Abstract
In this paper, we develop single valued neutrosophic type-2 hesitant fuzzy sets (SVNT2HFS), presented as a variation of single valued neutrosophic fuzzy sets and type-2 hesitant fuzzy sets that includes truth, indeterminacy, falsity sets but these parts have been determined from type-2 fuzzy elements with motivation of single valued neutrosophic hesitant fuzzy set (SVNHFS) and Interval neutrosophic hesitant fuzzy set (INHFS). The proposed cluster can present more advantages than SVNHFS and INHFS for decision makers because it can provide a wide scala while membership values are being appointed by experts. Also, SVNHFS, INHFS are special cases of SVNT2HFS as indicated into comparison analysis. Therefore, our cluster has more knowledge capacity. Then, we give some basic dice measures, weighted dice measures, generalized dice measures and generalized weighted dice measures between two SVNT2HFSs. In here, generalized dice measures of SVNT2HFS propose more flexible relation for different values of \(\lambda\) change according to decision maker’s need and requirements. Also, we offer a decision making method and survey similarity between obtained an optimal solution and decision maker’s ideas by using dice measures, weighted dice measures, generalized dice measures and generalized weighted dice measures. At the end of the paper, two illustrative examples and two comparative analysis are proposed to show the practicality and effectiveness of our measures.
Similar content being viewed by others
References
Ali Z, Mahmood T (2020) Complex neutrosophic generalized dice similarity measures and their application to decision making. Tech J 5:78–87
Ali Z, Mahmood T (2020) Picture hesitant fuzzy generalized dice similarity measures and their application in pattern recognitions. CAAI Trans Intell Technol 25:73–94
Atanassov KT (1986) Intuitionistic fuzzy sets. Fuzzy Sets Syst 20(1):87–96
Chen S, Li-na C (2013) Interval-valued Hesitant. Fuzzy Sets Fuzzy Syst Math 6:007
Chen N, Xu ZS, Xia MM (2013) Correlation coefficients of hesitant fuzzy sets and their applications to clustering analysis. Appl Math Model 4(37):2197–2211
Chen N, Xu ZS, Xia MM (2013) Interval-valued hesitant preference relations and their applications to group decision making. Knowl Based Syst 37:528–540
Deveci M, Ozcan E, John R, Oner SC (2018) Interval type-2 hesitant fuzzy set method for improving the service quality of domestic airlines in Turkey. J Air Transp Manag 69:83–98
Dice LR (1945) Measures of the amount of ecologic association between species. Ecology 26(3):297–302
Feng L, Chuan qiang F, Wei He X (2018) Type-2 hesitant fuzzy sets. Fuzzy Inf Eng 10(2):249–259
Garg H, Ali Z, Mahmood T (2020) Generalized dice similarity measures for complex q-rung Orthopair fuzzy sets and its application. Complex Intell Syst. https://doi.org/10.1007/s40747-020-00203-x
Hung WL, Yang MS (2004) Similarity measures of intuitionistic fuzzy sets based on Hausdorff distance. Pattern Recognit Lett 25(14):1603–1611
Jaccard P (1901) Distribution de la flore alpine dans le Bassin des Drouces et dans quelques regions voisines. Bull Soc Sci Nat 37(140):241–272
Jiang H, Zhan J, Sun B, Alcantud JCR (2020) An MADM approach to covering-based variable precision fuzzy rough sets: an application to medical diagnosis. Int J Mach Learn Cybern 11:2181–2207
Karaaslan F, Ozlu S (2020) Correlation coefficients of dual type-2 hesitant fuzzy sets and their applications in clustering analysis. Int J Intell Syst 35(7):1200–1229
Khan Q, Liu P, Mahmood T (2018) Some generalized dice measures for double-valued neutrosophic sets and their applications. Mathematics 6(7):121
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 271:125–142
