The Infinite Dimensional Product Possibility Space and Its Applications

This paper is devoted to the construction of infinite dimensional product possibility space as well as its applications in theory of fuzzy processes. First, the countably infinite dimensional product ample field, and the extension of countably many product possibility measures based on a continuous triangular norm are discussed. Then the results are generalized to the case of uncountably many factors. Finally, the obtained results about the product possibility space is applied to the construction of a fuzzy vector, a sequence of fuzzy variables and a fuzzy process.

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