in fuzzy sets for three years at the Milwaukee School of Engineering(MSOE) to electrical and computer engineers will also be presented.

Introduction

Fuzzy sets or fuzzy logic, as they are most often referred to, suffer from a number of problems in today's engineering marketplace. The first problem is the name itself, since their invention in 1965, the term "fuzzy" has been a significant source of confusion. To the uninitiated, saying that an engineering solution used "fuzzy logic" would normally cause immediate suspicion. Why would anyone want to use logic that was inexact? This is further compounded by the simplicity with which fuzzy sets and fuzzy logic can be implemented. In most cases the use of the functions MIN and MAX and simple first moment computation are all that is necessary to implement many fuzzy systems. Hence, a large number of engineers were using fuzzy logic without understanding why or how it worked and could not rigorously defend their use of the approach.

Having been exposed to fuzzy sets as a graduate student at Rensselaer Polytechnic Institute I had always considered the possibility of teaching a course in that area. In the 1991 technology issue of IEEE Spectrum I noted that fuzzy logic was mentioned in almost all the technology areas presented [1]. I made a proposal to my department chair to develop a senior technical elective in fuzzy logic which was accepted. I rapidly realized that I was facing two major obstacles. 1) Could students in a mathematical theory limited electrical engineering curriculum be able to grasp the fundamentals of fuzzy sets and still leave time for some practical uses. And 2) could sufficient breadth of material be presented so that the students would not be too specialized at such an early stage of their careers.

In the following sections this paper will address the stumbling blocks to teaching fuzzy sets. The first issue addressed will be the mathematical background in students that is necessary to teach fuzzy set theory. Suggestions on how to avoid limiting the topical scope of such a course (in a 10 week term) to just the theory and applications of fuzzy sets to control will then be presented. Finally the results from teaching EE481 - Fuzzy Sets and Applications over three academic years will be presented.

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Welch, P. D. H. L. (1997, June), The Obstacles To Teaching Fuzzy Set Theory And Its Applications Paper presented at 1997 Annual Conference, Milwaukee, Wisconsin. 10.18260/1-2--6718