An outranking approach for multi-criteria decision-making with hesitant fuzzy linguistic term sets. (English) Zbl 1355.91036
Summary: The main purpose of this paper is to suggest an approach of multi-criteria decision-making that combines a hesitant fuzzy linguistic term set (HFLTS) with an outranking method involving systematic comparisons of the assessment values of alternatives for each criterion. A HFLTS is more suitable than the traditional fuzzy linguistic set for describing decision-makers’ preferences when they prefer to use several linguistic terms in expressions. After reviewing existing studies of HFLTSs, a novel outranking relational system of HFLTSs is developed and dominance relations for HFLTSs are introduced using outranking degrees of HFLTSs. In order to verify the efficacy of the developed method, an illustrative example is given and comparisons are made between the proposed method and other existing ones.
MSC:
| 91B06 | Decision theory |
Keywords:
multiple criteria analysis; hesitant fuzzy linguistic term set; linguistic decision making; outranking approachSoftware:
ELECTREReferences:
| [1] | Augusto, M.; Figueira, J.; Lisboa, J.; Yasin, M., An application of a multi-criteria approach to assessing the performance of Portugal’s economic sectors: methodology, analysis and implications, Eur. Bus. Rev., 17, 113-132 (2005) |
| [2] | Beccali, M.; Cellura, M.; Mistretta, M., Decision-making in energy planning. Application of the Electre method at regional level for the diffusion of renewable energy technology, Renew. Energy, 28, 2063-2087 (2003) |
| [3] | Beg, I.; Rashid, T., TOPSIS for hesitant fuzzy linguistic term sets, Int. J. Intell. Syst., 28, 1162-1171 (2013) |
| [4] | Boran, F. E.; Genc, S.; Kurt, M.; Akay, D., A multi-criteria intuitionistic fuzzy group decision making for supplier selection with TOPSIS method, Expert Syst. Appl., 36, 11363-11368 (2009) |
| [5] | Bordogna, G.; Fedrizzi, M.; Pasi, G., A linguistic modeling of consensus in group decision making based on OWA operators, IEEE Trans. Syst. Man Cybern. Part A: Syst. Humans, 27, 126-133 (2002) |
| [6] | Brito, A. J.; Almeida, A. T.; Mota, C. M.M., A multicriteria model for risk sorting of natural gas pipelines based on ELECTRE TRI integrating utility theory, Eur. J. Oper. Res., 200, 812-821 (2010) · Zbl 1177.90263 |
| [7] | Buchanan, J.; Vanderpooten, D., Ranking projects for an electricity utility using ELECTRE III, Int. Trans. Oper. Res., 14, 309-323 (2007) |
| [8] | Chen, C. T., Extensions of the TOPSIS for group decision-making under fuzzy environment, Fuzzy Sets Syst., 114, 1-9 (2000) · Zbl 0963.91030 |
| [9] | Chen, Y. H.; Wang, T. C.; Wu, C. Y., Multi-criteria decision making with fuzzy linguistic preference relations, Appl. Math. Modelling, 35, 1322-1330 (2011) · Zbl 1211.91091 |
| [10] | Delgado, M.; Verdegay, J.; Vila, M., On aggregation operations of linguistic labels, Int. J. Intell. Syst., 8, 351-370 (1993) · Zbl 0794.68154 |
| [11] | Dong, Y. C.; Xu, Y.; Yu, S., Computing the numerical scale of the linguistic term set for the 2-tuple fuzzy linguistic representation model, IEEE Trans. Fuzzy Syst., 17, 1366-1378 (2009) |
| [12] | Dong, Y. C.; Zhang, G. Q.; Hong, W. C.; Yu, S., Linguistic computation model based on 2-tuples and intervals, IEEE Trans. Fuzzy Syst., 21, 1006-1018 (2013) |
| [13] | Dubois, D., The role of fuzzy sets in decision sciences: old techniques and new directions, Fuzzy Sets Syst., 184, 3-28 (2011) · Zbl 1242.91043 |
| [14] | Dyer, J. S.; Fishburn, P. C.; Steuer, R. E.; Wallenius, J.; Zionts, S., Multiple criteria decision making, multi attribute utility theory: the next ten years, Manage. Sci., 38, 645-654 (1992) · Zbl 0825.90620 |
