We investigate a partial non-numerical possibilistic measure taking its values in a complete lattice and defined on a nested system of subsets of the universe under consideration. Our aim is to extend this measure conservatively to the power-set of all systems of this universe using the same idea as that when introducing outer measures. Hence, we ascribe to each subset of the universe its minimal (in the sense of set inclusion) covering by a set from the nested domain and define its possibility degree as identical with the value ascribed to this covering. Also analyzed is the case when they are two lattice-valued possibilistic measures on the same universe, each with its own nested domain and our aim is to define one possibilistic measure on the power-set in question in a way sophistically taking profit of the information offered by both the particular partial lattice-valued measures.
It is a well-known fact that the Dempster combination rule for combination of uncertainty degrees coming from two or more sources is legitimate only if the combined empirical data, charged with uncertainty and taken as random variables, are statistically (stochastically) independent. We shall prove, however, that for a particular but large enough class of probability measures, an analogy of Dempster combination rule, preserving its extensional character but using some nonstandard and boolean-like structures over the unit interval of real numbers, can be obtained without the assumption of statistical independence of input empirical data charged with uncertainty.
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