### Abstract

In many fuzzy random optimization models, the objectives and constraints may consist of some distribution functions and critical value functions of prescribed fuzzy random variables. Therefore, we need to analyze the properties of those distribution functions and critical value functions so as to design more precise algorithms to solve such optimization problems. In this paper, we deal with the analytical properties of distributions functions of fuzzy random variables and discuss its applications to critical value functions. We first establish some continuity theorems for distribution functions of fuzzy random variables, which characterize the properties of right continuity, left continuity and continuity, respectively. Then, applying those continuity theorems, we study the properties of critical value functions of fuzzy random variables. The results obtained in this paper are useful in fuzzy random programming models.

Original language | English |
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Pages (from-to) | 279-292 |

Number of pages | 14 |

Journal | International Journal of Innovative Computing, Information and Control |

Volume | 5 |

Issue number | 2 |

Publication status | Published - 2009 Feb |

### Keywords

- Continuity theorem
- Critical value function
- Distribution function
- Fuzzy random optimization
- Fuzzy random variable

### ASJC Scopus subject areas

- Computational Theory and Mathematics
- Information Systems
- Software
- Theoretical Computer Science

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## Cite this

*International Journal of Innovative Computing, Information and Control*,

*5*(2), 279-292.