×

Subjective and objective information in linguistic multi-criteria group decision making. (English) Zbl 1346.91056

Summary: Linguistic decision making systems represent situations that cannot be assessed with numerical information but it is possible to use linguistic variables. This paper introduces new linguistic aggregation operators in order to develop more efficient decision making systems. The linguistic probabilistic weighted average (LPWA) is presented. Its main advantage is that it considers subjective and objective information in the same formulation and considering the degree of importance that each concept has in the aggregation. A key feature of the LPWA operator is that it considers a wide range of linguistic aggregation operators including the linguistic weighted average, the linguistic probabilistic aggregation and the linguistic average. Further generalizations are presented by using quasi-arithmetic means and moving averages. An application in linguistic multi-criteria group decision making under subjective and objective risk is also presented in the context of the European Union law.

MSC:

91B06 Decision theory
91B10 Group preferences
PDF BibTeX XML Cite
Full Text: DOI

References:

[1] Beliakov, G.; Pradera, A.; Calvo, T., Aggregation functions: A guide for practitioners, (2007), Springer-Verlag Berlin · Zbl 1123.68124
[2] Belles-Sampera, J.; Merigó, J. M.; Guillén, M.; Santolino, M., The connection between distortion risk measures and ordered weighted averaging operators, Insurance: Mathematics and Economics, 52, 411-420, (2013) · Zbl 1284.91204
[3] Canós, L.; Liern, V., Soft computing-based aggregation methods for human resource management, European Journal of Operational Research, 189, 669-681, (2008) · Zbl 1142.91395
[4] Carlsson, C.; Fuller, R., Benchmarking and linguistic importance weighted aggregations, Fuzzy Sets and Systems, 114, 35-42, (2000) · Zbl 0963.91028
[5] Chalmers, D.; Davies, G., European union law: cases and materials, (2010), Cambridge University Press Cambridge
[6] Engemann, K. J.; Filev, D. P.; Yager, R. R., Modelling decision making using immediate probabilities, International Journal of General Systems, 24, 281-294, (1996) · Zbl 0844.90001
[7] Figueira, J.; Greco, S.; Ehrgott, M., Multiple criteria decision analysis: state of the art surveys, (2005), Springer Boston · Zbl 1060.90002
[8] Fodor, J.; Marichal, J. L.; Roubens, M., Characterization of the ordered weighted averaging operators, IEEE Transactions on Fuzzy Systems, 3, 2, 236-240, (1995)
[9] Gao, J. W.; Li, M.; Liu, H. H., Generalized ordered weighted utility averaging-hyperbolic absolute risk aversion operators and their applications to group decision-making, European Journal of Operational Research, 243, 258-270, (2015) · Zbl 1346.91046
[10] Grabisch, M.; Marichal, J. L.; Mesiar, R.; Pap, E., Aggregation functions: means, Information Sciences, 181, 1-22, (2011) · Zbl 1206.68298
[11] He, Y. D.; Chen, H. Y.; Zhou, L. G.; Liu, J. P.; Tao, Z. F., Intuitionistic fuzzy geometric interaction averaging operators and their application to multi-criteria decision making, Information Sciences, 259, 142-159, (2014) · Zbl 1347.68332
[12] Herrera, F.; Herrera-Viedma, E.; Verdegay, J. L., A sequential selection process in group decision making with a linguistic assessment approach, Information Sciences, 85, 223-239, (1995) · Zbl 0871.90002
[13] Herrera, F.; Herrera-Viedma, E.; Martínez, L., A fuzzy linguistic methodology to deal with unbalanced linguistic term sets, IEEE Transactions on Fuzzy Systems, 16, 354-370, (2008)
[14] Herrera, F.; Martínez, L., A 2-tuple fuzzy linguistic representation model for computing with words, IEEE Transactions on Fuzzy Systems, 8, 746-752, (2000)
[15] Liao, H. C.; Xu, Z. S.; Zeng, X. J.; Merigó, J. M., Qualitative decision making with correlation coefficients of hesitant fuzzy linguistic term sets, Knowledge-Based Systems, 76, 127-138, (2015)
