Measure Methods for DHHFLTSs

  • Xunjie GouEmail author
  • Zeshui XuEmail author
Part of the Studies in Fuzziness and Soft Computing book series (STUDFUZZ, volume 396)


In decision-making processes, measure methods, such as distance and similarity measures, correlation measure, entropy and cross entropy measure, etc., play an important role in many research fields including decision-making (Liao et al. 2015b; Xu and Wang 2011; Xu and Xia 2011), pattern recognition (Arevalillo-Herráez et al. 2013; Li et al. 1993), intelligent computing (Chen et al. 2010), recommended system (Liao et al. 2014), distance learning techniques (Gao et al. 2017), electricity markets (Gao et al. 2018), and ontological sparse vector learning (Gao et al. 2015), etc.


  1. Arevalillo-Herráez M, Ferri FJ, Domingo J (2013) A naive relevance feedback model for content-based image retrieval using multiple similarity measures. Pattern Recogn 43(3):9–629zbMATHGoogle Scholar
  2. Biswas A, Sarkar B (2019) Pythagorean fuzzy TOPSIS for multicriteria group decision-making with unknown weight information through entropy measure. Int J Intell Syst 34(6):1108–1128Google Scholar
  3. Chen YS, Wang WH, Juang JG (2010) Application of intelligent computing to autonomous vehicle control. IEEE Cong Evolut Comput 1–8Google Scholar
  4. Danielsson PE (1980) Euclidean distance Mapping. Comput Graphics Image Proc 14:227–248Google Scholar
  5. Farhadinia B (2014) Distance and similarity measures for higher order hesitant fuzzy sets. Knowl-Based Syst 55:43–48zbMATHGoogle Scholar
  6. Gao W, Farahani MR, Aslam A, Hosamani S (2017) Distance learning techniques for ontology similarity measuring and ontology mapping. Cluster Comput 20(2):959–968Google Scholar
  7. Gao W, Sarlak V, Parsaei MR, Ferdosi M (2018) Combination of fuzzy based on a meta-heuristic algorithm to predict electricity price in an electricity markets. Chem Eng Res Des 131:333–345Google Scholar
  8. Gao W, Zhu LL, Wang KY (2015) Ontology sparse vector learning algorithm for ontology similarity measuring and ontology mapping via ADAL technology. Int J Bifurcat Chaos 25(14):1540034MathSciNetzbMATHGoogle Scholar
  9. Gou XJ, Liao HC, Xu ZS, Herrera F (2017) Double hierarchy hesitant fuzzy linguistic term set and MULTIMOORA method: a case of study to evaluate the implementation status of haze controlling measures. Inf Fusion 38:22–34Google Scholar
  10. Gou XJ, Xu ZS, Liao HC, Herrera F (2018) Multiple criteria decision making based on distance and similarity measures with double hierarchy hesitant fuzzy linguistic environment. Comput Ind Eng 126:516–530Google Scholar
  11. Grzegorzewski P (2004) Distances between intuitionistic fuzzy sets and/or interval-valued fuzzy sets based on the Hausdorff metric. Fuzzy Sets Syst 148:319–328MathSciNetzbMATHGoogle Scholar
  12. Hafezalkotob A, Hafezalkotob A, Liao HC, Herrera F (2019) An overview of MULTIMOORA for multi-criteria decision-making: theory, developments, applications, and challenges. Inf Fusion 51:145–177Google Scholar
  13. Hamming RW (1950) Error detecting and error correcting codes. Bell Syst Tech J 29(2):147–160MathSciNetzbMATHGoogle Scholar
  14. Hausdorff F (1957) Set theory. Chelsea, New YorkzbMATHGoogle Scholar
  15. Hung WL, Yang MS (2004) Similarity measures of intuitionistic fuzzy sets based on Hausdorff distance. Pattern Recogn Lett 25:1603–1611Google Scholar
  16. Hussian Z, Yang MS (2019) Distance and similarity measures of Pythagorean fuzzy sets based on the Hausdorff metric with application to fuzzy TOPSIS. Int J Intell Syst 34(10):2633–2654Google Scholar
  17. Li X, Hall NS, Humphreys GW (1993) Discrete distance and similarity measures for pattern candidate selection. Pattern Recogn 26(6):843–851Google Scholar
  18. Li DQ, Zeng WY, Li JH (2015) New distance and similarity measures on hesitant fuzzy sets and their applications in multiple criteria decision making. Eng Appl Artif Intell 40:11–16Google Scholar
  19. Liao HC, Wu XL, Liang XD, Yang JB, Xu DL, Herrera F (2018) A continuous interval-valued linguistic ORESTE method for multi-criteria group decision making. Knowl-Based Syst 153:65–77Google Scholar
  20. Liao HC, Xu ZS (2015) Approaches to manage hesitant fuzzy linguistic information based on the cosine distance and similarity measures for HFLTSs and their application in qualitative decision making. Expert Syst Appl 42(12):5328–5336Google Scholar
  21. Liao HC, Xu ZS, Zeng XJ (2014) Distance and similarity measures for hesitant fuzzy linguistic term sets and their application in multi-criteria decision making. Inf Sci 271:125–142MathSciNetzbMATHGoogle Scholar
