Shraddha Harode* | Manoj Jha | Namita Srivastava | Sujoy Das
OPEN ACCESS
According to the basic idea of financial market an investor used a decision making approach for the maximum return with respect to minimum risk. We test a novel decision making process to determine the optimal assets for making a portfolio and compare our method to Analytical Hierarchy Process. Based on measure of performance of two decision making process i.e. Fuzzy Soft Set and Analytical Hierarchy Process, the outcome is more reliable through fuzzy soft set from multi-input data set. The optimal portfolio is constructed using fuzzy soft set method. The aim of this paper is to select the optimal ratio of portfolio, in which multi objective portfolio optimization solved by the help of Butterfly Particle swarm optimization. This problem is formulated in mathematical programming in such a way that it has two main objectives, minimum risk and maximum return. In this paper the effectiveness of fuzzy soft set in financial problems is illustrated with example.
portfolio optimization, fuzzy set, soft set, decision making problem, butterfly particle swarm optimization (BFPSO), particle swarm optimization (PSO)
[1] Maji P, Roy AR, Biswas R. (2002). An application of soft sets in a decision making problem. Computers & Mathematics with Applications 1077-83. https://doi.org/10.1016/S0898-1221(02)00216-X
[2] Roy AR, Maji P. (2007). A fuzzy soft set theoretic approach to decision making problems. Journal of Computational and Applied Mathematics 412-18. https://doi.org/10.1016/j.cam.2006.04.008
[3] Çağman N, Enginoğlu S. (2010). Soft matrix theory and its decision making. Computers & Mathematics with Applications 3308-14. https://doi.org/10.1016/j.camwa.2010.03.015
[4] Çağman N, Enginoğlu S. (2010). Soft set theory and uni–int decision making. European Journal of Operational Research 848-55. https://doi.org/10.1016/j.ejor.2010.05.004
[5] Feng F, Jun Y B, Liu X, Li L. (2010). An adjustable approach to fuzzy soft set based decision making. Journal of Computational and Applied Mathematics 10-20. https://doi.org/10.1016/j.cam.2009.11.055
[6] Kong Z, Gao L, Wang L. (2009). Comment on “A fuzzy soft set theoretic approach to decision making problems”. Journal of Computational and Applied Mathematics 540-42. https://doi.org/10.1016/j.cam.2008.01.011
[7] Xiao Z, Xia S, Gong K, Li D. (2012). The trapezoidal fuzzy soft set and its application in MCDM. Applied Mathematical Modelling 5844-55. https://doi.org/10.1016/j.apm.2012.01.036
[8] Mao J, Yao D, Wang C. (2013). Group decision making methods based on intuitionistic fuzzy soft matrices. Applied Mathematical Modelling 6425-36. https://doi.org/10.1016/j.apm.2013.01.015
[9] Thakur G. (2014). Fuzzy soft traffic accident alert model. National Academy Science Letters 261-68.
https://doi.org/10.1007/s40009-014-0235-6
[10] Alcantud JCR. (2016). A novel algorithm for fuzzy soft set based decision making from multiobserver input parameter data set. Information Fusion 142-48. https://doi.org/10.1016/j.inffus.2015.08.007
[11] Saaty TL. (1977). A scaling method for priorities in hierarchical structures. Journal of Mathematical Psychology 234-81. https://doi.org/10.1016/0022-2496(77)90033-5
[12] Saaty TL. (1980). The analytic hierarchy process New York. Nachhaltigkeit im Einkauf von Logistikdienstleistungen.
[13] Eberhart R, Kennedy J. (1995). Particle swarm optimization. Proceeding of IEEE International Conference on Neural Network. Perth, Australia, pp. 1942-48. https://doi.org/10.1109/ICNN.1995.488968
[14] Eberhart R, Kennedy J. (1995). Micro Machine and Human Science, 1995 MHS'95., Proceedings of the Sixth International Symposium on IEEE. https://doi.org/10.1109/MHS.1995.494249
[15] Kennedy J. (1997). Evolutionary Computation. IEEE International Conference on IEEE.
[16] Sharma S, Bhattacharjee S, Bhattacharya A. (2015). Solution of multi-objective optimal dg placement problems using Swine Influenza Model Based Optimization (SIMBO). AMSE JOURNALS, 46-70.