| [15] | Figueira, J.; Mousseau, V.; Roy, B., ELECTRE methods, (Multiple Criteria Decision Analysis: State of the Art Surveys (2005), Springer: Springer Berlin), 133-153 · Zbl 1072.90531 |
| [16] | Greco, S.; Matarazzo, B.; Slowinski, R., Rough sets theory for multicriteria decision analysis, Eur. J. Oper. Res., 129, 1-47 (2001) · Zbl 1008.91016 |
| [17] | Herrera, F.; Herrera-Viedma, E., Linguistic decision analysis: steps for solving decision problems under linguistic information, Fuzzy Sets Syst., 115, 67-82 (2000) · Zbl 1073.91528 |
| [18] | Herrera, F.; Herrera-Viedma, E.; Martinez, L., A fusion approach for managing multi-granularity linguistic term sets in decision making, Fuzzy Sets Syst., 114, 43-58 (2000) · Zbl 0963.91025 |
| [19] | Herrera, F.; Herrera-Viedma, E.; Martinez, L., A fuzzy linguistic methodology to deal with unbalanced linguistic term sets, IEEE Trans. Fuzzy Syst., 16, 354-370 (2008) |
| [20] | Herrera, F.; Herrera-Viedma, E.; Verdegay, J. L., Choice processes for non-homogeneous group decision making in linguistic setting, Fuzzy Sets Syst., 94, 287-308 (1998) |
| [21] | Herrera, F.; Martinez, L., A 2-tuple fuzzy linguistic representation model for computing with words, IEEE Trans. Fuzzy Syst., 8, 746-752 (2000) |
| [22] | Hobbs, B. F.; Meier, P., Energy Decisions and the Environment: A Guide to the Use of Multicriteria Methods (2000), Springer: Springer Berlin |
| [23] | Hokkanen, J.; Salminen, P., Choosing a solid waste management system using multicriteria decision analysis, Eur. J. Oper. Res., 98, 19-36 (1997) · Zbl 0922.90101 |
| [24] | Lee, L. W.; Chen, S. M., Fuzzy decision making based on hesitant fuzzy linguistic term sets, ACIIDS, 1, 21-30 (2013) |
| [25] | Li, D. F.; Chen, G. H.; Huang, Z. G., Linear programming method for multiattribute group decision making using IF sets, Inf. Sci., 180, 1591-1609 (2010) · Zbl 1188.90132 |
| [26] | Liao, H. C.; Xu, Z. S.; Zeng, X. J., Distance and similarity measures for hesitant fuzzy linguistic term sets and their application in multi-criteria decision making, Inf. Sci., 271, 125-142 (2014) · Zbl 1341.68260 |
| [27] | Lin, L. Z.; Yeh, H. R., Fuzzy linguistic decision to provide alternatives to market mechanism strategies, Expert Syst. Appl, 37, 6986-6996 (2010) |
| [28] | Liu, H. B.; Rodriguez, R. M., A fuzzy envelope for hesitant fuzzy linguistic term set and its application to multicriteria decision making, Inf. Sci., 258, 220-238 (2014) · Zbl 1320.68192 |
| [29] | Marbini, A. H.; Tavana, M., An extension of the Electre I method for group decision-making under a fuzzy environment, Omega, 39, 373-386 (2011) |
| [30] | Mendel, J. M., Historical reflections and new positions on perceptual computing, Fuzzy Optim. Decis. Making, 8, 325-335 (2009) |
| [31] | Mendel, J. M.; Wu, D., Perceptual Computing: Aiding People in Making Subjective Judgments (2010), IEEE Press and John Wiley: IEEE Press and John Wiley New Jersey |
| [32] | Meng, F. Y.; Chen, X. H.; Zhang, Q., Multi-attribute decision analysis under a linguistic hesitant fuzzy environment, Inf. Sci., 267, 287-305 (2014) · Zbl 1339.91044 |
| [33] | Papadopoulos, A.; Karagiannidis, A., Application of the multi-criteria analysis method Electre III for the optimisation of decentralised energy systems, Omega, 36, 766-776 (2008) |
| [34] | Park, J. H.; Gwak, M. G.; Kwun, Y. C., Uncertain linguistic harmonic mean operators and their applications to multiple attribute group decision making, Computing, 93, 47-64 (2011) · Zbl 1225.90067 |
