Fuzzy Probability Theory II: Continuous Case

Continuous probability density functions are widely used in various domains. The characterization of the fuzzy continuous probability theory is similar to the discrete case. However, the possibility space is continuous and the integration between the minimum and the maximum values would set the fuzzy probability through the alpha-cuts. In this chapter, the foundations of fuzzy probability and possibility theory are described for the continuous case. A brief introduction summarized the key concepts in this area with recent applications. The expectation theory is interpreted using the relationship with fuzzy continuous random variables. Fuzzy continuous applications are enriched with different probability density functions. Therefore, fundamental distributions are detailed within their uses and their properties. In this chapter, fuzzy uniform, fuzzy exponential, fuzzy laplace, fuzzy normal and fuzzy lognormal distributions are examined. Several examples are given for the use of these fuzzy distributions regarding the fuzzy interval algebra. Finally, the future suggestions and applications are discussed in the conclusion.