The Spaces of Fuzzy Probability and Possibility (I)

Zhende Huang and Tong Zhengxiang
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Zhende Huang: Huazhong Institute of Technology, Research Section of Fuzzy Mathematics
Tong Zhengxiang: Shanghai Railway Institute, Research Section of Multi-Logic and Fuzzy System

A chapter in Advances in Fuzzy Sets, Possibility Theory, and Applications, 1983, pp 59-70 from Springer

Abstract: Abstract Zadeh1, 1978, pointed out that Fuzzy Sets’ theory can be a basis for a theory of possibility, which is similar to the role of measure theory for probability theory. He put emphasis on the fact that a variable usually relates with both probability distribution and possibility distribution. Though he developed the possibility/probability consistency principle, he found it difficult to investigate all the relations between probability distribution and possibility distribution2. Ellen Hisdal3, 1979, considered the relations between conditional possibilities independence and non-interaction in the case of 2-dimensional possibility distribution. Her results are not very satisfactory because the definition of possibility independence developed in [3] is analogous to that of probabilities independence. We feel that the results in [3] didn’t make the relations between independence and noninteraction of two fuzzy events clear. Following the basic definitions in [2], this paper discusses fuzzy events, develops the concept of fuzzy probability and possibility spaces and investigates some properties and weak relations between p-independence and π-noninteraction of two fuzzy events, setting the stage for further research.

Date: 1983
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DOI: 10.1007/978-1-4613-3754-6_6

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