Consistency of hesitant fuzzy linguistic preference relations: an interval consistency index. (English) Zbl 1444.91083
Summary: The study of hesitant consistency is very important in decision-making with hesitant fuzzy linguistic preference relations (HFLPRs), and generally the normalization method is used as a tool to measure the consistency degree of a HFLPR. In this paper we propose a new hesitant consistency measure, called interval consistency index, to estimate the consistency range of a HFLPR. The underlying idea of the interval consistency index consists of measuring the worst consistency index and the best consistency index of a HFLPR. Furthermore, by comparative study, a connection is shown between the interval consistency index and the normalization method, demonstrating that the normalization method should be considered as an approximate average consistency index of a HFLPR.
Keywords:
linguistic preference relation; hesitant fuzzy linguistic term sets; consistency measure; interval index; average indexSoftware:
FLINTSTONESReferences:
| [1] | Alonso, S.; Cabrerizo, F. J.; Chiclana, F.; Herrera, F.; Herrera-Viedma, E., Group decision making with incomplete fuzzy linguistic preference relations, Int. J. Intell. Syst., 24, 2, 201-222 (2009) · Zbl 1162.68647 |
| [2] | Alonso, S.; Chiclana, F.; Herrera, F.; Herrera-Viedma, E.; Alcalá-Fedz, J.; Porcel, C., A consistency-based procedure to estimate missing pairwise preference values, Int. J. Intell. Syst., 23, 2, 155-175 (2008) · Zbl 1148.68470 |
| [3] | Dong, Y. C.; Chen, X.; Herrera, F., Minimizing adjusted simple terms in the consensus reaching process with hesitant linguistic assessments in group decision making, Inf. Sci., 297, 95-117 (2015) |
| [4] | Dong, Y. C.; Herrera-Viedma, E., Consistency-driven automatic methodology to set interval numerical scales of 2-tuple linguistic term sets and its use in the linguistic GDM with preference relation, IEEE Trans. Cybern., 45, 4, 780-792 (2015) |
| [5] | Dong, Y. C.; Li, C. C.; Chiclana, F.; Herrera-Viedma, E., Average-case consistency measurement and analysis of interval-valued reciprocal preference relations, Knowl. Based. Syst., 114, 108-117 (2016) |
| [6] | Dong, Y. C.; Li, C. C.; Herrera, F., An optimization-based approach to adjusting unbalanced linguistic preference relations to obtain a required consistency level, Inf. Sci., 292, 5, 27-38 (2015) · Zbl 1355.91026 |
| [7] | Dong, Y. C.; Li, C. C.; Herrera, F., Connecting the linguistic hierarchy and the numerical scale for the 2-tuple linguistic model and its use to deal with hesitant unbalanced linguistic information, Inf. Sci., 367-368, 259-278 (2016) · Zbl 1428.68297 |
| [8] | Dong, Y. C.; Li, C. C.; Xu, Y. F.; Gu, X., Consensus-based group decision making under multi-granular unbalanced 2-tuple linguistic preference relations, Group Decis. Negotiation, 24, 2, 217-242 (2015) |
| [9] | Dong, Y. C.; Zhang, G. Q.; Hong, W. C.; Yu, S., Linguistic computational model based on 2-tuples and intervals, IEEE Trans. Fuzzy Syst., 21, 6, 1006-1018 (2013) |
| [10] | Gong, Z. W.; Forrest, J.; Yang, Y. J., The optimal group consensus models for 2-tuple linguistic preference relations, Knowl. Based Syst., 37, 2, 427-437 (2013) |
| [11] | Herrera, F.; Alonso, S.; Chiclana, F.; Herrera-Viedma, E., Computing with words in decision making: foundations, trends and prospects, Fuzzy Optim. Decis. Making, 8, 4, 337-364 (2009) · Zbl 1178.90175 |
| [12] | Herrera, F.; Herrera-Viedma, E.; Martínez, L., A fuzzy linguistic methodology to deal with unbalanced linguistic term sets, IEEE Trans. Fuzzy Syst., 16, 2, 354-370 (2008) |
| [13] | Herrera, F.; Martínez, L., A model based on linguistic 2-tuples for dealing with multigranular hierarchical linguistic contexts in multi-expert decision-making, IEEE Trans. Syst. Man, Cybernetics Part B, 31, 2, 227-234 (2001) |
| [14] | Herrera, F.; Martínez, L., A 2-tuple fuzzy linguistic representation model for computing with words, IEEE Trans. Fuzzy Syst., 8, 6, 746-752 (2000) |
| [15] | Herrera-Viedma, E.; Chiclana, F.; Herrera, F.; Alonso, S., Group decision-making model with incomplete fuzzy preference relations based on additive consistency, IEEE Trans. Syst. Man Cybernetics-Part B, 37, 176-189 (2007) · Zbl 1128.90513 |
