Interval linguistic fuzzy decision making in perspective of preference relations
Abstract
Consistency analysis is a crucial topic for preference relations. This paper studies the consistency of interval linguistic fuzzy preference relations (ILFPRs) using the constrained interval linguistic arithmetic and introduces a new consistency definition. Then, several properties of this definition are researched. Meanwhile, the connection between this concept and a previous one is discussed. Following this concept, programming models for judging the consistency and for deriving consistent ILFPRs are constructed, respectively. Considering the case that incomplete ILFPRs may be obtained, a programming model for obtaining missing judgments following the consistency discussion is built. Afterwards, the consensus for group decision making (GDM) is studied and a model for adjusting individual ILFPRs to reach the consensus threshold is established. Consequently, an interactive procedure for GDM with ILFPRs is presented. A practical problem is provided to illustrate the utilization of the new algorithm and comparative discussion is offered.
First published online 19 July 2019
Keyword : GDM, ILFPR, consistency, programming model, constrained interval linguistic arithmetic
How to Cite
Meng, F., Tang, J., & Zhang, S. (2019). Interval linguistic fuzzy decision making in perspective of preference relations. Technological and Economic Development of Economy, 25(5), 998-1015. https://doi.org/10.3846/tede.2019.10548
This work is licensed under a Creative Commons Attribution 4.0 International License.
References
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Chen, S. M., & Lee, L. W. (2012). Autocratic decision making using group recommendations based on the ILLOWA operator and likelihood-based comparison relations. IEEE Transactions on Systems, Man, and Cybernetics-Part A: Systems and Humans, 42(1), 115-129. https://doi.org/10.1109/TSMCA.2011.2157138
Cheng, H., Meng, F. Y., & Chen, K. (2017). Several generalized interval-valued 2-Tuple linguistic weighted distance measures and their application. International Journal of Fuzzy Systems, 19(4), 967-981. https://doi.org/10.1007/s40815-016-0218-5
Jin, F. F., Ni, Z. W., Pei, L. D., Chen, H. Y., Tao, Z. F., Zhu, X. H., & Ni, L. P. (2017). Approaches to group decision making with linguistic preference relations based on multiplicative consistency. Computers & Industrial Engineering, 114, 69-79. https://doi.org/10.1016/j.cie.2017.10.008
Herrera, F., Herrera-Viedma, E., & Verdegay, J. L. (1996). Direct approach processes in group decision making using linguistic OWA operators. Fuzzy Sets and Systems, 79(2), 75-190. https://doi.org/10.1016/0165-0114(95)00162-X
Herrera, F., & Herrera-Viedma, E. (2000). Choice functions and mechanisms for linguistic preference relations. European Journal of Operational Research, 120(1), 144-161. https://doi.org/10.1016/S0377-2217(98)00383-X
Herrera, F., & Martinez, L. (2000). A 2-tuple fuzzy linguistic representation model for computing with words. IEEE Transactions on Fuzzy Systems, 8(6), 746-752. https://doi.org/10.1109/91.890332
Herrera-Viedma, E., Martinez, L., Mata, F., & Chiclana, F. (2005). A consensus support system model for group decision-making problems with multigranular linguistic preference relations. IEEE Transactions on Fuzzy Systems, 13(5), 644-658. https://doi.org/10.1109/TFUZZ.2005.856561
Klir, G. J., & Yuan, B. (1998). Constrained fuzzy arithmetic: Basic questions and some answers. Soft Computing, 2(2), 100-108. https://doi.org/10.1007/s005000050038
Krejčí, J. (2017). On additive consistency of interval fuzzy preference relations. Computers & Industrial Engineering, 107, 128-140. https://doi.org/10.1016/j.cie.2017.03.002
Lodwick, W. A., & Jenkins, O. A. (2013). Constrained intervals and interval spaces. Soft Computing, 17(8), 1393-1402. https://doi.org/10.1007/s00500-013-1006-x
Meng, F. Y., Tan, C. Q., & Zhang, Q. (2014). An approach to multi-attribute group decision making under uncertain linguistic environment based on the Choquet aggregation operators. Journal of Intelligent & Fuzzy Systems, 26(2), 769-780. https://doi.org/10.3233/IFS-130767
