Interval 2-tuple linguistic distance operators and their applications to supplier evaluation and selection.

*(English)*Zbl 1400.91145Summary: With respect to multicriteria supplier selection problems with interval 2-tuple linguistic information, a new decision making approach that uses distance measures is proposed. Motivated by the ordered weighted distance (OWD) measures, in this paper, we develop some interval 2-tuple linguistic distance operators such as the interval 2-tuple weighted distance (ITWD), the interval 2-tuple ordered weighted distance (ITOWD), and the interval 2-tuple hybrid weighted distance (ITHWD) operators. These aggregation operators are very useful for the treatment of input data in the form of interval 2-tuple linguistic variables. We study some desirable properties of the ITOWD operator and further generalize it by using the generalized and the quasi-arithmetic means. Finally, the new approach is utilized to complete a supplier selection study for an actual hospital from the healthcare industry.

##### MSC:

91B06 | Decision theory |

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\textit{M.-M. Shan} et al., Math. Probl. Eng. 2016, Article ID 9893214, 12 p. (2016; Zbl 1400.91145)

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[1] | Yager, R. R., On ordered weighted averaging aggregation operators in multicriteria decision making, IEEE Transactions on Systems, Man, and Cybernetics, 18, 1, 183-190, (1988) · Zbl 0637.90057 |

[2] | Xu, Z.; Chen, J., Ordered weighted distance measure, Journal of Systems Science and Systems Engineering, 17, 4, 432-445, (2008) |

[3] | Merigó, J. M.; Gil-Lafuente, A. M., New decision-making techniques and their application in the selection of financial products, Information Sciences, 180, 11, 2085-2094, (2010) · Zbl 1194.91070 |

[4] | Merigó, J. M.; Xu, Y.; Zeng, S., Group decision making with distance measures and probabilistic information, Knowledge-Based Systems, 40, 81-87, (2013) |

[5] | Zeng, S.; Merigó, J. M.; Su, W., The uncertain probabilistic OWA distance operator and its application in group decision making, Applied Mathematical Modelling., 37, 9, 6266-6275, (2013) |

[6] | Merigó, J. M.; Casanovas, M.; Zeng, S. Z., Distance measures with heavy aggregation operators, Applied Mathematical Modelling, 38, 13, 3142-3153, (2014) |

[7] | Merigó, J. M.; Casanovas, M., Decision making with distance measures and linguistic aggregation operators, International Journal of Fuzzy Systems, 12, 3, 190-198, (2010) |

[8] | Zeng, S.; Su, W., Intuitionistic fuzzy ordered weighted distance operator, Knowledge-Based Systems, 24, 8, 1224-1232, (2011) |

[9] | Zeng, S., Some Intuitionistic Fuzzy Weighted Distance Measures and Their Application to Group Decision Making, Group Decision and Negotiation, 22, 2, 281-298, (2013) |

[10] | Xu, Z. S., Fuzzy ordered distance measures, Fuzzy Optimization and Decision Making, 11, 1, 73-97, (2012) · Zbl 1254.91119 |

[11] | Xian, S.; Sun, W., Fuzzy linguistic induced Euclidean OWA distance operator and its application in group linguistic decision making, International Journal of Intelligent Systems, 29, 5, 478-491, (2014) |

[12] | Su, W.; Zhang, C.; Zeng, S., Uncertain induced heavy aggregation distance operator and its application to decision making, Cybernetics and Systems, 46, 3-4, 172-187, (2015) |

[13] | Zhou, L.; Jin, F.; Chen, H.; Liu, J., Continuous intuitionistic fuzzy ordered weighted distance measure and its application to group decision making, Technological and Economic Development of Economy, 22, 1, 75-99, (2016) |

[14] | Zeng, S.; Chen, J.; Li, X., A hybrid method for pythagorean fuzzy multiple-criteria decision making, International Journal of Information Technology & Decision Making, 15, 02, 403-422, (2016) |

[15] | Xian, S.; Sun, W.; Xu, S.; Gao, Y., Fuzzy linguistic induced OWA Minkowski distance operator and its application in group decision making, PAA. Pattern Analysis and Applications, 19, 2, 325-335, (2016) |

[16] | Cheng, H.; Meng, F.; Chen, K., Several generalized interval-valued 2-tuple linguistic weighted distance measures and their application, International Journal of Fuzzy Systems, (2016) |

[17] | Meng, F.; Chen, X., A hesitant fuzzy linguistic multi-granularity decision making model based on distance measures, Journal of Intelligent and Fuzzy Systems, 28, 4, 1519-1531, (2015) · Zbl 1414.91114 |

[18] | Merigó, J. M.; Casanovas, M., Decision-making with distance measures and induced aggregation operators, Computers & Industrial Engineering, 60, 1, 66-76, (2011) |

[19] | Zhang, H.; Yu, L., New distance measures between intuitionistic fuzzy sets and interval-valued fuzzy sets, Information Sciences, 245, 181-196, (2013) · Zbl 1321.03074 |

[20] | Düğenci, M., A new distance measure for interval valued intuitionistic fuzzy sets and its application to group decision making problems with incomplete weights information, Applied Soft Computing Journal, 41, 120-134, (2016) |

[21] | Lu, C.; You, J. X.; Liu, H. C.; Li, P., Health-care waste treatment technology selection using the interval 2-tuple induced TOPSIS method, International Journal of Environmental Research and Public Health, 13, 6, 562, (2016) |

[22] | Xu, Z. S., Uncertain linguistic aggregation operators based approach to multiple attribute group decision making under uncertain linguistic environment, Information Sciences, 168, 1–4, 171-184, (2004) · Zbl 1170.91328 |

