Decision making for portfolio selection by fuzzy multi criteria linear programming

Year 2019, Volume: 68 Issue: 2, 2238 - 2257, 01.08.2019

Serkan Akbaş , Türkan Erbay Dalkılıç

https://doi.org/10.31801/cfsuasmas.467286

Cited By: 2

Abstract

In daily life events,
there are many complexities arising from lack of information and uncertainty.
Fuzzy linear programming model has been developed to reduce or eliminate this
complexity. Fuzzy linear programming is the process of choosing the optimum solution
from among the decision alternatives to achieve a specific purpose in cases
where the information is not certain. One
of the fields where the lack of information or uncertainty makes it difficult
to decide is financial markets. Investors who have a certain amount of
accumulations are aiming to increase in various ways as well as protecting the
value of their income. While doing this, encounter the problem of deciding to
which investment vehicle they need to invest in what extent. Therefore, investors
apply to fuzzy linear programming model to eliminate this uncertainty and to
create the optimal portfolio. In
the portfolio selection process suggestions in the literature, the
determination of criteria weights is based on triangular fuzzy numbers. In this
study, as an alternative to the Enea and Piazza's portfolio selection model,
which uses the triangular fuzzy numbers for criteria weighting, a new model
that uses the trapezoidal fuzzy numbers for the same aim was proposed. With the
solution of the linear programming model which is based on the determined
weights, an alternative solution has been produced to the problem of which
investment instrument will be invested at what proportion. The results obtained from the existing methods and the
results obtained from the proposed model were compared.

Keywords

Multi-criteria decision making, Linear Programming, Analytic hierarchy process, Trapezoidal fuzzy numbers, Portfolio selection