[16] Liu, P. D.; Jin, F., Methods for aggregating intuitionistic uncertain linguistic variables and their application to group decision making, Information Sciences, 205, 58-71, (2012) · Zbl 1250.91031
[17] Liu, P. D.; Jin, F.; Zhang, X.; Su, Y.; Wang, M. H., Research on the multi-attribute decision making under risk with interval probability based on prospect theory and the uncertain linguistic variables, Knowledge-Based Systems, 24, 554-561, (2011)
[18] Merigó, J. M., The probabilistic weighted average and its application in multi-person decision making, International Journal of Intelligent Systems, 27, 457-476, (2012)
[19] Merigó, J. M., Probabilities with OWA operators, Expert Systems with Applications, 39, 11456-11467, (2012)
[20] Merigó, J. M.; Casanovas, M., Decision making with distance measures and linguistic aggregation operators, International Journal of Fuzzy Systems, 12, 190-198, (2010)
[21] Merigó, J. M.; Casanovas, M.; Martínez, L., Linguistic aggregation operators for linguistic decision making based on the Dempster-Shafer theory of evidence, International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems, 18, 287-304, (2010) · Zbl 1214.68402
[22] Merigó, J. M.; Casanovas, M.; Palacios-Marqués, D., Linguistic group decision making with induced aggregation operators and probabilistic information, Applied Soft Computing, 24, 669-678, (2014)
[23] Merigó, J. M.; Casanovas, M.; Yang, J. B., Group decision making with expertons and uncertain generalized probabilistic weighted aggregation operators, European Journal of Operational Research, 235, 215-224, (2014) · Zbl 1305.91104
[24] Merigó, J. M.; Gil-Lafuente, A. M., The induced 2-tuple linguistic generalized OWA operator and its application in linguistic decision making, Information Sciences, 236, 1-16, (2013) · Zbl 1284.91121
[25] Merigó, J. M.; Lobato-Carral, C.; Carrilero-Castillo, A., Decision making in the European union under risk and uncertainty, European Journal of International Management, 6, 590-609, (2012)
[26] Merigó, J. M.; Palacios-Marqués, D.; Benavides-Espinosa, M. M., Aggregation methods to calculate the average price, Journal of Business Research, 68, 1574-1580, (2015)
[27] Merigó, J. M.; Yager, R. R., Generalized moving averages, distance measures and OWA operators, International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems, 21, 533-559, (2013) · Zbl 1323.68506
[28] Shannon, C. E., A mathematical theory of communication, Bell System Technical Journal, 27, 379-423, (1948) · Zbl 1154.94303
[29] Torra, V., The weighted OWA operator, International Journal of Intelligent Systems, 12, 153-166, (1997) · Zbl 0867.68089
[30] Wang, J. Q.; Peng, L.; Zhang, H. Y.; Chen, X. H., Method of multi-criteria group decision-making based on cloud aggregation operators with linguistic information, Information Sciences, 274, 177-191, (2014) · Zbl 1341.91047
[31] Wei, G. W.; Zhao, X., Some dependent aggregation operators with 2-tuple linguistic information and their application to multiple attribute group decision making, Expert Systems with Applications, 39, 5881-5886, (2012)
[32] Wei, G. W.; Zhao, X.; Lin, R.; Wang, H. J., Uncertain linguistic bonferroni mean operators and their application to multiple attribute decision making, Applied Mathematical Modelling, 37, 5277-5285, (2013) · Zbl 1427.91102
[33] Xu, Y. J.; Merigó, J. M.; Wang, H. M., Linguistic power aggregation operators and their application to multiple attribute group decision making, Applied Mathematical Modelling, 36, 5427-5444, (2012) · Zbl 1254.91112
[34] Xu, Z. S., EOWA and EOWG operators for aggregating linguistic labels based on linguistic preference relations, International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems, 12, 791-810, (2004) · Zbl 1076.91508
[35] Xu, Z. S., A method based on linguistic aggregation operators for group decision making with linguistic preference relations, Information Sciences, 166, 19-30, (2004) · Zbl 1101.68849