[23] | Wei, G.-W., Uncertain linguistic hybrid geometric mean operator and its application to group decision making under uncertain linguistic environment, International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems, 17, 2, 251-267, (2009) · Zbl 1162.90486 |

[24] | 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, 1, 47-64, (2011) · Zbl 1225.90067 |

[25] | Zhang, H., Some interval-valued 2-tuple linguistic aggregation operators and application in multiattribute group decision making, Applied Mathematical Modelling, 37, 6, 4269-4282, (2013) · Zbl 1270.91082 |

[26] | 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 Computing, 19, 2, 389-405, (2015) · Zbl 1349.91098 |

[27] | Singh, A.; Gupta, A.; Mehra, A., Energy planning problems with interval-valued 2-tuple linguistic information, Operational Research, (2016) |

[28] | Liu, H.-C.; You, J.-X.; You, X.-Y., Evaluating the risk of healthcare failure modes using interval 2-tuple hybrid weighted distance measure, Computers & Industrial Engineering, 78, 249-258, (2014) |

[29] | Shan, M.; You, J.; Liu, H., Some interval 2-tuple linguistic harmonic mean operators and their application in material selection, Advances in Materials Science and Engineering, 2016, (2016) |

[30] | Meng, F.; Zhu, M.; Chen, X., Some generalized interval-valued 2-tuple linguistic correlated aggregation operators and their application in decision making, Informatica, 27, 1, 111-139, (2016) · Zbl 1390.91113 |

[31] | Herrera, F.; Martínez, L., A 2-tuple fuzzy linguistic representation model for computing with words, IEEE Transactions on Fuzzy Systems, 8, 6, 746-752, (2000) |

[32] | Tai, W.-S.; Chen, C.-T., A new evaluation model for intellectual capital based on computing with linguistic variable, Expert Systems with Applications, 36, 2, 3483-3488, (2009) |

[33] | Herrera, F.; Martínez, L., A model based on linguistic 2-tuples for dealing with multigranular hierarchical linguistic contexts in multi-expert decision-making, IEEE Transactions on Systems, Man, and Cybernetics Part B: Cybernetics, 31, 2, 227-234, (2001) |

[34] | Zhang, H., The multiattribute group decision making method based on aggregation operators with interval-valued 2-tuple linguistic information, Mathematical and Computer Modelling, 56, 1-2, 27-35, (2012) · Zbl 1255.91079 |

[35] | Liu, X.; Tao, Z.; Chen, H.; Zhou, L., A new interval-valued 2-tuple linguistic bonferroni mean operator and its application to multiattribute group decision making, International Journal of Fuzzy Systems, (2016) |

[36] | Wu, Q.; Wu, P.; Zhou, Y.; Zhou, L.; Chen, H.; Ma, X., Some 2-tuple linguistic generalized power aggregation operators and their applications to multiple attribute group decision making, Journal of Intelligent and Fuzzy Systems, 29, 1, 423-436, (2015) |

[37] | Liu, H. C.; You, J. X.; Li, P.; Su, Q., Failure mode and effect analysis under uncertainty: an integrated multiple criteria decision making approach, IEEE Transactions on Reliability, 65, 3, 1380-1392, (2016) |

[38] | Liu, H.; You, J.; Chen, S.; Chen, Y., An integrated failure mode and effect analysis approach for accurate risk assessment under uncertainty, IIE Transactions, 48, 11, 1027-1042, (2016) |

[39] | Martínez, L.; Herrera, F., An overview on the 2-tuple linguistic model for computing with words in decision making: extensions, applications and challenges, Information Sciences, 207, 1-18, (2012) |

[40] | Xu, Z., Uncertain Multi-Attribute Decision Making: Methods and Applications, (2014), New York, NY, USA: Springer, New York, NY, USA |

[41] | Wei, G.-W., Extension of TOPSIS method for 2-tuple linguistic multiple attribute group decision making with incomplete weight information, Knowledge and Information Systems, 25, 3, 623-634, (2010) |

[42] | Xu, Z., An overview of methods for determining OWA weights, International Journal of Intelligent Systems, 20, 8, 843-865, (2005) · Zbl 1073.90020 |

[43] | Yari, G.; Chaji, A. R., Maximum Bayesian entropy method for determining ordered weighted averaging operator weights, Computers & Industrial Engineering, 63, 1, 338-342, (2012) |

[44] | Ahn, B. S.; Park, H., Least-squared ordered weighted averaging operator weights, International Journal of Intelligent Systems, 23, 1, 33-49, (2008) · Zbl 1128.68091 |

[45] | Xu, Z. S.; Xia, M. M., Distance and similarity measures for hesitant fuzzy sets, Information Sciences, 181, 11, 2128-2138, (2011) · Zbl 1219.03064 |

[46] | Yager, R. R., Generalized OWA aggregation operators, Fuzzy Optimization and Decision Making, 3, 1, 93-107, (2004) · Zbl 1057.90032 |

[47] | Wang, J. Q.; Wu, J. T.; Wang, J.; Zhang, H. Y.; Chen, X. H., Multi-criteria decision-making methods based on the Hausdorff distance of hesitant fuzzy linguistic numbers, Soft Computing, 20, 4, 1621-1633, (2016) |

[48] | Zadeh, L. A., The concept of a linguistic variable and its application to approximate reasoning. I, Information Sciences, 8, 3, 199-249, (1975) · Zbl 0397.68071 |

[49] | Xu, Z., A method based on linguistic aggregation operators for group decision making with linguistic preference relations, Information Sciences, 166, 1–4, 19-30, (2004) · Zbl 1101.68849 |

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.