Maximal United Utility Degree Model for Fund Distributing in Higher School

Title & Authors
Maximal United Utility Degree Model for Fund Distributing in Higher School
Zhang, Xingfang; Meng, Guangwu;

Abstract
The paper discusses the problem of how to allocate the fund to a large number of individuals in a higher school so as to bring a higher utility return based on the theory of uncertain set. Suppose that experts can assign each invested individual a corresponding nondecreasing membership function on a close interval I according to its actual level and developmental foreground. The membership degree at the fund $\small{x{\in}I}$ is called utility degree from fund x, and product (minimum) of utility degrees of distributed funds for all invested individuals is called united utility degree from the fund. Based on the above concepts, we present an uncertain optimization model, called Maximal United Utility Degree (or Maximal Membership Degree) model for fund distribution. Furthermore, we use nondecreasing polygonal functions defined on close intervals to structure a mathematical maximal united utility degree model. Finally, we design a genetic algorithm to solve these models.
Keywords
Uncertain Programming;Membership Function;Utility Degree;Higher School;
Language
English
Cited by
References
1.
Abiyev, R. H. and Menekay, M. (2007), Fuzzy portfolio selection using genetic algorithm, Soft Computing, 11(12), 1157-1163.

2.
Chen, X. and Ralescu, D. A. (2011), A note on truth value in uncertain logic, Expert Systems with Applications, 38(12), 15582-15586.

3.
Chen, X., Kar, S., and Ralescu, D. A. (2012), Crossentropy measure of uncertain variables, Information Sciences, 201, 53-60.

4.
Crama, Y. and Schyns, M. (2003), Simulated annealing for complex portfolio selection problems, European Journal of Operational Research, 150(3), 546-571.

5.
Deng, X. T., Li, Z. F., and Wang, S. Y. (2005), A minimax portfolio selection strategy with equilibrium, European Journal of Operational Research, 166(1), 278-292.

6.
Dai, W. and Chen, X. (2012), Entropy of function of uncertain variables, Mathematical and Computer Modelling, 55(3/4), 754-760.

7.
Gao, X. (2009), Some properties of continuous uncertain measure, International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems, 17(3), 419-426.

8.
Gao, Y. (2011), Shortest path problem with uncertain arc lengths, Computers and Mathematics with Applications, 62(6), 2591-2600.

9.
Gao, Y. (2012), Uncertain models for single facility location problem on networks, Applied Mathematical Modelling, 36(6), 2592-2599.

10.
Hirschberger, M., Qi, Y., and Steuer, R. E. (2007), Randomly generating portfolio-selection covariance matrices with specified distributional characteristics, European Journal of Operational Research, 177(3), 1610-1625.

11.
Huang, X. (2011), Mean-risk model for uncertain portfolio selection, Fuzzy Optimization and Decision Making, 10(1), 71-89.

12.
Leung, M. T., Daouk, H., and Chen, A. S. (2001), Using investment portfolio return to combine forecasts: a multiobjective approach, European Journal of Operational Research, 134(1), 84-102.

13.
Li, D. F. and Yang, J. B. (2004), Fuzzy linear programming technique for multiattribute group decision in fuzzy environments, Information Sciences, 158, 263-275.

14.
Li, X. and Liu, B. (2009), Hybrid logic and uncertain logic, Journal of Uncertain Systems, 3(2), 83-94.

15.
Li, Z. F., Wang, S. Y., and Deng, X. T. (2000), A liner programming algorithm for optimal portfolio selection with transaction costs, International Journal of Systems Science, 31(1), 107-117.

16.
Lin, C. C. and Liu, Y. T. (2008), Genetic algorithms for portfolio selection problems with minimum transaction lots, European Journal of Operational Research, 185(1), 393-404.

17.
Liu, B. (2007), Uncertainty Theory (2nd ed.), Springer-Verlag, Berlin.

18.
Liu, B. (2009a), Theory and Practice of Uncertain Programming (2nd ed.), Springer-Verlag, Berlin.

19.
Liu, B. (2009b), Some research problems in uncertainty theory, Journal of Uncertain Systems, 3(1), 3-10.

20.
Liu, B. (2010), Uncertainty Theory: A Branch of Mathematics for Modeling Human Uncertainty, Springer-Verlag, Berlin.

21.
Liu, B. (2013), Uncertainty Theory (4th ed.), Uncertainty Theory Laboratiory, Beijing.

22.
Liu, S., Wang, S. Y., and Qiu, W. (2003), Mean-variance- skewness model for portfolio selection with transaction costs, International Journal of Systems Sciences, 34(4), 255-262.

23.
Meng, G. and Zhang, X. (2013), Optimization uncertain measure model for uncertain vehicle routing problem, Information, 16(2), 1201-1206.

24.
Peng, J. and Yao, K. (2011), A new option pricing model for stocks in uncertainty markets, International Journal of Operations Research, 8(2), 18-26.

25.
Perold, A. F. (1984), Large-scale portfolio optimization, Management Science, 30(10), 1143-1160.

26.
Qin, Z., Li, X., and Ji, X. (2009), Portfolio selection based on fuzzy cross-entropy, Journal of Computational and Applied Mathematics, 228(1), 139-149.

27.
Sheng, Y. and Yao, K. (2012), Fixed charge transportation problem and its uncertain programming model, Industrial Engineering and Management Systems, 11(2), 183-187.

28.
Rong, L. (2011), Two new uncertainty programming models of inventory with uncertain costs, Journal of Information and Computational Science, 8(2), 280-288.

29.
Wang, X., Gao, X., and Guo, H. (2012), Uncertain hypothesis testing for two experts' empirical data, Mathematical and Computer Modelling, 55(3/4), 1478-1482.

30.
Xia, Y., Liu, B., Wang, S., and Lai, K. K. (2000), A model for portfolio selection with order of expected returns, Computers and Operations Research, 27 (5), 409-422.

31.
Yao, K. and Li, X. (2012), Uncertain alternating renewal process and its application, IEEE Transactions on Fuzzy Systems, 20(6), 1154-1160.

32.
Zhang, X. and Meng, G. (2013), Expected-variance-entropy model for uncertain parallel machine scheduling, Information: An International Interdisciplinary Journal, 16(2), 903-908.

33.
Zhang, X., Ning, Y., and Meng, G. (2013), Delayed renewal process with uncertain interarrival times, Fuzzy Optimization and Decision Making, 12(1), 79-87.

34.
Zhang, X. and Chen, X. (2012), A new uncertain programming model for project problem, Information, 15(10), 3901-3910.

35.
Zhu, Y. (2010), Uncertain optimal control with application to a portfolio selection model, Cybernetics and Systems, 41(7), 535-547.