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Fuzzy Set Theory and Probability Theory: What is the Relationship?

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International Encyclopedia of Statistical Science

Fuzzy Set Theory and Probability Theory: What is the Relationship?

Relationship between probability theory and fuzzy set theory is associated with a long history of discussion and debate. My first paper on fuzzy sets was published in 1965 (Zadeh 1965). In a paper published in 1966, Loginov suggested that the membership function of a fuzzy set may be interpreted as a conditional probability (Loginov 1966). Subsequently, related links to probability theory were suggested and analyzed by many others (Coletti and Scozzafava 2004; Freeling 1981; Hisdal 1986a, b; Nurmi 1977; Ross et al. 2002; Singpurwalla and Booker 2004; Stallings 1977; Thomas 1995; Viertl 1987; Yager 1984). Among such links are links to set-valued random variables (Goodmanm and Nguyen 1985; Orlov 1980; Wang and Sanchez 1982) and to the Dempster–Shafer theory (Dempster 1967; Shafer 1976). A more detailed discussion of these links may be found in my l995 paper “Probability theory and fuzzy logic are complementary rather...

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References and Further Reading

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Author information

Authors and Affiliations

  1. University of California-Berkeley, Berkeley, CA, USA

    Lotfi A. Zadeh (Professor Emeritus)

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  1. Lotfi A. Zadeh
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Editors and Affiliations

  1. Department of Statistics and Informatics, Faculty of Economics, University of Kragujevac, City of Kragujevac, Serbia

    Miodrag Lovric

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Zadeh, L.A. (2011). Fuzzy Set Theory and Probability Theory: What is the Relationship?. In: Lovric, M. (eds) International Encyclopedia of Statistical Science. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-04898-2_614

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