FUZZY STATISTICAL DECISION-MAKING: THEORY AND APPLICATIONS, vol.343, pp.13-34, 2016 (SCI-Expanded)
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.