A type of similarity measure between two vague soft sets, which contains subitem satisfying properties instead of single value parameters defined within a value range, is introduced. Some properties of the proposed similarity measure are studied. Eight detailed expression examples derived from the subitem are given. A real-world problem in handling landmark preference is solved based on this technique of similarity measure of vague soft sets. The results of an analysis of the landmark preference example are based on a comparison of the proposed similarity measure with the existing similarity measures, which is meant to demonstrate the advantages of the proposed approach.
W.Xu, J.Ma, S.Wang and G.Hao, Vague soft sets and their properties, Computers and Mathematics with Applications59(2) (2010), 787–794.
2.
P.K.Maji, R.Biswas and A.R.Roy, Intuitionistic fuzzy soft sets, Journal of Fuzzy Mathematics9(3) (2001), 677–692.
3.
P.K.Maji, R.Biswas and A.R.Roy, On intuitionistic fuzzy soft sets, Journal of Fuzzy Mathematics12(3) (2004), 669–683.
4.
W.L.Gau and D.J.Buehrer, Vague sets, IEEE Transactions on Systems, Man and Cybernetics23(2) (1993), 610–614.
5.
K.Atanassov, Intuitionistic fuzzy sets, Fuzzy Sets and Systems20(1) (1986), 87–96.
6.
H.Bustince and P.Burillo, Vague sets are intuitionistic fuzzy sets, Fuzzy Sets and Systems79(3) (1996), 403–405.
7.
A.Lu and W.Ng, Vague sets or intuitionistic fuzzy sets for handling vague data: Which one is better?Proceedings of the 24th International Conference on Conceptual Modeling, 2005, pp. 401–416.
8.
L.A.Zadeh, Fuzzy sets, Information and Control8(3) (1965), 338–353.
9.
D.Molodtsov, Soft set theory-First results, Computers and Mathematics with Applications37(4-5) (1999), 19–31.
10.
J.C.R.Alcantud and G.Santos-Garcia, A new criterion for soft set based decision making problems under incomplete information, International Journal of Computational Intelligence Systems10 (2017), 394–404.
11.
T.Q.Deng and X.F.Wang, An object-parameter approach to predicting unknown data in incomplete fuzzy soft sets, Applied Mathematical Modelling37 (2013), 4139–4146.
12.
Y.Zou and Z.Xiao, Data analysis approaches of soft sets under incomplete information, Knowledge-Based Systems21(8) (2008), 941–945.
13.
F.Fatimah, D.Rosadi, R.F.Hakim and J.C.R.Alcantud, Probabilistic soft sets and dual probabilistic soft sets in decision-making, Neural Computing and Applications, in press.
14.
P.K.Maji, R.Biswas and A.R.Roy, Fuzzy soft sets, Journal of Fuzzy Mathematics9(3) (2001), 589–602.
15.
P.Majumdar and S.K.Samanta, Generalised fuzzy soft sets, Computers and Mathematics with Applications59(4) (2010), 1425–1432.
16.
W.L.Hung and M.S.Yang, Similarity measures of intuition-istic fuzzy sets based on the Hausdorff distance, Pattern Recognition Letters25(14) (2004), 1603–1611.
17.
H.B.Mitchell, On the Dengfeng-Chuntian similarity measure and its application to pattern recognitions, Pattern Recognition Letters24(16) (2003), 3101–3104.
18.
J.Ye, Cosine similarity measures for intuitionistic fuzzy sets and their applications, Mathematical and Computer Modeling53(1-2) (2011), 91–97.
19.
F.R.Boran and D.Akay, A biparametric similarity measure on intuitionistic fuzzy sets with applications to pattern recognition, Information Sciences255 (2014), 45–57.
20.
S.M.Chen and C.H.Chang, A novel similarity between Atanassov's intuitionistic fuzzy sets based on transformation techniques with applications to pattern recognition, Information Sciences291(2015), 96–114.
21.
D.F.Li and C.Cheng, New similarity measures of intu-itionistic fuzzy sets and application to pattern recognition, Pattern Recognition Letters23(1-3) (2002), 221–225.
22.
Y.F.Song, X.D.Wang, L.Lei and A.J.Xue, A novel similarity measure on intuitionistic fuzzy sets with its applications, Applied Intelligence42 (2015).
23.
H.Nguyen, A novel similarity/dissimilarity measure for intuitionistic fuzzy sets and its application in pattern recognition, Expert Systems With Applications45(C) (2016), 97–107.
24.
P.Majumdar and S.K.Samanta, Decision making based on similarity measure of vague soft sets, Journal of Intelligent & Fuzzy Systems24(3) (2013), 637–646.
25.
J.Lu, X.Yan, D.Yuan and Z.Xu, A new similarity measure for vague sets, IEEE Intelligent Informatics Bulletin6(2) (2005), 14–18.
26.
C.Wang and A.J.Qu, Entropy, similarity measure and distance measure of vague soft sets and their relations, Information Sciences244 (2013), 92–106.
27.
F.Li and Z.Y.Xu, Measures of similarity between vague sets, Journal of Software12(6) (2001), 922–927.
28.
P.Muthukumar and G.Sai Sundara Krishnan, A similarity measure of intuitionistic fuzzy soft sets and its application in medical diagnosis, Applied Soft Computing41 (2016), 148–156.
29.
P.Majumdar and S.K.Samanta, Similarity measure of soft sets, New Mathematics & Natural Computation4(1) (2008), 1–12.
30.
Z.Z.Liang and P.F.Shi, Similarity measures on intuitionis-tic fuzzy sets, Pattern Recognition Letters, 24(15) (2003), 2687–2693.
31.
Y.H.Li, D.L.Olson and Z.Qin, Similarity measures between intuitionistic fuzzy (vague) sets: A comparative analysis, Pattern Recognition Letters28(2) (2007), 278–285.
32.
C.Tan and X.Chen, Dynamic similarity measures between intuitionistic fuzzy sets and its application, International Journal of Fuzzy Systems16(4) (2014), 511–519.
33.
C.Nothegger, S.Winter and M.Raubal, Computation of the salience of features, Spatial Cognition and Computation4 (2004), 113–136.
34.
P.Grzegorzewski, Distances between intuitionistic fuzzy sets and/or interval-valued fuzzy sets based on the hausdorff metric, Fuzzy sets and systems148(2) (2004), 319–328.
35.
J.Wang, S.Y.Liu and J.Zhang, Fuzzy multiple objectives decision making based on vague sets, Systems Engineering — Theory & Practice25(2) (2005), 119–122.
36.
A.Bigand and O.Colot, Fuzzy filter based on interval-valued fuzzy sets for image filtering, Fuzzy Sets and Systems161(1) (2010), 96–117.
37.
S.M.Chen, Similarity measures between vague sets and between elements, IEEE Transactionsons on System, Man and Cybernetics(Part B)27(1) (1997), 153–168.
38.
D.H.Hong and C.A.Kim, Note on similarity measure between vague sets and elements, Information Sciences115 (1999), 83–96.
