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**Generalized triangular fuzzy correlated averaging operator and their application to multiple attribute decision making.**
*(English)*
Zbl 1252.90099

Summary: We investigate the multiple attribute decision making problems with triangular fuzzy information. Motivated by the ideal of Choquet integral [G. Choquet, Ann. Inst. Fourier 5, 131–295 (1953/54; Zbl 0064.35101)] and generalized OWA operator [R. R. Yager, Fuzzy Optim. Decis. Mak. 3, No. 1, 93–107 (2004; Zbl 1057.90032)], we develop a generalized triangular fuzzy correlated averaging (GTFCA) operator. The prominent characteristic of the operators is that they cannot only consider the importance of the elements or their ordered positions, but also reflect the correlation among the elements or their ordered positions. We apply the GTFCA operator to multiple attribute decision making problems with triangular fuzzy information. Finally an illustrative example is given to show the developed method.

### MSC:

90C70 | Fuzzy and other nonstochastic uncertainty mathematical programming |

91B14 | Social choice |

03E72 | Theory of fuzzy sets, etc. |

### Keywords:

multiple attribute decision making; triangular fuzzy number; generalized triangular fuzzy correlated averaging (GTFCA) operator
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\textit{G. Wei} et al., Appl. Math. Modelling 36, No. 7, 2975--2982 (2012; Zbl 1252.90099)

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### References:

[1] | Yager, R.R.; Kacprzyk, J., The ordered weighted averaging operator: theory and application, (1997), Kluwer Boston |

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

[3] | Yager, R.R.; Filev, D.P., Induced ordered weighted averaging operators, IEEE trans. syst. man cybernet. part B, 29, 141-150, (1999) |

[4] | Yager, R.R., Centered OWA operators, Soft comput., 11, 631-639, (2007) · Zbl 1113.68106 |

[5] | Yager, R.R., Using stress functions to obtain OWA operators, IEEE trans. fuzzy syst., 15, 1122-1129, (2007) |

[6] | Chiclana, F.; Herrera, F.; Herrera-Viedma, E.; Alonso, S., Induced ordered weighted geometric operators and their use in the aggregation of multiplicative preference relations, Int. J. intell. syst., 19, 233-255, (2004) · Zbl 1105.68095 |

[7] | Merigó, J.M.; Gil-Lafuente, A.M., Unification point in methods for the selection of financial products, Fuzzy econ. rev., 12, 35-50, (2007) |

[8] | Merigó, J.M.; Gil-Lafuente, A.M., The induced generalized OWA operator, Inform. sci., 179, 729-741, (2009) · Zbl 1156.91336 |

[9] | Herrera, F.; Martı´nez, L., An approach for combining linguistic and numerical information based on 2-tuple fuzzy linguistic representation model in decision-making, Int. J. uncertainty fuzziness knowl.-based syst., 8, 5, 539-562, (2000) · Zbl 1113.68518 |

[10] | Merigo, J.M.; Casanovas, M., Induced aggregation operators in decision making with the dempster – shafer belief structure, Int. J. intell. syst., 24, 934-954, (2009) · Zbl 1176.68202 |

[11] | Wei, G.W., Some geometric aggregation functions and their application to dynamic multiple attribute decision making in intuitionistic fuzzy setting, Int. J. uncertainty fuzziness knowl. based syst., 17, 2, 179-196, (2009) · Zbl 1162.90485 |

[12] | Wei, G.W., Uncertain linguistic hybrid geometric Mean operator and its application to group decision making under uncertain linguistic environment, Int. J. uncertainty fuzziness knowl.-based syst., 17, 2, 251-267, (2009) · Zbl 1162.90486 |

[13] | Wei, G.W., Some induced geometric aggregation operators with intuitionistic fuzzy information and their application to group decision making, Appl. soft comput., 10, 2, 423-431, (2010) |

