# The Calculus of Fuzzy Quantities

• Didier Dubois
Chapter

## Abstract

This chapter gives methods of calculation for expressions containing imprecise quantities, represented by possibility distributions on the real numbers. These methods are in complete agreement with what is commonly called interval analysis, of which they constitute an extension to the case of weighted intervals. Their usefulness is illustrated by some examples at the end of the chapter. Moreover, fuzzy quantities will enter extensively in Chapters 3, 5, and 6. In essence, the calculus of fuzzy quantities constitutes a refinement of sensitivity analysis, which thereby acquires nuance, and this without great increase in the amount of calculation required. The calculus of fuzzy quantities can replace the calculus of random functions (cf. Papoulis [21]) when this proves too intractable, though of course with more or less loss of information according to the type of problem. A more detailed account of the theoretical part of this chapter may be found in Ref. 27. An introductory text is Ref. 28.

## Keywords

Membership Function Fuzzy Number Interval Analysis Fuzzy Relation Possibility Distribution

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