Meng, F. Y., & Chen, X. H. (2015). An approach to uncertain linguistic multi-attribute group decision making based on interactive index. International Journal of Uncertainty Fuzziness and KnowledgeBased Systems, 23(3), 319-344. https://doi.org/10.1142/s0218488515500130
Meng, F. Y., Tang, J., & Xu, Z. S. (2019). Exploiting the priority weights from interval linguistic fuzzy preference relations. Soft Computing, 23(2), 583-597. https://doi.org/10.1007/s00500-017-2878-y
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Meng, F. Y., & Chen, X. H. (2016). Entropy and similarity measure for Atannasov’s interval-valued intuitionistic fuzzy sets and their applications. Fuzzy Optimization and Decision Making, 15(1), 75-101. https://doi.org/10.1007/s10700-015-9215-7
Park, J. H., Gwak, M. G., & Kwun, Y. C. (2011). Uncertain linguistic harmonic mean operators and their applications to multiple attribute group decision making. Computing, 93(1), 47-64. https://doi.org/10.1007/s00607-011-0151-2
Saaty, T. L. (1977). A scaling method for priorities in hierarchical structures. Journal of Mathematical Psychology, 15(3), 234-281. https://doi.org/10.1016/0022-2496(77)90033-5
Tapia García, J. M., del Moral, M. J., Martinez, M. A., & Herrera-Viedma, E. (2012). A consensus model for group decision making problems with linguistic interval fuzzy preference relations. Expert Systems with Applications, 39(11), 10022-10030. https://doi.org/10.1016/j.eswa.2012.02.008
Tang, J., Meng, F. Y., Li, C. L., & Li, C. H. (2018). A consistency-based approach to group decision making with uncertain multiplicative linguistic fuzzy preference relations. Journal of Intelligent & Fuzzy Systems, 35(1), 1037-1054. https://doi.org/10.3233/JIFS-17365
Wang, T. C., & Chen, Y. H. (2008). Applying fuzzy linguistic preference relations to the improvement of consistency of fuzzy AHP. Information Sciences, 178(19), 3755-3765. https://doi.org/10.1016/j.ins.2008.05.028
Xu, Z. S. (2004a). EOWA and EOWG operators for aggregating linguistic labels based on linguistic preference relations. International Journal of Uncertainty Fuzziness and Knowledge-Based Systems, 12(6), 791-810. https://doi.org/10.1142/S0218488504003211
Xu, Z. S. (2004b). A method based on linguistic aggregation operators for group decision making with linguistic preference relations. Information Sciences, 166(1-4), 19-30. https://doi.org/10.1016/j.ins.2003.10.006
Xu, Z. S. (2004c). Uncertain linguistic aggregation operators based approach to multiple attribute group decision making under uncertain linguistic environment. Information Sciences, 168(1-4), 171-184. https://doi.org/10.1016/j.ins.2004.02.003
Xu, Z. S. (2005). Deviation measures of linguistic preference relations in group decision making. Omega, 33(3), 249-254. https://doi.org/10.1016/j.omega.2004.04.008
Xu, Z. S. (2006a). Incomplete linguistic preference relations and their fusion. Information Fusion, 7(3), 331-337. https://doi.org/10.1016/j.inffus.2005.01.003
Xu, Z. S. (2006b). Induced uncertain linguistic OWA operators applied to group decision making. Information Fusion, 7(2), 231-238. https://doi.org/10.1016/j.inffus.2004.06.005
Xu, Z. S. (2006c). An approach based on the uncertain LOWG and induced uncertain LOWG operators to group decision making with uncertain multiplicative linguistic preference relations. Decision Support Systems, 41(2), 488-499. https://doi.org/10.1016/j.dss.2004.08.011
Xu, Z. S. (2008). Group decision making based on multiple types of linguistic preference relations. Information Sciences, 178(2), 452-467. https://doi.org/10.1016/j.ins.2007.05.018
Xu, J. P., & Wu, Z. B. (2013). A maximizing consensus approach for alternative selection based on uncertain linguistic preference relations. Computers & Industrial Engineering, 64(4), 999-1008. https://doi.org/10.1016/j.cie.2013.01.009
Xu, Y. J., Wu, D., & Wang, H. M. (2017). A Gower plot-based approach to ascertain and adjust the ordinal and additive inconsistencies for fuzzy linguistic preference relations. International Journal of Fuzzy Systems, 19(6), 2003-2019. https://doi.org/10.1007/s40815-017-0337-7
Zadeh, L. A. (1975). The concept of a linguistic variable and its application to approximate reasoning – Part I. Information Sciences, 8(3), 199-249 https://doi.org/10.1016/0020-0255(75)90036-5
