Fuzzy information processing by the Monte Carlo simulation technique

Abstract

This paper presents a new method utilizing the Monte Carlo simulation technique for processing fuzzy information. The method was primarily developed for determining the weighted average of a group of ratings that are represented by fuzzy subsets. By generating a uniform random number, normalizing it with respect to the maximum functional value of the cumulative membership function, and then equating the normalized uniform random number to the cumulative function F(x), a value x can be back-calculated for each fuzzy subset. The resulting value x is a random number representing that fuzzy subset. The weighted average was then calculated with these random numbers. The first through fourth moment parameters were obtained and used to fit the random values of the weighted average with a beta distribution. By normalizing the curve-fitted beta distribution function with respect to its maximum functional value, the membership function of the final fuzzy subset was obtained. Comparison is made between the new method and the vertex method which provides an exact but discrete solution. The results show that the new method always yields a very good approximation in a significantly shorter computation time-as much as two orders of magnitude in some of the cases presented.

Keywords:

• Monte Carlo simulation
• fuzzy sets
• risk analysis