Abstract
Fuzzy probability theory based on fuzzy specifications is a new aspect of fuzzy set theory with potential applications in manufacturing and production reliability prediction. In this paper, the development of the new theory is carried out in parallel with that of classical probability theory in order to highlight their similarities and differences. The presentation can be divided into four parts, introducing successively: non-random fuzzy events on [0, 1]; random fuzzy events on [0, 1]; non-random fuzzy events on an Heyting lattice; random fuzzy events on an Heyting lattice. In each section, an interpretation of the actual manufacturing data will be refined into appropriate mathematical definitions. These definitions will, in turn, permit the derivation of propositions pertaining to the evaluation of certain manufacturing parameters. A simplistic automobile manufacturing example illustrates the theory.
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