[17] Bohre AK, Agnihotri G, Dubey MBhadoriya JS. (2014). A novel method to find optimal solution based on modified butterfly particle swarm optimization. International Journal of Soft Computing, Mathematics and Control (IJSCMC) 1-14. https://doi.org/10.14810/ijscmc.2014.3401
[18] Bohre AK, Agnihotri G, Dubey M. (2014). Networks & Soft Computing (ICNSC). First International Conference on IEEE. https://doi.org/10.14810/ijscmc.2015.4302
[19] Deep K, Bansal J C. (2009). Mean particle swarm optimisation for function optimisation. International Journal of Computational Intelligence Studies 72-92. https://doi.org/10.1504/IJCISTUDIES.2009.025339
[20] Ghali NI, El-Dessouki N, Mervat ABakrawi L. (2009). Exponential particle swarm optimization approach for improving data clustering. International Journal of Electrical, Computer, and Systems Engineering 208-12. https://doi.org/10.1016/j.eswa.2007.01.028
[21] Liu Y, Qin Z, Shi Z, Lu J. (2007). Center particle swarm optimization. Neurocomputing, 672-79. https://doi.org/10.1016/j.neucom.2006.10.002
[22] Villalobos-Arias M. (2009). portfolio optimization using particle swarms with stripes. Revista de Matemática: Teoríay Aplicaciones. https://doi.org/10.15517/rmta.v16i2.301
[23] Jana P, Roy T, Mazumder S. (2009). Multi-objective possibilistic model for portfolio selection with transaction cost. Journal of Computational and Applied Mathematics 188-96. https://doi.org/10.1016/j.cam.2008.09.008
[24] León T, Liern V, Vercher E. (2002). Viability of infeasible portfolio selection problems: A fuzzy approach. European Journal of Operational Research, 178-89. https://doi.org/10.1016/S0377-2217(01)00175-8
[25] Ehrgott M, Klamroth K, Schwehm C. (2004). An MCDM approach to portfolio optimization. European Journal of Operational Research 155(3): 752-770. https://doi.org/10.1016/S0377-2217(02)00881-0
[26] Ramaswamy S. (1998). Portfolio selection using fuzzy decision theory.
[27] Gupta P, Inuiguchi M, Mehlawat MK. (2011). A hybrid approach for constructing suitable and optimal portfolios. Expert Systems with Applications, 5620-32. https://doi.org/10.1016/j.eswa.2010.10.073
[28] Sets F. (1965). L. Zadeh. Information and Control.–NY, 338-353. https://doi.org/10.1016/S0019-9958(65)90241-X
[29] Molodtsov D. (1999). Soft set theory—first results. Computers & Mathematics with Applications 19-31. https://doi.org/10.1016/S0898-1221(99)00056-5
[30] Maji PK, Biswas R, Roy A. (2001). Fuzzy soft sets.
[31] Xiao Z, Gong K, Zou Y. (2009). A combined forecasting approach based on fuzzy soft sets. Journal of Computational and Applied Mathematics 326-33. https://doi.org/10.1016/j.cam.2008.09.033
[32] Saaty TL. (2000). Fundamentals of decision making and priority theory with the analytic hierarchy process. Analytic Hierarchy Process Series 6. Auflage, Pittsburg.
[33] Basu TM, Mahapatra NK, Mondal SK. (2012). A balanced solution of a fuzzy soft set based decision making problem in medical science. Applied Soft Computing 3260-75. https://doi.org/10.1016/j.asoc.2012.05.006
[34] Selection P. (1952). Harry Markowitz. The Journal of Finance 77-91. https://doi.org/10.1111/j.1540-6261.1952.tb01525.x
[35] It WR. (1959). Portfolio selection: efficient diversification of investments. https://doi.org/10.2307/2326204
[36] Sharpe WF. (1964). Capital asset prices: A theory of market equilibrium under conditions of risk. The Journal of Finance 425-42. https://doi.org/10.2307/2977928
[37] Konno H, Yamazaki H. (1991). Mean-absolute deviation portfolio optimization model and its applications to Tokyo stock market. Management Science 519-31. https://doi.org/10.1287/mnsc.37.5.519
[38] Speranza MG. (1993). Linear programming models for portfolio optimization.
[39] Simaan Y. (1997). Estimation risk in portfolio selection: the mean variance model versus the mean absolute deviation model. Management Science 1437-46. https://doi.org/10.1287/mnsc.43.10.1437
[40] Fang Y, Xue R, Wang S (2009). Computational Sciences and Optimization, 2009. CSO 2009. International Joint Conference on IEEE.
[41] Zadeh LA. (1999). Fuzzy sets as a basis for a theory of possibility. Fuzzy Sets and Systems 9-34.
[42] Fang Y, Lai KK, Wang SY. (2006). Portfolio rebalancing model with transaction costs based on fuzzy decision theory. European Journal of Operational Research 879-93. https://doi.org/10.1016/j.ejor.2005.05.020
[43] Gupta P, Mehlawat MK, Saxena A. (2008). Asset portfolio optimization using fuzzy mathematical programming. Information Sciences 1734-55. https://doi.org/10.1016/j.ins.2007.10.025
[44] Linstone HA, Turoff M. (1975). The Delphi method: Technology and application. Reading: Addison-Wesley.
[45] Gupta L, Jain N, Choudhury U, Gupta S. (2005). Indian household investors survey-2004. Society for Capital Market Research & Development, New Delhi.