A similarity measure determines the similarity between two objects. As important roles of similarity measure in chance theory, this paper introduces the concept of partial similarity measure for two uncertain random variables. Based on maximum similarity principle, partial similarity measure are used to recognize pattern problems. As an application in finance, partial similarity measure is applied to optimize portfolio selection of uncertain random returns via Monte-Carlo simulation and craw search algorithm.
AhmadzadeH., GaoR., Covariance of uncertain random variables and its application to portfolio optimization, Journal of Intelligent and Fuzzy Systems https://doi.org/10.1007/s12652-019-01323-0.
2.
AhmadzadeH., GaoR., NaderiH. and FarahikiaM., Partial divergence measure of uncertain random variables and its application, Soft Computing24(1) (2020), 501–512.
3.
AhmadzadeH., GaoR., DehghanM.H. and ShengY., Partial Entropy of Uncertain Random Variables, Journal of Intelligent and Fuzzy Systems33 (2017), 105–112.
4.
AhmadzadeH., GaoR. and ZareiH., Partial Quadratic Entropy of Uncertain Random Variables, Journal of Uncertain Systems10(4) (2016), 292–301.
5.
AhmadzadeH., ShengY.H. and Hassantabar DarziF., Some results of moments of uncertain random variables, Iranian Journal of Fuzzy Systems14(2) (2017), 1–21.
6.
AskarzadehA., A novel metaheuristic method for solving constrained engineering optimization problems: Crow search algorithm, Computers and Structures169(1) (2016), 1–12.
7.
CapitaineH., A relevance-based learning model of fuzzy similarity measures, IEEE Transactions on Fuzzy Systems20 (2012), 57–68.
8.
ChenX.W., KarS. and RalescuD.A., Cross-entropy measure of uncertain variables, Information Sciences201 (2012), 53–60.
9.
ChenS., Similarity measure between vague sets and between elements, IEEE Transactions on Systems Man Cybernetics27 (1997), 153–158.
10.
ChenS., MaB. and ZhangK., On the similarity metric and the distance metric, Theoretical Computer Science410 (2009), 2365–2376.
11.
ChouC., A new similarity measure of fuzzy numbers, Journal of Intelligent and Fuzzy Systems26 (2014), 287294.
12.
GaoX., JiaL. and KarS., A new definition of cross-entropy for uncertain variables, Soft Computing22 (2018), 5617–5623.
13.
HollandJ., Adaptation in natural and artificial systems, Ann Anbor: University of Michigan Press (1975).
14.
HouY.C., Subadditivity of Chance Measure, Journal of Uncertainty Analysis and Applications2(14) (2014), 1–8.
15.
KennedyJ. and EberhartR.C., Particle swarm optimization, Proc of IEEE International Conference on Neural Networks, Piscataway, (1995), 42–48.
16.
LiY., OlsonD. and QinZ., Similarity measures between intuitionistic fuzzy (vague) sets: A comparative analysis, Pattern Recognition Letters28 (2007), 278–285.
17.
LiD. and ChengC., New similarity measures of intuitionistic fuzzy sets and application to pattern recognition, Pattern Recognition Letters23 (2002), 221–225.
18.
LiX. and LiuB., On distance between fuzzy variables, Journal of Intelligent and Fuzzy Systems19 (2008), 197–204.
19.
LiX. and LiuY., Distance and similarity measures between uncertain variables, Journal of Intelligent and Fuzzy Systems28(5) (2015), 2073–2081.
LiuB., Some research problems in uncertainty theory, Journal of Uncertain Systems3(1) (2009), 3–10.
22.
LiuY.H. and HaM.H., Expected value of function of uncertain variables, Journal of Uncertain Systems4(3) (2010), 181–186.
23.
LiuY.H., Uncertain random variables: a mixture of uncertainty and randomness, Soft Computing17(4) (2013), 625–634.
24.
LiuY.H., Uncertain random programming with applications, Fuzzy Optimization and Decision Making12(2) (2013), 153–169.
25.
MajumdarP. and SamantaS., On similarity and entropy of neutrosophic sets, Journal of Intelligent and Fuzzy Systems26 (2014), 1245–1252.
26.
PengZ.X. and IwamuraK., A sufficient and necessary condition of uncertainty distribution, Journal of Interdisciplinary Mathematics13(3) (2010), 277–285.
27.
RezaeiK. and RezaeiH., New distance and similarity measures for hesitant fuzzy soft sets, Iranian Journal of Fuzzy Systems DOI: 10.22111/IJFS.2019.4571
28.
WangX. and DongC., Improving generalization of fuzzy ifthen rules by maximizing fuzzy entropy, IEEE Transactions on Fuzzy Systems17 (2009), 556–567.
29.
YangX.S. and DebS., Cuckoo search via Levy flights. In: Proceedings of World Congress on Nature and Biologically Inspired Computing (NaBIC), Coimbatore, India, 2009.
30.
YangX.S., Firefly algorithm, stochastic test functions and design optimisation, Int J Bio Inspired Comput2(2) (2010), 78–84.
31.
ZwickR., CarlsteinE. and BudescuD., Measures of similarity among fuzzy sets: A comparative analysis, International Journal of Aproximat Reasoning1 (1987), 221–242.
