ANALYSIS OF INVESTMENT DECISIONS WITH FUZZY DATA

Abstract

Finding the best investment is an interesting optimization problem. In practice the unit costs/profits of new products or new projects, the lending and borrowing interest rates and cash flows are always imprecise. This imprecise nature has long been studied with help of the probability theory. Probability theory used to be the unique way to handle the uncertain problems in traditional decision analysis. When fuzzy data are incorporated into the investment problems, the optimization problem becomes more difficult. The fuzzy data can be viewed as possibilistic data, i.e., data over which a possibility distribution is defined. We may process such possibilistic data by applying fuzzy set theory to arrive at a selection of investment proposals. But this method has failed to provide: (1) an efficient and effective calculus for investment decisions; (2) a measure of risk from fuzzy data; (3) a suitable ranking procedure and a decision criterion. We propose another method: first transform possibilistic data to probabilistic data m accordance with a suitable possibility-probability consistence principle, then take advantage of the rich structure of the probability theory for investment decisions. In this study we discuss the relationship between probability and fuzzy set theory and define a possibility-probability consistency principle for investment decisions. We also present a method to convert fuzzy data into probability distribution and compare the two ranking methods and arithmetic operations of fuzzy numbers. To illustrate the applications of the method we solve several typical investment problems with fuzzy data and compare the procedures and results of the two methods - by possibility and by probability.