ABSTRACT
Crisp logic is traditionally used in decision making and related analyses. The theory of probability is based on this logic, through the medium of classical set theory. In crisp logic, there are only two discrete states: “yes” or “no,” 0 or 1, –1 or +1, and “off” or “on.” There is no third possibility here-either a person is in the room or not, an event will occur on not, a light bulb is on or off, and so on. Real-life experiences prove that many more conditions than these two options are possible: the light could be dim, the day could be a certain degree of brightness or darkness, the weather could be warm, hot, hotter, or cold, very cold, and so on. This complexity necessitates variations in the degree of uncertainty, and hence, truth and falsity (1 or 0, respectively) are the two extremes of a continuous spectrum of uncertainty. This leads to multivalued logic and to fuzzy logic (FL)—a theory of sets wherein the characteristic function is generalized to assume an infi nite number of values between 0 and 1 (e.g., a triangular form). In fact, the theory of possibility [4] is based on FL, in a manner similar to the theory of probability, which is based on crisp logic (via set theory).
