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The maximizing deviation method for group multiple attribute decision making under linguistic environment. (English) Zbl 1301.91014

Summary: The aim of this paper is to put forward a method for multi-attribute decision making problems with linguistic information, in which the preference values take the form of linguistic variables. An aggregating operator named linguistic weighted arithmetic averaging (LWAA) operator is introduced to aggregate the given decision information to get the overall preference value of each alternative. Some properties of the LWAA operator are also investigated. Based on the idea that the attribute with a larger deviation value among alternatives should be evaluated a larger weight, a method to determine the optimal weighting vector of LWAA operator is developed under the assumption that attribute weights are completely unknown. The based approach is extended to the situation where partially weight information can be obtained by solving a constrained nonlinear optimization problem. Then a procedure to group multiple attribute decision making is provided under linguistic environment. Finally, an example of risk investment problem is given to verify the proposed approach; a comparative study to fuzzy ordered weighted averaging (F-OWA) operator methods is also demonstrated.

MSC:

91B10 Group preferences
91B06 Decision theory
91F20 Linguistics
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[1] Ben-Arieh, D.; Chen, Z.F., Linguistic-labels aggregation and consensus measure for autocratic decision making using group recommendations, IEEE trans. systems man cybernet. part A, 36, 558-568, (2006)
[2] Bordogna, G.; Fedrizzi, M.; Pasi, G., A linguistic modeling of consensus in group decision making based on OWA operators, IEEE trans. systems man cybernet. part A, 27, 126-132, (1997)
[3] Byeong, S.A., On the properties of OWA operator weights functions with constant level of orness, IEEE trans. fuzzy systems, 14, 511-515, (2006)
[4] Chiclana, F.; Herrera, F.; Herrera-Viedma, E., Integrating multiplicative preference relations in a multipurpose decision-making model based on fuzzy preference relations, Fuzzy sets and systems, 122, 277-291, (2001) · Zbl 1098.90523
[5] Chiclana, F.; Herrera-Viedma, E.; Herrera, F.; Alonso, S., Induced ordered weighted geometric operators and their use in the aggregation of multiplicative preference relations, Internat. J. intell. systems, 19, 891-913, (2004) · Zbl 1105.68095
[6] Cordon, O.; Herrera, F.; Zwir, I., Linguistic modeling by hierarchical systems of linguistic rules, IEEE trans. fuzzy systems, 10, 2-20, (2002)
[7] Herrera, F.; Herrera-Viedma, E., Aggregation operators for linguistic weighted information, IEEE trans. systems man cybernet. part A, 27, 646-656, (1997)
[8] Herrera, F.; Herrera-Viedma, E., Linguistic decision analysis: steps for solving decision problems under linguistic information, Fuzzy sets and systems, 115, 67-82, (2000) · Zbl 1073.91528
[9] Herrera, F.; Herrera-Viedma, E.; Martinez, L., A fusion approach for managing multi-granularity linguistic term sets in decision making, Fuzzy sets and systems, 114, 43-58, (2000) · Zbl 0963.91025
[10] 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
[11] Herrera-Viedma, E.; Martinez, L.; Mata, F.; Chiclana, F., A consensus support system model for group decision-making problems with multigranular linguistic preference relations, IEEE trans. fuzzy systems, 13, 644-658, (2005)
[12] Huynh, V.A.; Nakamori, Y., A satisfactory-oriented approach to multi-expert decision-making with linguistic assessments, IEEE trans. systems man cybernet. part B, 35, 184-196, (2005)
[13] Levrat, E.; Voisin, A.; Bombardier, S.; Bremont, J., Subjective evaluation of car seat comfort with fuzzy techniques, Internat. J. intell. systems, 12, 891-913, (1997)
[14] Marimin, M.; Uano, M.; Hatono, I., Hierarchical semi-numeric method for pairwise fuzzy group decision making, IEEE trans. systems man cybernet. part B, 32, 691-700, (2002)
[15] Peláez, J.I.; Doňa, J.M., LAMA: a linguistic aggregation of majority additive operator, Internat. J. intell. systems, 18, 809-820, (2003) · Zbl 1048.68109
[16] Roubens, M., Fuzzy sets and decision analysis, Fuzzy sets and systems, 90, 199-206, (1997) · Zbl 0921.90007
[17] Tang, Y.C.; Zheng, J.C., Linguistic modeling based on semantic similarity relation among linguistic labels, Fuzzy sets and systems, 157, 1662-1673, (2006) · Zbl 1101.68886
[18] Wang, J.H.; Hao, J.Y., A new version of 2-tuple fuzzy linguistic representation model for computing with words, IEEE trans. fuzzy systems, 14, 435-445, (2006)
[19] Wang, Y.M., Using the method of maximizing deviations to make decision for multi-indices, System eng. electron., 7, 24-26, (1998), 31
[20] Wang, Y.M.; Parkan, C., A general multiple attribute decision-making approach for integrating subjective preferences and objective information, Fuzzy sets and systems, 157, 1333-1345, (2006) · Zbl 1132.91382
[21] Xu, Z.S., Uncertain multiple attribute decision making: methods and applications, (2004), Tsinghua University Press Beijing
[22] Xu, Z.S., A method based on linguistic aggregation operators for group decision making with linguistic preference relations, Inform. sci., 166, 19-30, (2004) · Zbl 1101.68849
[23] Xu, Z.S., Uncertain linguistic aggregation operators based approach to multiple attribute group decision making under uncertain linguistic environment, Inform. sci., 168, 171-184, (2004) · Zbl 1170.91328
[24] Xu, Z.S., Deviation measures of linguistic preference relations in group decision making, Omega, 33, 249-254, (2005)
[25] Xu, Z.S., An overview of methods for determining OWA weights, Internat. J. intell. systems, 20, 843-865, (2005) · Zbl 1073.90020
[26] Xu, Z.S., An approach based on the uncertain LOWG and induced uncertain LOWG operators to group decision making with uncertain multiplicative linguistic preference relations, Deci. support systems, 41, 488-499, (2006)
[27] Xu, Z.S., Induced uncertain linguistic OWA operators applied to group decision making, Inform. fusion, 7, 231-238, (2006)
[28] Xu, Z.S.; Da, Q.L., The ordered weighted geometric averaging operators, Internat. J. intell. systems, 17, 709-716, (2002) · Zbl 1016.68110
[29] Xu, Z.S.; Da, Q.L., An overview of operators for aggregating information, Internat. J. intell. systems, 18, 953-969, (2003) · Zbl 1069.68612
[30] Yager, R.R., On ordered weighted averaging aggregation operators in multi-criteria decision making, IEEE trans. systems man cybernet., 18, 183-190, (1988) · Zbl 0637.90057
[31] Yager, R.R., Non-numerical multi-criteria multi-person decision making, Group deci. negot., 2, 81-93, (1993)
[32] Yager, R.R.; Filev, D.P., Induced ordered weighted averaging operators, IEEE trans. systems man cybernet. part B, 29, 141-150, (1999)
[33] Yager, R.R.; Xu, Z.S., The continuous ordered weighted geometric operator and its application to decision making, Fuzzy sets and systems, 157, 1393-1402, (2006) · Zbl 1132.91385
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