Zhou, L. G., He, Y. D., Chen, H. Y., & Liu, J. P. (2014). On compatibility of uncertain multiplicative linguistic preference relations based on the linguistic COWGA. Applied Intelligence, 40(2), 229-243. https://doi.org/10.1007/s10489-013-0454-4
Zeng, S. Z., Mu, Z. M., & Baležentis, T. (2017). A novel aggregation method for Pythagorean fuzzy multiple attribute group decision making. International Journal of Intelligent Systems, 40(2), 573-585. https://doi.org/10.1002/int.21953
Büyüközkan, G., & Güleryüz, S. (2014). A new GDM based AHP framework with linguistic interval fuzzy preference relations for renewable energy planning. Journal of Intelligent & Fuzzy Systems, 27(6), 3181-3195. https://doi.org/10.3233/IFS-141275
Chen, H. Y., Zhou, L. G., & Han, B. (2011). On compatibility of uncertain additive linguistic preference relations and its application in the group decision making. Knowledge-Based Systems, 24(6), 816823. https://doi.org/10.1016/j.knosys.2011.03.003
Chen, S. M., & Lee, L. W. (2012). Autocratic decision making using group recommendations based on the ILLOWA operator and likelihood-based comparison relations. IEEE Transactions on Systems, Man, and Cybernetics-Part A: Systems and Humans, 42(1), 115-129. https://doi.org/10.1109/TSMCA.2011.2157138
Cheng, H., Meng, F. Y., & Chen, K. (2017). Several generalized interval-valued 2-Tuple linguistic weighted distance measures and their application. International Journal of Fuzzy Systems, 19(4), 967-981. https://doi.org/10.1007/s40815-016-0218-5
Jin, F. F., Ni, Z. W., Pei, L. D., Chen, H. Y., Tao, Z. F., Zhu, X. H., & Ni, L. P. (2017). Approaches to group decision making with linguistic preference relations based on multiplicative consistency. Computers & Industrial Engineering, 114, 69-79. https://doi.org/10.1016/j.cie.2017.10.008
Herrera, F., Herrera-Viedma, E., & Verdegay, J. L. (1996). Direct approach processes in group decision making using linguistic OWA operators. Fuzzy Sets and Systems, 79(2), 75-190. https://doi.org/10.1016/0165-0114(95)00162-X
Herrera, F., & Herrera-Viedma, E. (2000). Choice functions and mechanisms for linguistic preference relations. European Journal of Operational Research, 120(1), 144-161. https://doi.org/10.1016/S0377-2217(98)00383-X
Herrera, F., & Martinez, L. (2000). A 2-tuple fuzzy linguistic representation model for computing with words. IEEE Transactions on Fuzzy Systems, 8(6), 746-752. https://doi.org/10.1109/91.890332
Herrera-Viedma, E., Martinez, L., Mata, F., & Chiclana, F. (2005). A consensus support system model for group decision-making problems with multigranular linguistic preference relations. IEEE Transactions on Fuzzy Systems, 13(5), 644-658. https://doi.org/10.1109/TFUZZ.2005.856561
Klir, G. J., & Yuan, B. (1998). Constrained fuzzy arithmetic: Basic questions and some answers. Soft Computing, 2(2), 100-108. https://doi.org/10.1007/s005000050038
Krejčí, J. (2017). On additive consistency of interval fuzzy preference relations. Computers & Industrial Engineering, 107, 128-140. https://doi.org/10.1016/j.cie.2017.03.002
Lodwick, W. A., & Jenkins, O. A. (2013). Constrained intervals and interval spaces. Soft Computing, 17(8), 1393-1402. https://doi.org/10.1007/s00500-013-1006-x
Meng, F. Y., Tan, C. Q., & Zhang, Q. (2014). An approach to multi-attribute group decision making under uncertain linguistic environment based on the Choquet aggregation operators. Journal of Intelligent & Fuzzy Systems, 26(2), 769-780. https://doi.org/10.3233/IFS-130767
Meng, F. Y., & Chen, X. H. (2015). An approach to uncertain linguistic multi-attribute group decision making based on interactive index. International Journal of Uncertainty Fuzziness and KnowledgeBased Systems, 23(3), 319-344. https://doi.org/10.1142/s0218488515500130
Meng, F. Y., Tang, J., & Xu, Z. S. (2019). Exploiting the priority weights from interval linguistic fuzzy preference relations. Soft Computing, 23(2), 583-597. https://doi.org/10.1007/s00500-017-2878-y
Meng, F. Y., An, Q. X., & Chen, X. H. (2016). A consistency and consensus-based method to group decision making with interval linguistic preference relations. Journal of the Operational Research Society, 67(11), 1419-1437. https://doi.org/10.1057/jors.2016.28
