Fuzzy Logic (Finance)

In the last thirty years one of the more controversial introductions into the range of decision-making tools, have been the ideas of fuzzy logic, fuzzy systems, and fuzzy analysis. Conventional set theory expressed in Aristotelian terms has a binary or boolean logic; an object (value) is in a set with a truth value of 1 or it is not, with a truth value of 0. Fuzzy logic is by contrast, multivalued, and permits degrees of membership of a logical set, with continuous membership values between 0 and 1. The proponents of the methodology argue that classical set theory is simply a special case of fuzzy logic (Zadeh and Kacprzyk, 1992; Watson et al., 1979; Bezdek, 1993; The Economist, 1994). Opponents argue the reverse, that fuzzy logic, if it exists at all, is merely a subset of traditional logic. Fuzzy logic has its own language and its own mathematics, including crisp sets (Boolean Sets), and degrees of belief, as a means of measuring fuzzy set membership (Kilger and Folger, 1988; Kaufmann and Gupta, 1991).

The main applications of fuzzy logic to date have been in the field of engineering control systems. Controllers have been developed using fuzzy decision rules to provide continuous and variable control for a variety of devices ranging from washing machines to subway trains. It is also important to note that the Japanese have been responsible for most of the development of such systems, reflecting in some peoples’ minds the fundamental difference in thinking which fuzzy logic seems to require, and with which many still argue!


In the context of softer systems such as those used for management, the present position is one of limited progress. It has been argued that fuzzy methods can be used effectively to make decisions that consist of hard (or well understood) elements and soft, uncertain or vague (fuzzy) factors. In that sense it is clai med to offer an alternative decision analysis paradigm particularly under conditions of un certainty (Zadeh and Kacprzyk, 1992). It is argued that since the approach calls for an assessment of “possibilities” rather than formal probabilities, it will be more amenable to use by essentially non-quantitative decision makers, and software systems are available to assist in this.

With the increasing interest among financial analysts in the use of expert systems and neural networks to model financial dealing processes and market performance, it is important to recognize that the other major area where fu zzy methods are gaining popularity is in the ongoing development of hybridized expert and neural network software systems. In fuzzy expert systems, “fuzzified” rules allow a greater variety in the response of the system, dependent upon the degree of belief built into the decision rules. In neural networks, fuzzy logic assists in the necessary learning process when building the network. Assuming, as seems likely, that these systems come to technical maturity and have an impact on the industry, financial analysts may well have to come to understand the terminology of fuzziness.

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