Two Interpretations of Multidimensional RDM Interval Arithmetic-Multiplication and Division

The paper presents two possible interpretations and realization ways of interval multiplication and division: the possibilistic, unconditional interpretation that is of great meaning for fuzzy arithmetic and fuzzy systems, and the probabilistic, conditional interpretation that requires either knowledge of probability density distributions or assumptions concerning these distributions. The possibilistic interpretation has a great significance not only for fuzzy arithmetic but also for other sciences that use it such as Computing with Words, Grey Systems, etc. These two interpretations are explained in frame of a new, multidimensional RDM interval-arithmetic. The possibility of realization of interval-arithmetic operations in two ways is an argument for reconciliation of two competing scientific groups that propagate two approaches to uncertainty modeling: the probabilistic and possibilistic one. For many years Professor Zadeh has been claiming in his publications that both approaches are not contradictory but rather complementary.

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