Fuzzy Set Theory Movement in the Social Sciences

Abstract

Some very familiar constructs in the realm of public administration discourse are supervisor-worker, teacherstudent, public-private, democracy-autocracy, conservatism-liberalism, patronage-merit, individualism-collectivism, and centralized-decentralized. These and other constructs and theories in public management are bantered about through iterations of paired comparisons of contrasting relationships that are framed in a language of dichotomous symbolism. Even when a construct does not appear to lend itself readily to a bi-polar structure, it will implicitly exist, as in the familiar constructs of representation, efficiency, effectiveness, equity, and property; in these examples the negative of the terms form the bipolar comparison point - no representation, no efficiency, effectiveness, no equity, no property. Our temporal process is uniquely bi-polar (Kelly 1955; Adams-Webber 1979; Rychlak 1981), where our constructs tend to be labeled by their similarity pole. When we speak of what something means, we are always referring to a relationship between similarities and differences. Kelly's personal construct theory is based on the notion of a construing process where thought is only possible because humans dichotomize experience into similarities and contrasts, as our bi-polar nature. Personal construct theory can be extended into an ontological case for fuzziness as presented by Kosko (1989) wherein: The universe consists of all subsets of the universe. The only subsets of the universe that are not fuzzy are the constructs of classical mathematics. All other sets - sets of particles, cells, tissues, people, ideas, galaxies - in principle contain elements to different degrees. Their membership is partial, graded, inexact, ambiguous, or uncertain. To the extent that the human construes reality as sets of bi-polar constructs, the strength of any construct would then be based on its membership gradient value at the time an event occurs. The membership gradient of any construct is a matter of perceived similarities and contrasts. At this point, it may be best to stop and back up, because we have the cart before the horse. Presenting an historical introduction to logic and fuzzy theory will better orient our frame of reference. Currently in the United States, people who are over 30 years of age were traditionally raised using a nonmetric system of weights and measures - using terms such as feet, ounces, and quarts. The younger generations have been raised using the metric system of weights and measures of meters, grams, and liters. The transition of the older generation to using the metric system has not been very successful. The old ways are still thoroughly embedded in society. There is a split between the conflicting institutionalized old way and the new. The same may hold true in the coming years between the use of classical set theory and the rise in the use of fuzzy set theory. Classical set theory has a long documented history starting with Aristotle; fuzzy theory is a mere child of the 1960s. The dialogue between the human sciences and fuzzy set theory has been scattered, unsystematic, and slow to develop. According to Smithson (1987) ... fuzzy set mathematics are couched in foreign and rather obtuse notation which is forbidding even to the more mathematically sophisticated behavioral scientist. Virtually all texts on the topic assume either a mathematical or computer science and engineering orientation. Smithson's book was an attempt to bridge the gap and lighten the burden of the mathematics to illustrate the basic elements of fuzzy set theory in real-world research examples taken from cognitive psychology, social psychology, sociology, social anthropology, political science, and evaluation research. In the same spirit of Smithson, the goal of this expository article on fuzzy theory is to minimize the obtrusion of mathematics and make the topic more palatable to a wider audience. This initial paper sets out to provide some structure for handling fuzzy concepts and illustrate their use in budgeting and decision making. …

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