Dubois and Prade introduced the mean value of a fuzzy number as a closed interval bounded by the expectations calculated from its upper and lower distribution functions. In this paper introducing the notations of lower possibilistic and upper possibilistic mean values we definine the interval-valued possibilistic mean and investigate its relationship to the interval-valued probabilistic mean. W...

In 2001 Carlsson and Fullér introduced the possibilistic mean value, variance and covariance of fuzzy numbers. In 2002 Fullér and Majlender introduced the notations of crisp weighted possibilistic mean value, variance and covariance of fuzzy numbers, which are consistent with the extension principle. In this paper we will show some (normative) properties of possibility distributions.

Compared with the conventional probabilistic mean-variance methodology, fuzzy number can better describe an uncertain environment with vagueness and ambiguity. Based on this fact, possibilistic mean-variance utilities to portfolio selection for bounded assets are discussed in this paper. The possibilistic mean value of the expected return is termed measure of investment return and the possibili...

In 1987 Dubois and Prade defined an interval-valued expectation of fuzzy numbers, viewing them as consonant random sets. In 2001 Carlsson and Fullér defined an interval-valued mean value of fuzzy numbers, viewing them as possibility distributions, and they introduced the notation of crisp possibilistic mean value and crisp possibilistic variance of continuous possibility distributions, which ar...

In 2001 we introduced the notions of possibilistic mean value and variance of fuzzy numbers. In this paper we list some works that use these notions. We shall mention some application areas as well. 1 Possibilistic mean value, variance, covariance and correlation A fuzzy number A is a fuzzy set R with a normal, fuzzy convex and continuous membership function of bounded support. The family of fu...

Dubois and Prade defined an interval-valued expectation of fuzzy numbers, viewing them as consonant random sets. Carlsson and Fullér defined an interval-valued mean value of fuzzy numbers, viewing them as possibility distributions. In this paper we shall introduce the notation of weighted interval-valued possibilistic mean value of fuzzy numbers and investigate its relationship to the interval-...

In this paper we will summarize some normative properties of possibility distributions. 1 Probability and Possibility In 2001 Carlsson and Fullér [1] introduced the possibilistic mean value, variance and covariance of fuzzy numbers. In 2003 Fullér and Majlender [4] introduced the notations of crisp weighted possibilistic mean value, variance and covariance of fuzzy numbers, which are consistent...