Mahmood T, Ye J, Khan Q (2016) Vector similarity measures for simplified neutrosophic hesitant fuzzy set and their applications. J Inequal Spec Funct 7:176–194
Ozlu S, Karaaslan F (2019) Some distance measures for type-2 hesitant fuzzy sets and their application to multi-criteria group decision making problems. Soft Comput 24:9965–9980
Pramanik S, Mondal K (2017) Some rough neutrosophic similarity measure and their application to multi attribute decision making. Glob J Eng Sci Res Manag 2(7):61–74
Rodriquez RM et al (2016) A position and perspective analysis of hesitant fuzzy sets on information fusion in decision making. Towards High Qual Prog Inf Fusion 29:89–97
Singh P (2014) Some new distance measures for type-2 fuzzy sets and distance measure based ranking for group decision making problems. Front Comput Sci 8(5):741–752
Salton G, Mc Gill MJ (1987) Introduction to modern information retrieval. Mc Graw-Hill, New York
Torra V, Narukawa Y (2009) On hesitant fuzzy sets and decision. The 18th IEEE international conference on fuzzy systems. Jeju Island, Korea, pp 1378–1382
Torra V (2010) Hesitant fuzzy sets. Int J Intell Syst 25:529–539
Qian G, Wang H, Feng XQ (2013) Generalized hesitant fuzzy sets and their application in decision support system. Knowl Based Syst 37:357–365
Wang H, Smarandache F, Zhang Q, Sunderraman R (2010) Single valued neutrosophic sets. Multi Space Multi Struct 4:410–413
Wei GW (2018) Some similarity measures for picture fuzzy sets and their applications. Iran J Fuzzy Syst 15(1):77–89
Wang J, Gao H, Wei G (2019) The generalized Dice similarity measures for Pythagorean fuzzy multiple attribute group decision making. Int J Intell Syst 34:1158–1183
Wei G, Gao H (2018) The generalized Dice similarity measures for picture fuzzy sets and their applications. Informatica 29(1):107–124
Ye J (2014) Multiple-attribute decision making method under a single valued neutrosophic hesitant fuzzy environment. J Intell Syst 24(1):23–36
Ye J (2016) Correlation coefficients of interval neutrosophic hesitant fuzzy sets and its application in a multiple attribute decision making method. Informatica 27(1):179–202
Ye J (2014) Vector similarity measures of hesitant fuzzy sets and their multiple attribute decision making. J Econ Comput Econ Cybern Stud Res 48(4):215–226
Ye J (2018) Generalized Dice measures for multiple attribute decision making under intuitionistic and interval-valued intuitionistic fuzzy environments. Neural Comput Appl 30:3623–3632
Zadeh LA (1965) Fuzzy sets. Inf Control 8:338–353
Zadeh LA (1975) The concept of a linguistic variable and its application to approximate reasoning.1. Inf Sci 8:199–249
Zhu B, Xu ZS, Xia MM (2012) Dual hesitant fuzzy sets. J Appl Math 879629:1–13
Zhua B, Xub Z (2014) Some results for dual hesitant fuzzy sets. J Intell Fuzzy Syst 26:1657–1668
Zhang K, Zhan J, Wu WZ (2020) On multi-criteria decision making method based on a fuzzy rough set model with fuzzy \(\alpha\)-neighborhoods. IEEE Trans Fuzzy Syst. https://doi.org/10.1109/TFUZZ.2020.3001670
Zhan J, Jiang H, Yao Y (2020) Three-way multi-attribute decision-making based on outranking relations. IEEE Trans Fuzzy Syst. https://doi.org/10.1109/TFUZZ.2020.3007423
Zhan J, Jiang H, Yao Y (2020) Covering-based variable precision fuzzy rough sets with PROMETHEE-EDAS methods. Inf Sci 538:314–336
Author information
Authors and Affiliations
Corresponding author
Additional information
Publisher's Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
About this article
Cite this article
Özlü, Ş. Generalized Dice measures of single valued neutrosophic type-2 hesitant fuzzy sets and their application to multi-criteria decision making problems. Int. J. Mach. Learn. & Cyber. 14, 33–62 (2023). https://doi.org/10.1007/s13042-021-01480-9
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s13042-021-01480-9