[14] | Wei, G.W., A method for multiple attribute group decision making based on the ET-WG and ET-OWG operators with 2-tuple linguistic information, Exp. syst. appl., 37, 12, 7895-7900, (2010) |

[15] | Wei, G.W.; Zhao, X.F.; Lin, R., Some induced aggregating operators with fuzzy number intuitionistic fuzzy information and their applications to group decision making, Int. J. comput. intell. syst., 3, 1, 84-95, (2010) |

[16] | Zhang, X.; Liu, P.D., Method for aggregating triangular fuzzy intuitionistic fuzzy information and its application to decision making, Tech. econ. develop. econ., 16, 2, 280-290, (2010) |

[17] | Xu, Z.S.; Da, Q.L., The ordered weighted geometric averaging operators, Int. J. intell. syst., 17, 709-716, (2002) · Zbl 1016.68110 |

[18] | F. Chiclana, F. Herrera, E. Herrera-Viedma, The ordered weighted geometric operator: properties and application, in: Proceedings of the 8th International Conference on Information Processing and Management of Uncertainty in Knowledge-Based Systems, Madrid, Spain, 2000, pp. 985-991. · Zbl 1015.68182 |

[19] | Xu, Z.S., A priority method for triangular fuzzy number complementary judgement matrix, Syst. eng.-theory prac., 23, 10, 86-89, (2003) |

[20] | Wang, X.R.; Fan, Z.P., Fuzzy ordered weighted averaging (FOWA) operator and its application, Fuzzy syst. math., 17, 4, 67-72, (2003) · Zbl 1333.03194 |

[21] | Xu, Z.S., A fuzzy ordered weighted geometric operator and its application to in fuzzy AHP, J. syst. eng. electron., 31, 4, 855-858, (2002) |

[22] | Xu, Z.S.; Wu, D., Method based on fuzzy linguistic judgement matrix and fuzzy fuzzy induced ordered weighted averaging (FIOWA) operator for decision making problems with a limited set of alternatives, Fuzzy syst. math., 18, 1, 76-80, (2004) |

[23] | Xu, Z.S.; Da, Q.L., Method based on fuzzy linguistic scale and FIOWGA operator for decision making problems, J. southeast univ. (English edition), 19, 1, 88-91, (2003) · Zbl 1137.68605 |

[24] | Xu, Z.S., Fuzzy harmonic Mean operators, Int. J. intell. syst., 24, 152-172, (2009) · Zbl 1295.68190 |

[25] | Wei, G.W., Fuzzy ordered weighted harmonic averaging operator and its application to decision making, J. syst. eng. electron., 31, 4, 855-858, (2009) |

[26] | Wei, G.W., FIOWHM operator and its application to multiple attribute group decision making, Exp. syst. appl., 38, 4, 2984-2989, (2010) |

[27] | Choquet, G., Theory of capacities, Ann. inst. Fourier, 5, 131-295, (1953) · Zbl 0064.35101 |

[28] | Yager, R.R., Generalized OWA aggregation operators, Fuzzy optim. dec. making, 3, 93-107, (2004) · Zbl 1057.90032 |

[29] | Van Laarhoven, P.J.M.; Pedrycz, W., A fuzzy extension of saaty’s priority theory, Fuzzy sets syst., 11, 229-241, (1983) · Zbl 0528.90054 |

[30] | Keeney, R.L.; Raiffa, H., Decision with multiple objectives, (1976), Wiley New York · Zbl 0488.90001 |

[31] | Wakker, P., Additive representations of preferences, (1999), Kluwer Academic Publishers |

[32] | Wang, Z.; Klir, G., Fuzzy measure theory, (1992), Plenum Press New York |

[33] | Grabisch, M.; Murofushi, T.; Sugeno, M., Fuzzy measure and integrals, (2000), Physica-Verlag New York · Zbl 1113.91313 |

[34] | Liao, X.W.; Li, Y.; Lu, B., A model for selecting an ERP system based on linguistic information processing, Inform. syst., 32, 7, 1005-1017, (2007) |

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