Preference relations on a set of fuzzy utilities as a basis for decision making.

*(English)*Zbl 0618.90001The author investigates the reasonability of fuzzy orderings of unidimensional fuzzy utilities (FU’s) and constructs a reasonable fuzzy order relation on a given set of FU’s as one step of the decision making procedure in problems where the information on the states of a system’s environment is imprecisely obtained. These relations are called fuzzy preference relations. The basic notions and the required properties for reasonable fuzzy orderings are introduced in the way as in a paper by the reviewer [BUSEFAL 20, 90-97 (1984; Zbl 0547.04004)]. A new method for constructing a fuzzy preference relation on a set of FU’s is proposed and it is shown that its properties are consistent with reasonable fuzzy orderings. The proposed method is considered as a method of direct comparison, whose conceptual idea originates from Hurwicz’ criterion in the conventional theory of decision making under uncertainty with complete ignorance.

Reviewer: K.Piasecki

Full Text:
DOI

##### References:

[1] | Adamo, J.M., Fuzzy decision trees, Fuzzy sets and systems, 4, 207-219, (1980) · Zbl 0444.90004 |

[2] | Baas, S.M.; Kwakernaak, H., Rating and ranking of multiple-aspect alternatives using fuzzy sets, Automatica, 13, 47-58, (1977) · Zbl 0363.90010 |

[3] | Baldwin, J.F.; Guild, N.C.F., Comparison of fuzzy sets on the same decision space, Fuzzy sets and systems, 2, 213-231, (1979) · Zbl 0422.90004 |

[4] | Baldwin, J.F.; Pilsworth, B.W., Axiomatic approach to implication for approximate reasoning with fuzzy logic, Fuzzy sets and systems, 3, 193-219, (1980) · Zbl 0434.03021 |

[5] | Basu, K., Fuzzy revealed preference theory, J. economic theory, 32, 212-227, (1984) · Zbl 0536.90003 |

[6] | Bellman, R.E.; Zadeh, L.A., Decision-making in a fuzzy environment, Management sci., 17, B141-164, (1979) · Zbl 0224.90032 |

[7] | Bezdek, J.C.; Spillman, B.; Spillman, R., A fuzzy relation space for group decision theory, Fuzzy sets and systems, 1, 255-268, (1978) · Zbl 0398.90009 |

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

[9] | Bortolan, G.; Degani, R., A review of some methods for ranking fuzzy subsets, Fuzzy sets and systems, 15, 1-19, (1985) · Zbl 0567.90056 |

[10] | Cheng, Y.M.; McInnis, B., An algorithm for multiple attribute, multiple alternative decision problems based on fuzzy sets with application to medical diagnosis, IEEE trans. systems man cybernet., 10, 645-650, (1980) |

[11] | Chow, L.R.; Chang, W., A new ranking technique of fuzzy alternatives and its applications to decision making, Policy and information, 7, 31-48, (1983) |

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

[13] | Dubois, D., Linear programming with fuzzy data, () · Zbl 0657.90064 |

[14] | Freeling, A.N.S., Fuzzy sets and decision analysis, IEEE trans. systems man cybernet., 10, 341-354, (1980) |

[15] | Hannan, E.L., Fuzzy decision making with multiple objectives and discrete membership functions, Internat. J. man-machine stud., 18, 49-54, (1983) |

[16] | Jain, R., Decisionmaking in the presence of fuzzy variables, IEEE trans. systems man cybernet., 6, 698-703, (1976) · Zbl 0337.90005 |

[17] | Jain, R., Procedure for multi-aspect decision-making using fuzzy sets, Internat. systems sci., 8, 1-7, (1977) · Zbl 0347.90001 |

[18] | Kaufmann, A., () |

[19] | Luce, R.D.; Suppes, P., Preference, utility, and subjective probability, (), 249-410 |

[20] | Luce, R.D.; Raiffa, H., Games and decisions, (1957), John Wiley & Sons New York · Zbl 0084.15704 |

[21] | Nola, A.D.; Fadani, A., A hyperspatial representation of a particular set of fuzzy preference relations, Fuzzy sets and systems, 7, 79-87, (1982) · Zbl 0468.90007 |

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

[23] | Orlovski, S.A., On formalization of a general mathematical programming problem, Fuzzy sets and systems, 3, 311-321, (1980) · Zbl 0435.90008 |

[24] | Ovchinnikov, S.V., Structure of fuzzy binary relations, Fuzzy sets and systems, 6, 169-195, (1981) · Zbl 0464.04004 |

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

[26] | Tong, R.M.; Bonissone, P.P., A linguistic approach to decisionmaking with fuzzy sets, IEEE trans. systems man cybernet., 10, 716-723, (1980) |

[27] | Tsukamoto, Y.; Nikiforuk, P.N.; Gupta, M.M., On the comparison of fuzzy sets using fuzzy chopping, (), V46-V51 |

[28] | Watson, S.R.; Weiss, J.J.; Donnell, M.L., Fuzzy decision analysis, IEEE trans. systems man cybernet., 9, 1-9, (1979) |

[29] | Zadeh, L.A., Similarity relations and fuzzy orderings, Inform. sci., 3, 177-200, (1971) · Zbl 0218.02058 |

[30] | Zadeh, L.A., Linguistic characterization of preference relations as a basis for choice in social systems, () |

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.