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**Integrating three representation models in fuzzy multipurpose decision making based on fuzzy preference relations.**
*(English)*
Zbl 0932.91012

Summary: The purpose of this paper is to study a fuzzy multipurpose decision making problem, where the information about the alternatives provided by the experts can be of a diverse nature. The information can be represented by means of preference orderings, utility functions and fuzzy preference relations, and our objective is to establish a general model which cover all possible representations. Firstly, we must make the information uniform, using fuzzy preference relations as uniform preference context. Secondly, we present some selection processes for multiple preference relations based on the concept of fuzzy majority. Fuzzy majority is represented by a fuzzy quantifier, and applied in the aggregation, by means of an OWA operator whose weights are calculated by the fuzzy quantifier. We use two quantifier guided choice degrees of alternatives, a dominance degree used to quantity the dominance that one alternative has over all the others, in a fuzzy majority sense, and a non dominance degree, that generalises Orlovski’s non dominated alternative concept. The application of the two above choice degrees can be carried out according to two different selection processes, a sequential selection process and a conjunction selection process.

### Keywords:

fuzzy majority; fuzzy multipurpose decision making; preference orderings; utility functions; fuzzy preference relations; selection process
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\textit{F. Chiclana} et al., Fuzzy Sets Syst. 97, No. 1, 33--48 (1998; Zbl 0932.91012)

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### References:

[1] | Blin, J.M., Fuzzy relations in group decision theory, J. cybernet., 4, 17-22, (1974) · Zbl 0363.90011 |

[2] | Blin, J.M.; Whinston, A.P., Fuzzy sets and social choice, J. cybernet., 3, 28-36, (1974) · Zbl 0303.90009 |

[3] | Chiclana, F.; Herrera, F.; Herrera-Viedma, E.; Poyatos, M.C., A classification method of alternatives for multiple preference ordering criteria based on fuzzy majority, J. fuzzy math., 4, (1996) · Zbl 0870.90003 |

[4] | Chiclana, F.; Herrera, F.; Herrera-Viedma, E., Preference relations as the information representation base in multiperson decision making, (), 459-464 · Zbl 0980.90041 |

[5] | Dombi, J., A general framework for the utility-based and outranking methods, (), 202-208 · Zbl 0954.91500 |

[6] | fodor, J.; Roubens, M., Fuzzy preference modelling and multicriteria decision support, (1994), Kluwer Academic Publishers Dordrecht · Zbl 0827.90002 |

[7] | Herrera, F.; Herrera-Viedma, E.; Verdegay, J.L., A sequential selection process in group decision making with linguistic assessment, Inform. sci., 85, 223-239, (1995) · Zbl 0871.90002 |

[8] | Herrera, F.; Herrera-Viedma, E.; Verdegay, J.L., A model of consensus in group decision making under linguistic assessments, Fuzzy sets and systems, 78, 73-87, (1996) · Zbl 0870.90007 |

[9] | Kacprzyk, J., Group decision making with a fuzzy linguistic majority, Fuzzy sets and systems, 18, 105-118, (1986) · Zbl 0604.90012 |

[10] | Kacprzyk, J., On some fuzzy cores and ‘soft’ consensus measures in group decision making, (), 119-130 |

[11] | Kacprzyk, J.; Roubens, M., Non-conventional preference relations in decision making, (1988), Springer Berlin · Zbl 0642.00025 |

[12] | Kacprzyk, J.; Fedrizzi, M., Multiperson decision making models using fuzzy sets and possibility theory, (1990), Kluwer Academic Publishers Dordrecht · Zbl 0724.00034 |

[13] | Kickert, W.J.M., Fuzzy theories on decision making, (1978), Nijhoff Dordrecht · Zbl 0364.93022 |

[14] | Kitainik, L., Fuzzy decision procedures with binary relations, towards an unified theory, (1993), Kluwer Academic Publishers Dordrecht · Zbl 0821.90001 |

[15] | Korhonen, P.; Moskowitz, H.; Wallenius, J., Multiple criteria decision support — a review, European J. oper. res., 51, 223-332, (1991) |

[16] | Luce, R.D.; Suppes, P., Preferences, utility and subject probability, (), 249-410 |

[17] | Orlovski, S.A., Decision-making with a fuzzy preference relation, Fuzzy sets and systems, 1, 155-167, (1978) · Zbl 0396.90004 |

[18] | Orlovski, S.A., Calculus of descomposable properties, fuzzy sets and decisions, (1994), Allerton Press |

[19] | Seo, F.; Sakawa, M., Fuzzy multiattribute utility analysis for collective choice, IEEE trans. systems man cybernet., 15, 45-53, (1985) · Zbl 0592.90001 |

[20] | Tanino, T., Fuzzy preference orderings in group decision making, Fuzzy sets and systems, 12, 117-131, (1984) · Zbl 0567.90002 |

[21] | Tanino, T., Fuzzy preference relations in group decision making, (), 54-71 |

[22] | Tanino, T., On group decision making under fuzzy preferences, (), 172-185 |

[23] | Yager, R.R., On ordered weighted averaging aggregation operators in multicriteria decision making, IEEE trans. systems man cybernet., 18, 183-190, (1988) · Zbl 0637.90057 |

[24] | Yager, R.R., Families of OWA operators, Fuzzy sets and systems, 59, 125-148, (1993) · Zbl 0790.94004 |

[25] | Zadeh, L.A., A computational approach to fuzzy quantifiers in natural languages, Comput. math. appl., 9, 149-184, (1983) · Zbl 0517.94028 |

[26] | Zimmermann, H.J., Multi criteria decision making in crisp and fuzzy environments, (), 233-256 |

This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.