The idea of granular computing goes back to Zadeh (1979). The basic idea of granular computing is that an object is described by a bunch of values in possible dimensions like indistinguishability, similarity, and proximity. If a granular is labeled by a linguistic expression it is called a linguistic variable.
Published in Chapter:
Uncertainty and Vagueness Concepts in Decision Making
Georg Peters (Munich University of Applied Sciences, Germany)
Copyright: © 2008
|Pages: 9
DOI: 10.4018/978-1-59904-843-7.ch101
Abstract
One of the main challenges in decision making is how to deal with uncertainty and vagueness. The classic uncertainty concept is probability, which goes back to the 17th century. Possible candidates for the title of father of probability are Bernoulli, Laplace, and Pascal. Some 40 years ago, Zadeh (1965) introduced the concept of fuzziness, which is sometimes interpreted as one form of probability. However, we will show that the terms fuzzy and probability are complementary. Recently, in the beginning of the ’80s, Pawlak (1982) suggested rough sets to manage uncertainties. The objective of this article is to give a basic introduction into probability, fuzzy set, and rough set theory and show their potential in dealing with uncertainty and vagueness. The article is structured as follows. In the next three sections we will discuss the basic principles of probability, fuzzy sets, and rough sets, and their relationship with each other. The article concludes with a short summary.