A Comparative Study of Cloud Model and Extended Fuzzy Sets

Abstract

Since Zadeh introduced fuzzy sets in 1965 to generalize the indicator functions of classical sets to a membership function valued in the interval [0,1], a lot of extensions of original fuzzy sets have been proposed. For example, the interval-valued fuzzy sets, intuitionistic fuzzy sets and vague sets approximate the crisp degree of membership by an interval, while the type-2 fuzzy sets generalize it by a fuzzy set in [0,1]. Other than the above, a recent extension named cloud model attracts many attentions, which incorporates probability measure into fuzzy sets, and permits the simultaneous consideration of randomness and fuzziness of linguistic concepts, by extending the degree of membership to random variables defined in the interval [0,1]. Basically, with the three numerical characteristics, cloud model can randomly generate a degree of membership of an element and implement the uncertain transformation between linguistic concepts and its quantitative instantiations. This paper mainly focuses on a comparative study of cloud model and other extensions of fuzzy sets, especially the theoretical significance of cloud model. And the comparative study shows that, compared with other extensions, cloud model suggests a brand new method to handle and represent the inherent uncertainty of linguistic concepts, especially fuzziness, randomness and its relationship.