Possibilistic Indicators

Abstract

Possibility theory initiated by Zadeh in [75] aims to be a substitute for probability theory in modelling some uncertainty situations ( for example, when we have a small volume of data). The construction of possibility theory has been realized by regarding the fundamental probabilistic notions and results . Possibility measure and necessity measure replaced probability measure, and possibilistic distributions replaced probabilistic distributions (random variables). Several types of possibilistic indicators were defined to replace the main probabilistic indicators (expected value, variance, covariance, etc.) and to offer similar information on the behaviour of possibilistic distributions (see [7], [8], [10], [11], [16], [18], [24], [25], [29], [34], [37], [44], [55], [63], [71], [76], [77]). The fuzzy numbers are the most utilized class of possibilistic distributions. They generalize the real numbers and have a rich algebraic structure. For this reason,the fuzzy numbers are very present in various applications of possibility theory [9], [10], [12], [30], [55], [59], [71], [72]. In this chapter we shall study the main indicators of fuzzy numbers and their properties.