  22. Liao HC, Xu ZS, Zeng XJ (2015a) Hesitant fuzzy linguistic VIKOR method and its application in qualitative multiple criteria decision making. IEEE Trans Fuzzy Syst 23(5):1343–1355Google Scholar
  23. Liao HC, Xu ZS, Zeng XJ (2015b) Novel correlation coefficients between hesitant fuzzy sets and their application in decision-making. Knowl-Based Syst 82:115–127Google Scholar
  24. Liu DH, Liu YY, Wang LZ (2019) Distance measure for Fermatean fuzzy linguistic term sets based on linguistic scale function: an illustration of the TODIM and TOPSIS methods. Int J Intell Syst 34(11):2807–2834Google Scholar
  25. Merigó JM, Gil-Lafuente AM (2010) New decision-making techniques and their application in the selection of financial products. Inf Sci 180:2085–2094MathSciNetzbMATHGoogle Scholar
  26. Ren PJ, Xu ZS, Gou XJ (2016) Pythagorean fuzzy TODIM approach to multi-criteria decision making. Appl Soft Comput 42:246–259Google Scholar
  27. Ren ZL, Xu ZS, Wang H (2017) Dual hesitant fuzzy VIKOR method for multi-criteria group decision-making based on fuzzy measure and new comparison method. Inf Sci 396:1–16zbMATHGoogle Scholar
  28. Tan QY, Wei CP, Liu Q, Feng XQ (2016) The hesitant fuzzy linguistic TOPSIS method based on novel information measures. Asia Pac J Oper Res 33(5):1–22MathSciNetzbMATHGoogle Scholar
  29. Wang XD, Gou XJ, Xu ZS (2020) Assessment of Traffic congestion with ORESTE method under double hierarchy hesitant fuzzy linguistic term set. Appl Soft Comput 86:105864Google Scholar
  30. Wang W, Pang YF (2019) Hesitant interval-valued Pythagorean fuzzy VIKOR method. Int J Intell Syst 34(5):754–789Google Scholar
  31. Wei CP, Ren ZL, Rodríguez RM (2015) A hesitant fuzzy linguistic TODIM method based on a score function. Int J Comput Intell Syst 8(4):701–712Google Scholar
  32. Wu XL, Liao HC (2018) An approach to quality function deployment based on probabilistic linguistic term sets and ORESTE method for multi-expert multi-criteria decision making. Inf Fusion 43:13–26Google Scholar
  33. Wu ZB, Xu JP, Jiang XL, Zhong L (2019) Two MAGDM models based on hesitant fuzzy linguistic term sets with possibility distributions: VIKOR and TOPSIS. Inf Sci 473:101–120MathSciNetGoogle Scholar
  34. Xian SD, Liu Z, Gou XL, Wan WH (2020) Interval 2-tuple Pythagorean fuzzy linguistic MULTIMOORA method with CIA and their application to MCGDM. Int J Intell Syst. Scholar
  35. Xu ZS (2005) An approach based on similarity measure to multiple attribute decision making with trapezoid fuzzy linguistic variables. Fuzzy Syst Knowl Dis Lect Notes Comput Sci 3613:110–117Google Scholar
  36. Xu ZS (2012) Fuzzy ordered distance measures. Fuzzy Optim Decis Mak 11:73–97MathSciNetzbMATHGoogle Scholar
  37. Xu ZS, Chen J (2008a) Ordered weighted distance measure. J Syst Sci Syst Eng 16:529–555Google Scholar
  38. Xu ZS, Chen J (2008b) An overview of distance and similarity measures of intuitionistic fuzzy sets. Int J Uncertain Fuzziness Knowl-Based Syst 16:529–555MathSciNetzbMATHGoogle Scholar
  39. Xu YJ, Wang HM (2011) Distance measure for linguistic decision making. Syst Eng Proc 1:450–456Google Scholar
  40. Xu ZS, Xia MM (2011) Distance and similarity measures for hesitant fuzzy sets. Inf Sci 181:2128–2138MathSciNetzbMATHGoogle Scholar
  41. Xue WT, Xu ZS, Zhang XL, Tian XL (2018) Pythagorean fuzzy LINMAP method based on the entropy theory for railway project investment decision making. Int J Intell Syst 33(1):93–125Google Scholar
  42. Yager RR (1988) On ordered weighted averaging aggregation operators in multi-criteria decision-making. IEEE Trans Syst Man Cybern 18:183–190zbMATHGoogle Scholar
  43. Yager RR (2004) Generalized OWA aggregation operators. Fuzzy Optim Decis Mak 3:93–107MathSciNetzbMATHGoogle Scholar
  44. Yager RR (2010) Norms induced from OWA operators. IEEE Trans Fuzzy Syst 18:57–66Google Scholar
  45. Zavadskas EK, Mardani A, Turskis Z, Jusoh A, Nor KM (2016) Development of TOPSIS method to solve complicated decision-making problems—an overview on developments from 2000 to 2015. Int J Inf Tech Decis Mak 15(3):645–682Google Scholar
  46. Zavadskas EK, Turskis Z, Volvaciovas R, Kildiene S (2013) Multi-criteria assessment model of technologies. Stud Inform Control 22(4):249–258Google Scholar
  47. Zhang CZ, Chen C, Streimikiene D, Balezentis T (2019) Intuitionistic fuzzy MULTIMOORA approach for multi-criteria assessment of the energy storage technologies. Appl Soft Comput 79:410–423Google Scholar

Copyright information

© The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2021

Authors and Affiliations

  1. 1.Business SchoolSichuan UniversityChengduChina

Personalised recommendations