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**Inequality relation between fuzzy numbers and its use in fuzzy optimization.**
*(English)*
Zbl 0574.04005

The inequality relation between two fuzzy numbers is investigated. A certain type of such a relation motivated by practical interpretation is proposed, and its correspondence with the usual lattice-type relation generated by the extended maximum and minimum operators and its possible interpretation are discussed. The concept of R-L fuzzy number is introduced, the class of all R-L fuzzy numbers covering practically the whole set of normal convex fuzzy numbers. Comparing two R-L fuzzy numbers of the same type, the relation introduced in the paper may be replaced by four ordinary inequalities. This fact may be taken advantage of in optimization problems with linear fuzzy constraints.

### MSC:

03E20 | Other classical set theory (including functions, relations, and set algebra) |

91B06 | Decision theory |

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\textit{J. Ramík} and \textit{J. Římánek}, Fuzzy Sets Syst. 16, 123--138 (1985; Zbl 0574.04005)

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### References:

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[2] | Dubois, D.; Prade, H., Ranking fuzzy numbers in the setting of possibility theory, Inform. Sci., 30, 183-224 (1983) · Zbl 0569.94031 |

[3] | Freeling, A. N.S., Fuzzy sets and decision analysis, IEEE Trans. Systems Man Cybernet., 10, 341-354 (1980) |

[4] | Mizumoto, M.; Tanaka, K., Some properties of fuzzy numbers, (Gupta, M. M.; Ragade, R. K.; Yager, R. R., Advances in Fuzzy Set Theory and Applications (1979), North-Holland: North-Holland Amsterdam), 153-164 |

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