Meng, F. Y., & Chen, X. H. (2016). Entropy and similarity measure for Atannasov’s interval-valued intuitionistic fuzzy sets and their applications. Fuzzy Optimization and Decision Making, 15(1), 75-101. https://doi.org/10.1007/s10700-015-9215-7
Park, J. H., Gwak, M. G., & Kwun, Y. C. (2011). Uncertain linguistic harmonic mean operators and their applications to multiple attribute group decision making. Computing, 93(1), 47-64. https://doi.org/10.1007/s00607-011-0151-2
Saaty, T. L. (1977). A scaling method for priorities in hierarchical structures. Journal of Mathematical Psychology, 15(3), 234-281. https://doi.org/10.1016/0022-2496(77)90033-5
Tapia García, J. M., del Moral, M. J., Martinez, M. A., & Herrera-Viedma, E. (2012). A consensus model for group decision making problems with linguistic interval fuzzy preference relations. Expert Systems with Applications, 39(11), 10022-10030. https://doi.org/10.1016/j.eswa.2012.02.008
Tang, J., Meng, F. Y., Li, C. L., & Li, C. H. (2018). A consistency-based approach to group decision making with uncertain multiplicative linguistic fuzzy preference relations. Journal of Intelligent & Fuzzy Systems, 35(1), 1037-1054. https://doi.org/10.3233/JIFS-17365
Wang, T. C., & Chen, Y. H. (2008). Applying fuzzy linguistic preference relations to the improvement of consistency of fuzzy AHP. Information Sciences, 178(19), 3755-3765. https://doi.org/10.1016/j.ins.2008.05.028
Xu, Z. S. (2004a). EOWA and EOWG operators for aggregating linguistic labels based on linguistic preference relations. International Journal of Uncertainty Fuzziness and Knowledge-Based Systems, 12(6), 791-810. https://doi.org/10.1142/S0218488504003211
Xu, Z. S. (2004b). A method based on linguistic aggregation operators for group decision making with linguistic preference relations. Information Sciences, 166(1-4), 19-30. https://doi.org/10.1016/j.ins.2003.10.006
Xu, Z. S. (2004c). Uncertain linguistic aggregation operators based approach to multiple attribute group decision making under uncertain linguistic environment. Information Sciences, 168(1-4), 171-184. https://doi.org/10.1016/j.ins.2004.02.003
Xu, Z. S. (2005). Deviation measures of linguistic preference relations in group decision making. Omega, 33(3), 249-254. https://doi.org/10.1016/j.omega.2004.04.008
Xu, Z. S. (2006a). Incomplete linguistic preference relations and their fusion. Information Fusion, 7(3), 331-337. https://doi.org/10.1016/j.inffus.2005.01.003
Xu, Z. S. (2006b). Induced uncertain linguistic OWA operators applied to group decision making. Information Fusion, 7(2), 231-238. https://doi.org/10.1016/j.inffus.2004.06.005
Xu, Z. S. (2006c). An approach based on the uncertain LOWG and induced uncertain LOWG operators to group decision making with uncertain multiplicative linguistic preference relations. Decision Support Systems, 41(2), 488-499. https://doi.org/10.1016/j.dss.2004.08.011
Xu, Z. S. (2008). Group decision making based on multiple types of linguistic preference relations. Information Sciences, 178(2), 452-467. https://doi.org/10.1016/j.ins.2007.05.018
Xu, J. P., & Wu, Z. B. (2013). A maximizing consensus approach for alternative selection based on uncertain linguistic preference relations. Computers & Industrial Engineering, 64(4), 999-1008. https://doi.org/10.1016/j.cie.2013.01.009
Xu, Y. J., Wu, D., & Wang, H. M. (2017). A Gower plot-based approach to ascertain and adjust the ordinal and additive inconsistencies for fuzzy linguistic preference relations. International Journal of Fuzzy Systems, 19(6), 2003-2019. https://doi.org/10.1007/s40815-017-0337-7
Zadeh, L. A. (1975). The concept of a linguistic variable and its application to approximate reasoning – Part I. Information Sciences, 8(3), 199-249 https://doi.org/10.1016/0020-0255(75)90036-5
Zhou, L. G., He, Y. D., Chen, H. Y., & Liu, J. P. (2014). On compatibility of uncertain multiplicative linguistic preference relations based on the linguistic COWGA. Applied Intelligence, 40(2), 229-243. https://doi.org/10.1007/s10489-013-0454-4
Zeng, S. Z., Mu, Z. M., & Baležentis, T. (2017). A novel aggregation method for Pythagorean fuzzy multiple attribute group decision making. International Journal of Intelligent Systems, 40(2), 573-585. https://doi.org/10.1002/int.21953