### 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 |
---|---|

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 |

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### 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

### Cite this

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

*5*(2), 279-292.

**Studying distribution functions of fuzzy random variables and its applications to critical value functions.** / Wang, Shuming; Watada, Junzo.

Research output: Contribution to journal › Article

*International Journal of Innovative Computing, Information and Control*, vol. 5, no. 2, pp. 279-292.

}

TY - JOUR

T1 - Studying distribution functions of fuzzy random variables and its applications to critical value functions

AU - Wang, Shuming

AU - Watada, Junzo

PY - 2009/2

Y1 - 2009/2

N2 - 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.

AB - 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.

KW - Continuity theorem

KW - Critical value function

KW - Distribution function

KW - Fuzzy random optimization

KW - Fuzzy random variable

UR - http://www.scopus.com/inward/record.url?scp=61749100218&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=61749100218&partnerID=8YFLogxK

M3 - Article

VL - 5

SP - 279

EP - 292

JO - International Journal of Innovative Computing, Information and Control

JF - International Journal of Innovative Computing, Information and Control

SN - 1349-4198

IS - 2

ER -