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Fuzzy Statistical Decision-Making Read chapter Read first chapter

2016 | OriginalPaper | Chapter

Fuzzy Probability Theory I: Discrete Case

Authors : I. Burak Parlak, A. Cağrı Tolga

Published in: Fuzzy Statistical Decision-Making

Publisher: Springer International Publishing

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Abstract

This chapter introduces the underlying theory of Fuzzy Probability and Statistics related to the differences and similarities between discrete probability and possibility spaces. Fuzzy Probability Theory for Discrete Case starts with the fundamental tools to implement an immigration of crisp probability theory into fuzzy probability theory. Fuzzy random variables are the initial steps to develop this theory. Different models for fuzzy random variables are designated regarding the fuzzy expectation and fuzzy variance. In order to derive the observation related to fuzzy discrete random variables, a brief summary of alpha-cuts is introduced. Furthermore, essential properties of fuzzy probability are derived to present the measurement of fuzzy conditional probability, fuzzy independency and fuzzy Bayes theorem. The fuzzy expectation theory is studied in order to characterize fuzzy probability distributions. Fuzzy discrete distributions; Fuzzy Binomial and Fuzzy Poisson are introduced with different examples. The chapter is concluded with further steps in the discrete case.

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previous chapter Fuzzy Statistical Decision-Making
next chapter Fuzzy Probability Theory II: Continuous Case
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Metadata
Title
Fuzzy Probability Theory I: Discrete Case
Authors
I. Burak Parlak
A. Cağrı Tolga
Copyright Year
2016
Book
Fuzzy Statistical Decision-Making

Print ISBN: 978-3-319-39012-3

Electronic ISBN: 978-3-319-39014-7

Copyright Year: 2016

DOI
https://doi.org/10.1007/978-3-319-39014-7_2

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