POSSIBILITY THEORY .3. POSSIBILISTIC INDEPENDENCE

The introduction of the notion of independence in possibility theory i s a problem of long-standing interest. Many of the measure-theoretic d efinitions that have up to now been given in the literature face some difficulties as far as interpretation is concerned. Also, there are in consistencies between the definition of independence of measurable set s and possibilistic variables. After a discussion of these definitions and their shortcomings, a new measure-theoretic definition is suggest ed, which is consistent in this respect, and which is a formal counter part of the definition of stochastic independence in probability theor y. In discussing the properties of possibilistic independence, I draw from the measure- and integral-theoretic treatment of possibility theo ry, discussed in Part I of this series of three papers. I also investi gate the relationship between this definition of possibilistic indepen dence and the definition of conditional possibility, discussed in deta il in Part II of this series. Furthermore, I show that in the special case of classical, two-valued possibility the definition given here ha s a straightforward and natural interpretation.