| [35] | Parreiras, R. O.; Ekel, P. Y.; Martini, J. S.C.; Palhares, R. M., A flexible consensus scheme for multicriteria group decision making under linguistic assessments, Inf. Sci., 180, 1075-1089 (2010) |
| [36] | Peng, B.; Ye, C. M.; Zeng, S. Z., Uncertain pure linguistic hybrid harmonic averaging operator and generalized interval aggregation operator based approach to group decision making, Knowl. Based Syst., 36, 175-181 (2012) |
| [37] | Rodríguez, R. M.; Martínez, L.; Herrera, F., Hesitant fuzzy linguistic term sets, Foundations Intell. Syst., 287-295 (2011) |
| [38] | Rodríguez, R. M.; Martínez, L.; Herrera, F., Hesitant fuzzy linguistic term sets for decision making, IEEE Trans. Fuzzy Syst., 20, 109-119 (2012) |
| [39] | Rodríguez, R. M.; Martínez, L.; Herrera, F., A group decision making model dealing with comparative linguistic expressions based on hesitant fuzzy linguistic term sets, Inf. Sci., 241, 28-42 (2013) · Zbl 1320.91050 |
| [40] | Rodríguez, R. M.; Martínez, L.; Torra, V.; Xu, Z. S.; Herrera, F., Hesitant fuzzy sets: state of the art and future directions, Int. J. Intell. Syst., 29, 495-524 (2014) |
| [41] | Roy, B., Classement et choix en présence de points de vue multiples La méthode Electre, Rev. Fr. Inf. Rech. Op., 8, 57-75 (1968) |
| [42] | Roy, B., The outranking approach and the foundations of ELECTRE methods, Theory Decis., 31, 49-73 (1991) |
| [43] | Roy, B.; Martel, J. M., Analyse de la signifiance de diverses procéedures d’agrégation multicritère, Inf. Syst. Oper. Res., 44, 191-215 (2006) · Zbl 07682465 |
| [44] | Shanian, A.; Milani, A. S.; Carson, C.; Abeyaratne, R. C., A new application of ELECTRE III and revised Simos’ procedure for group material selection under weighting uncertainty, Knowl. Based Syst., 21, 709-720 (2008) |
| [45] | Stewart, T. J., A critical survey on the status of multiple criteria decision making theory and practice, Omega, 20, 569-586 (1992) |
| [46] | Wang, T. C.; Chen, Y. H., Applying fuzzy linguistic preference relations to the improvement of consistency of fuzzy AHP, Inf. Sci., 178, 3755-3765 (2008) · Zbl 1142.91411 |
| [47] | Wang, J. H.; Hao, J. Y., A new version of 2-tuple fuzzy linguistic representation model for computing with words, IEEE Trans. Fuzzy Syst., 14, 435-445 (2006) |
| [48] | 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, Inf. Sci., 274, 177-191 (2014) · Zbl 1341.91047 |
| [49] | Wang, J. Q.; Peng, J. J.; Zhang, H. Y.; Liu, T.; Chen, X. H., An uncertain linguistic multi-criteria group decision-making method based on a cloud model, Group Decis. Negot. (2014) |
| [50] | Wang, J. Q.; Wang, D. D.; Zhang, H. Y.; Chen, X. H., Multi-criteria group decision making method based on interval 2-tuple linguistic information and Choquet integral aggregation operators, Soft Comput. (2014) |
| [51] | Wang, J. Q.; Wang, P.; Wang, J.; Zhang, H. Y.; Chen, X. H., Atanassov’s Interval-valued Intuitionistic Linguistic Multi-criteria Group Decision-making Method Based on Trapezium Cloud Model, IEEE Trans. Fuzzy Syst. (2014) |
| [52] | Wang, W. P., Evaluating new product development performance by fuzzy linguistic computing, Expert Syst. Appl., 36, 9759-9766 (2009) |
| [53] | Wang, W. P., A fuzzy linguistic computing approach to supplier evaluation, Appl. Math. Modelling, 34, 3130-3141 (2010) · Zbl 1201.90212 |
| [55] | Wei, C. P.; Zhao, N.; Tang, X. J., Operators and comparisons of hesitant fuzzy linguistic term sets, IEEE Trans. Fuzzy Syst. (2013) |
| [56] | 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, Expert Syst. Appl., 37, 7895-7900 (2010) |
