Fuzzy random variables — I. definitions and theorems

H. Kwakernaak

Research output: Contribution to journalArticleAcademic

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Abstract

Fuzziness is discussed in the context of multivalued logic, and a corresponding view of fuzzy sets is given. Fuzzy random variables are introduced as random variables whose values are not real but fuzzy numbers, and subsequently redefined as a particular kind of fuzzy set. Expectations of fuzzy random variables, characteristic functions of fuzzy events, probabilities connected to fuzzy random variables, and conditional expectations and probabilities relating to fuzzy random variables are defined as images of the fuzzy set representing the fuzzy random variable under appropriate mappings. Several theorems, some of which relate to independent fuzzy random variables, are proved.
Original languageUndefined
Pages (from-to)1-29
JournalInformation sciences
Volume15
Issue number1
DOIs
Publication statusPublished - 1978

Keywords

  • IR-68407

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