| [16] | Herrera-Viedma, E.; Herrera, F.; Chiclana, F.; Luque, M., Some issues on consistency of fuzzy preference relations, Eur. J. Oper. Res., 154, 1, 98-109 (2004) · Zbl 1099.91508 |
| [17] | Li, C. C.; Dong, Y. C.; Herrera, F.; Herrera-Viedma, E.; Martínez, L., Personalized individual semantics in computing with words for supporting linguistic group decision making. an application on consensus reaching, Inf. Fusion, 33, 29-40 (2017) |
| [18] | Li, C. C.; Dong, Y. C.; Herrera, F.; Martínez, L., An optimization-based approach to estimate the range of consistency in hesitant fuzzy linguistic preference relations, 2016 IEEE International Conference on Fuzzy Systems (FUZZ-IEEE) (2016) |
| [19] | Martínez, L.; Liu, J.; Ruan, D.; Yang, J. B., Dealing with heterogeneous information in engineering evaluation processes, Inf. Sci., 177, 7, 1533-1542 (2007) |
| [20] | Martínez, L.; Espinilla, M.; Pérez., L. G., Sensory evaluation based on linguistic decision analysis, Int. J. Approx. Reason., 44, 2, 148-164 (2007) |
| [21] | Martínez, L.; Espinilla, M.; Pérez, L., A linguistic multigranular sensory evaluation model for olive oil, Int. J. Comput. Intell. Syst., 1, 2, 148-158 (2008) |
| [22] | Martínez, L.; Herrera, F., An overview on the 2-tuple linguistic model for computing with words in decision making: extensions, applications and challenges, Inf.Sci., 207, 1, 1-18 (2012) |
| [23] | Martínez, L.; Ruan, D.; Herrera, F., Computing with words in decision support systems: an overview on models and applications, Int. J. Comput. Intell. Syst., 3, 4, 382-395 (2010) |
| [24] | Mendel, J. M.; Wu, D., Perceptual Computing: Aiding People in Making Subjective Judgments (2010), Wiley and Sons |
| [25] | Rodríguez, R. M.; Bedregal, B.; Bustince, H.; Dong, Y. C.; Farhadinia, B.; Kahraman, C.; Martínez, L.; Torra, V.; Xu, Y. J.; Xu, Z. S.; Herrera, F., A position and perspective analysis of hesitant fuzzy sets on information fusion in decision making. towards high quality progress, Inf. Fusion, 29, 89-97 (2016) |
| [26] | Rodríguez, R. M.; Labella, Á.; Martínez, L., An overview on fuzzy modelling of complex linguistic preferences in decision making, Int. J. Comput. Intell. Syst., 9, 81-94 (2016) |
| [27] | Rodríguez, R. M.; Martínez, L.; Herrera, F., Hesitant fuzzy linguistic term sets for decision making, IEEE Trans. Fuzzy Syst., 20, 1, 109-119 (2012) |
| [28] | Rodríguez, R. M.; Martínez, L.; Torra, V.; Xu, Z.; Herrera, F., Hesitant fuzzy sets: state of the art and future directions, Int. J. Intell. Syst., 29, 6, 495-524 (2014) |
| [29] | Tao, Z.; Chen, H.; Zho, L.; Liu, J., On new operational laws of 2-tuple linguistic information using archimedean t-norm and s-norm, Knowl. Based Syst., 66, 156-165 (2014) |
| [30] | Torra, V., Hesitant fuzzy sets, Int. J. Intell. Syst., 25, 6, 529-539 (2010) · Zbl 1198.03076 |
| [31] | Wan, S. P., 2-Tuple linguistic hybrid arithmetic aggregation operators and application to multi-attribute group decision making, Knowl. Based Syst., 45, 3, 31-40 (2013) |
| [32] | Wang, J. H.; Hao, J. Y., A new version of 2-tuple fuzzy linguistic representation model for computing with words. ieee trans fuzzy syst, IEEE Trans. Fuzzy Syst., 14, 3, 435-445 (2006) |
| [33] | Wei, C. P.; Zhao, N.; Tang, X. J., Operators and comparisons of hesitant fuzzy linguistic term sets, IEEE Trans. Fuzzy Syst., 22, 3, 575-585 (2014) |
| [34] | Wu, Z. B.; Xu, J. P., Managing consistency and consensus in group decision making with hesitant fuzzy linguistic preference relations, Omega, 65, 3, 28-40 (2016) |
| [35] | Zadeh, L. A., The concept of a linguistic variable and its application to approximate reasoning i, Inf. Sci., 8, 199-249 (1975) · Zbl 0397.68071 |
| [36] | Zadeh, L. A., The concept of a linguistic variable and its application to approximate reasoning II, Inf. Sci., 8, 301-353 (1975) · Zbl 0404.68074 |
| [37] | Zadeh, L. A., The concept of a linguistic variable and its application to approximate reasoning III, Inf. Sci., 9, 43-80 (1975) · Zbl 0404.68075 |
| [38] | Zhang, G.; Dong, Y. C.; Xu, Y., Consistency and consensus measures for linguistic preference relations based on distribution assessments, Inf. Fusion, 17, 1, 46-55 (2014) |
| [39] | Zhu, B.; Xu, Z. S., Consistency measures for hesitant fuzzy linguistic preference relations, IEEE Trans. Fuzzy Syst., 22, 1, 35-45 (2014) |
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.
