Possibility distributions of fuzzy decision variables obtained from possibilistic linear programming problems.

*(English)*Zbl 0961.90136Summary: Several kinds of possibility distributions of fuzzy variables are studied in possibilistic linear programming problems to reflect the inherent fuzziness in fuzzy decision problems. Interval and triangular possibility distributions are used to express the non-interactive cases between the fuzzy decision variables, and exponential possibility distributions are used to represent the interrelated cases. Possibilistic linear programming problems based on exponential possibility distributions become nonlinear optimization problems. In order to solve optimization problems easily, algorithms for obtaining center vectors and distribution matrices in sequence are proposed. By the proposed algorithms, the possibility distribution of fuzzy decision variables can be obtained.

##### MSC:

90C70 | Fuzzy and other nonstochastic uncertainty mathematical programming |

90C08 | Special problems of linear programming (transportation, multi-index, data envelopment analysis, etc.) |

##### Keywords:

interval variable; triangular possibility distribution; exponential possibility distribution; fuzzy decision variable; possibilistic linear programming
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\textit{H. Tanaka} et al., Fuzzy Sets Syst. 113, No. 2, 323--332 (2000; Zbl 0961.90136)

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