References

• Cevik, O. and Yildirim, Y., An Application in Milk Products Factory with Fuzzy Linear Programming, Karamanoglu Mehmetbey University Journal of Social Economic Research,12(18) (2010), 15-26.
• Zhao, D. and Fang, Y., Representation Bias, Return Forecast, and Portfolio Selection in the Stock Market of China, Mathematical Problems in Engineering, 2014(2014), 1-8.
• Liu, Y. and Wu, X., A Class of Fuzzy Portfolio Optimization Problems: E-S Models, International Conference in Swam Intelligence,, (2010), 43-50.
• Chen, L., Li, B., Dong, S. and Pan, H., A Combined CFAHP - FTOPSIS Approach for Portfolio Selection, China Finance Review International, 3(4) (2013), 381-395.
• Zhang, W. G., Mei, Q., Lu, Q. and Xiao, W. L., Evaluating Methods of Investment Project and Optimizing Models of Portfolio Selection in Fuzzy Uncertainty, Computers & Industrial Engineering, 61(3) (2011), 721-728.
• Nguyen, T. T. and Gordon-Brown, L., Constrained Fuzzy Hierarchical Analysis for Portfolio Selection Under Higher Moments, IEEE Transactions on Fuzzy Systems, 20(4) (2011), 666-682.
• Xu, W., Deng, X. and Li, J., A New Fuzzy Portfolio Model Based on Background Risk Using MCFOA, International Journal of Fuzzy Systems, 17(2) (2015), 246-255.
• Ostermark, R., A Fuzzy Control Model (FCM) for Dynamic Portfolio Management, Fuzzy Sets and Systems, 78(3) (1996), 243-254.
• Ramaswamy, S., Portfolio Selection Using Fuzzy Decision Theory, Bank for International Settlements, 59 (1998).
• Inuiguchi, M. and Ramik, J., Possibilistic Linear Programming: A Brief Review of Fuzzy Mathematical Programming and A Comparison With Stochastic Programming in Portfolio Selection Problem, Fuzzy Sets and Systems, 111(1) (2000), 3-28.
• Sadjadi, S. J., Seyedhosseini, S. M. and Hassanlou, K., Fuzzy Multi Period Portfolio Selection With Different Rates for Borrowing and Lending, Applied Soft Computing, 11(4) (2011), 3821-3826.
• Ghapanchi, A. H., Tavana, M., Khakbaz, M. H. and Low, G., A Methodology for Selecting Portfolios of Projects With Interactions and Under Uncertainty, International Journal of Project Management, 30(7) (2012), 791-803.
• Rahmani, N., Talebpour, A., and Ahmadi, T., Developing aMulti Criteria Model for Stochastic IT Portfolio Selection by AHP Method, Procedia-Social and Behavioral Sciences, 62 (2012), 1041-1045.
• Gupta, P., Mehlawat, M. K. and Saxena, A., Hybrid Optimization Models of Portfolio Selection Involving Financial and Ethical Considerations, Knowledge-Based Systems, 37 (2013), 318-337.
• Yue, W. and Wang, Y., A New Fuzzy Multi-Objective Higher Order Moment Portfolio Selection Model for Diversified Portfolios, Physica A: Statistical Mechanics and its Applications, 465 (2017), 124-140.
• Kemaloglu, S. A., Inan, G. E. and Apaydin, A., Portfolio Optimization Under Parameter Uncertainty Using the Risk Aversion Formula, Communications Series A1 Mathematics & Statistics, 67(2) (2018), 50-63.
• Kim, J., and Kim, J., Optimal Portfolio for LNG Importation in Korea Using a Two-Step Portfolio Model and a Fuzzy Analytic Hierarchy Process, Energies, 11(11) (2018), 3049.
• Liagkouras, K., A New Three-Dimensional Encoding Multiobjective Evolutionary Algorithm With Application to the Portfolio Optimization Problem, Knowledge-Based Systems, 163 (2019), 186-203.
• Ceylan, A. and Korkmaz, T., Borsada Uygulamalı Portföy Yönetimi, Ekin Kitabevi Yayınlari, 1998.
• Enea, M. and Piazza, T., Project Selection by Constrained Fuzzy AHP, Fuzzy optimization and decision making, 3(1) (2004), 39-62.
• Tiryaki, F. and Ahlatcioglu, B., Fuzzy portfolio selection using fuzzy analytic hierarchy process, Information Sciences, 179(1-2) (2009), 53-69.
• Ahari, S. G., Ghaffari-Nasab, N., Makui, A. and Ghodsypour, S. H., A Portfolio Selection Using Fuzzy Analytic Hierarchy Process: A Case Study of Iranian Pharmaceutical Industry, International Journal of Industrial Engineering Computations, 2(2) (2011), 225-236.
• Krejci, J., Pavlacka, O. and Talasova, J., A Fuzzy Extension of Analytic Hierarchy Process Based on the Constrained Fuzzy Arithmetic, Fuzzy Optimization and Decision Making, 16(1) (2017), 89-110.
• Dong, J. and Wan, S. P., A New Trapezoidal Fuzzy Linear Programming Method Considering the Acceptance Degree of Fuzzy Constraints Violated, Knowledge-Based Systems, 148 (2018), 100-114.
• Ebrahimnejad, A., A Method for Solving Linear Programming With Interval-Valued Trapezoidal Fuzzy Variables, RAIRO-Operations Research, 52(3) (2018), 955-979.
• Darby-Dowman, K., Lucas, C., Mitra, G. and Yadegar, J., Linear, Integer, Separable and Fuzzy Programming Problems: A Unified Approach towards Reformulation, Journal of the Operational Research Society, 39(3) (1988), 161-171.
• Sharma, U. and Aggarwal, S., Solving Fully Fuzzy Multi-objective Linear Programming Problem Using Nearest Interval Approximation of Fuzzy Number and Interval Programming, International Journal of Fuzzy Systems, 20(2) (2018), 488-499.
• Nakamura, K., Some Extensions of Fuzzy Linear Programming, Fuzzy Sets and Systems, 14(3) (1984), 211-229.
• Tanaka, H. and Asai, K., Fuzzy Linear Programming problems With Fuzzy Numbers, Fuzzy Sets and Systems, 13(1) (1984), 1-10.
• Verdegay, J. L., A Dual Approach to Solve the Fuzzy Linear Programming Problem, Fuzzy Sets and Systems, 14(2) (1984), 131-141.
• Saaty, T. L., The Analytic Hierarchy Process, New York:McGraw-Hill, 1980.
• Wind, Y. and Saaty, T. L., Marketing Applications of the Analytic Hierarchy Process, Management Science, 26(7) (1980), 641-658.
• Deng, H., Multicriteria Analysis With Fuzzy Pairwise Comparison, International Journal of Approximate Reasoning, 21(3) (1999), 215-231.
• Tam, M. C. Y. and Tummala, V. M. R., An Application of the AHP in Vendor Selection of a Telecommunications System, Omega , 29(2) (2001), 171-182.
• Roychowdhury, S. and Pedrycz, W., A Survey of Defuzzification Strategies, International Journal of Intelligent Systems, 16(6) (2001), 679-695.
• Ahlatcioglu, B., Fuzzy Approaches to Portfolio Selection, Marmara University, Institute of Banking and Insurance, 2005.