| [57] | Wei, G. W., Some generalized aggregating operators with linguistic information and their application to multiple attribute group decision making, Comput. Ind. Eng., 61, 32-38 (2011) |
| [58] | Wei, G. W.; Zhao, X. F., Some dependent aggregation operators with 2-tuple linguistic information and their application to multiple attribute group decision making, Expert Syst. Appl., 39, 5881-5886 (2012) |
| [59] | Wu, M. C.; Chen, T. Y., The ELECTRE multi-criteria analysis approach based on Atanassov’s intuitionc fuzzy sets, Expert Syst. Appl., 38, 12318-12327 (2011) |
| [60] | Xu, Y. J.; Da, Q., A method for multiple attribute decision making with incomplete weight information under uncertain linguistic environment, Knowl. Based Syst., 21, 837-841 (2008) |
| [61] | Xu, Y. J.; Wang, H. M., Approach based on 2-tuple linguistic power aggregation operators for multiple attribute group decision making under linguistic environment, Appl. Soft Comput., 11, 3988-3997 (2011) |
| [62] | Xu, Z. S., Uncertain linguistic aggregation operators based approach to multiple attribute group decision making under uncertain linguistic environment, Inf. Sci., 168, 171-184 (2004) · Zbl 1170.91328 |
| [63] | Xu, Z. S., An approach based on the uncertain LOWG and the induced uncertain OWG operators to group decision making with uncertain mutiplicative linguistic preference relations, Decis. Support Syst., 41, 488-499 (2006) |
| [64] | Xu, Z. S., Induced uncertain linguistic OWA operators applied to group decision making, Inf. Fusion, 7, 231-238 (2006) |
| [65] | Xu, Z. S., Linguistic aggregation operators: an overview, (Bustince, H.; Herrera, F.; Montero, J., Fuzzy Sets and Their Extensions: Representation, Aggregation and Models (2008), Springer: Springer Berlin), 163-181 · Zbl 1147.68083 |
| [66] | Xu, Z. S., Fuzzy harmonic mean operators, Int. J. Intell. Syst., 24, 152-172 (2009) · Zbl 1295.68190 |
| [67] | Yang, W.; Chen, Z. P., New aggregation operators based on the Choquet intergral and 2-tuple linguistic information, Expert Syst. Appl., 39, 2662-2668 (2012) |
| [68] | Zadeh, L., The concept of a linguistic variable and its application to approximate reasoning—I, Inf. Sci., 8, 199-249 (1975) · Zbl 0397.68071 |
| [69] | Zhang, Z. M.; Wu, C., Hesitant fuzzy linguistic aggregation operators and their applications to multiple attribute group decision making, J. Intell. Fuzzy Syst., 26, 2185-2202 (2014) · Zbl 1305.91141 |
| [70] | Zhou, S. M.; Chiclana, F.; John, R. I.; Garibaldi, J. M., Type-1 OWA operators for aggregating uncertain information with uncertain weights induced by type-2 linguistic quantifiers, Fuzzy Sets Syst., 159, 3281-3296 (2008) · Zbl 1187.68619 |
| [71] | Zhou, S. M.; Chiclana, F.; John, R. I.; Garibaldi, J. M., Alpha-level aggregation: a practical approach to type-1 OWA operation for aggregating uncertain information with applications to breast cancer treatments, IEEE Trans. Knowl. Data Eng., 23, 1455-1468 (2011) |
| [72] | Zhou, S. M.; John, R. I.; Chiclana, F.; Garibaldi, J. M., On aggregating uncertain information by type-2 OWA operators for soft decision making, Int. J. Intell. Syst., 25, 540-558 (2010) · Zbl 1192.68691 |
| [73] | Zhu, B.; Xu, Z. S., Consistency measures for hesitant fuzzy linguistic preference relations, IEEE Trans. Fuzzy Syst., 22, 35-45 (2014) |
| [74] | Zopounidis, C.; Doumpos, M., Multicriteria classification and sorting methods: a literature review, Eur. J. Oper. Res., 138, 229-246 (2002) · Zbl 1010.90032 |
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. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