[36] Xu, Z. S., Uncertain linguistic aggregation operators based approach to multiple attribute group decision making under uncertain linguistic environment, Information Sciences, 168, 171-184, (2004) · Zbl 1170.91328
[37] Xu, Z. S., A note on linguistic hybrid arithmetic averaging operator in group decision making with linguistic information, Group Decision and Negotiation, 15, 581-591, (2006)
[38] Xu, Z. S., An interactive approach to multiple attribute group decision making with multigranular uncertain linguistic information, Group Decision and Negotiation, 18, 119-145, (2009)
[39] Xu, Z. S., Linguistic decision making: theory and methods, (2012), Springer-Verlag Berlin · Zbl 1260.91225
[40] Xu, Z. S.; Da, Q. L., An overview of operators for aggregating information, International Journal of Intelligent Systems, 18, 953-969, (2003) · Zbl 1069.68612
[41] Yager, R. R., On ordered weighted averaging aggregation operators in multi-criteria decision making, IEEE Transactions on Systems, Man and Cybernetics, B, 18, 183-190, (1988) · Zbl 0637.90057
[42] Yager, R. R., Families of OWA operators, Fuzzy Sets and Systems, 59, 125-148, (1993) · Zbl 0790.94004
[43] Yager, R. R., Time series smoothing and OWA aggregation, IEEE Transactions on Fuzzy Systems, 16, 994-1007, (2008)
[44] Yager, R. R., On generalized bonferroni mean operators for multi-criteria aggregation, International Journal of Approximate Reasoning, 50, 1279-1286, (2009) · Zbl 1186.91076
[45] Yager, R. R.; Engemann, K. J.; Filev, D. P., On the concept of immediate probabilities, International Journal of Intelligent Systems, 10, 373-397, (1995) · Zbl 0846.62007
[46] Yager, R. R.; Kacprzyk, J.; Beliakov, G., Recent developments on the ordered weighted averaging operators: theory and practice, (2011), Springer-Verlag Berlin
[47] Yang, W. E.; Wang, J. Q., Multi-criteria semantic dominance: A linguistic decision aiding technique based on incomplete preference information, European Journal of Operational Research, 231, 171-181, (2013) · Zbl 1317.91031
[48] Yu, X.; Xu, Z. S.; Liu, S.; Chen, Q., Multicriteria decision making with 2-dimension linguistic aggregation techniques, International Journal of Intelligent Systems, 27, 539-562, (2012)
[49] Zadeh, L. A., Fuzzy sets, Information and Control, 8, 338-353, (1965) · Zbl 0139.24606
[50] Zadeh, L. A., The concept of a linguistic variable and its application to approximate reasoning. part 1, Information Sciences, 8, 199-249, (1975) · Zbl 0397.68071
[51] Zarghami, M.; Szidarovszky, F., Revising the OWA operator for multi criteria decision making problems under uncertainty, European Journal of Operational Research, 198, 259-265, (2009) · Zbl 1163.90571
[52] Zavadskas, E. K.; Turskis, Z., Multiple criteria decision making (MCDM) methods in economics: an overview, Technological and Economic Development of Economy, 17, 397-427, (2011)
[53] Zeng, S. Z., Some intuitionistic fuzzy weighted distance measures and their application to group decision making, Group Decision and Negotiation, 22, 281-298, (2013)
[54] Zeng, S. Z.; Su, W., Linguistic induced generalized aggregation distance operators and their application to decision making, Economic Computation and Economic Cybernetics Studies and Research, 46, 155-172, (2012)
[55] Zhou, L. G.; Chen, H. Y., A generalization of the power aggregation operators for linguistic environment and its application in group decision making, Knowledge-Based Systems, 26, 216-224, (2012)
[56] Zhou, L. G.; Wu, J. X.; Chen, H. Y., Linguistic continuous ordered weighted distance measure and its application to multiple attributes group decision making, Applied Soft Computing, 25, 266-276, (2014)
[57] Zimmermann, H. J., Operators in models of decision making, (Dubois, D.; Prade, H.; Yager, R. R., Fuzzy Information Engineering, (1997), John Wiley & Sons New York), 471-496
[58] Zimmermann, H. J.; Zysno, P., Latent connectives in human decision making, Fuzzy Sets and Systems, 4, 37-51, (1980) · Zbl 0435.90009
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.