Dr. Liu's research is in optimization under uncertainty and related fields. Uncertainty in an optimization problem may be introduced in many ways such as probabilistic uncertainty and possibilistic uncertainty. The fuzzy programming methodology extends linear and nonlinear programming models by assigning a possibility distribution to the uncertain parameters in a problem. The fuzzy random programming methodology combines both fuzziness and randomness in an optimization setting, and the uncertain parameters are characterized by fuzzy random variables. Since such uncertain programming problems include parameters defined only through a possibility distribution or a probability distribution, they are inherently infinite-dimensional optimization problems. Therefore, algorithmic procedures for solving them must rely on approximation schemes or heuristic algorithms. Even then, the approximating problems may be extremely large, and solution procedures will depend largely on the structures of the underlying problems. My interests concentrate on these and related issues of modeling and computation, at both theoretical and applied levels.

1. Education

1. Ph.D., 2003.1, Department of Mathematical Sciences, Tsinghua University, Beijing
2. M.S., 1992.6, Department of Mathematics, Hebei University, Baoding
3. B.S., 1989.6, Department of Mathematics, Hebei University, Baoding

2. Career

1. Professor, College of Mathematics & Computer Science, Hebei University, 2003-
2. Associate Professor, College of Mathematics & Computer Science, Hebei University, 2000-2003
3. Lecturer, Department of Mathematics, Hebei University, 1994-2000
4. Assistant, Department of Mathematics, Hebei University, 1992-1994
5. Research Fellow, School of Creative Media, City University of Hong Kong, 7 September 2006 - 6 December 2006.

3. Areas of Interests

1. Nonadditive Measure Theory: fuzzy measures, fuzzy integrals, and their applications
2. Set-valued Analysis: set-valued measures, Aumann integrals of set-valued functions, and their applications
3. Uncertain Programming: fuzzy Programming, fuzzy random programming, random fuzzy programming, and their applications
4. Intelligent Systems: genetic algorithms, neural networks, stochastic simulation, fuzzy simulation, hybrid algorithms
5. Uncertainty Theory: random set theory, credibility measure theory, mean chance theory, equilibrium chance theory

4. Book

1. Liu, Y.-K. and S. Wang, Theory of Fuzzy Random Optimization, China Agricultural University Press, Beijing, 2006.

5. Publications

1. Liu, YK, Zhang, G, On the completeness of fuzzy measure-space, Fuzzy Sets and Systems, vol.102, no.2, pp.345-351, 1999.
2. Liu, YK, On the convergence of measurable set-valued function sequence on fuzzy measure space, Fuzzy Sets and Systems, vol.112, no.2, pp.241-249, 2000.
3. Liu, YK, Liu, B, The relationship between structural characteristics of fuzzy measure and convergences of sequences of measurable functions, Fuzzy Sets and Systems, vol.120, no.3, pp.511-516, 2001.
4. Liu, YK, The completion of a fuzzy measure and its applications, Fuzzy Sets and Systems, vol.123, no.2, pp.137-145, 2001.
5. Liu, B, Liu, YK, Expected value of fuzzy variable and fuzzy expected value models, IEEE Transactions on Fuzzy Systems, vol.10, no.4, pp.445-450, 2002.
6. Liu, YK, Liu, B, Random fuzzy programming with chance measures defined by fuzzy integrals, Mathematical and Computer Modelling, vol.36, nos.4-5, pp.509-524, 2002.
7. Liu, YK, Liu, B, Fuzzy random variables: A scalar expected value operator, Fuzzy Optimization and Decision Making, vol.2, no.2, pp.143-160, 2003.
8. Liu, YK, Liu, B, Expected value operator of random fuzzy variable and random fuzzy expected value models, International Journal of Uncertainty, Fuzziness & Knowledge-Based Systems, vol.11, no.2, pp.195-215, 2003.
9. Liu, YK, Liu, B, A class of fuzzy random optimization: Expected value models, Information Sciences, vol.155, nos.1-2, pp.89-102, 2003.
10. Liu, YK, Liu, B, On minimum-risk problems in fuzzy random decision systems, Computers & Operations Research, vol.32, no.2, pp.257-283, 2005.
11. Liu, YK, Liu, B, Fuzzy random programming with equilibrium chance constraints, Information Sciences, vol.170, nos.2-4, pp.363-395, 2005.
12. Liu, YK, Fuzzy programming with recourse, International Journal of Uncertainty, Fuzziness & Knowledge-Based Systems, vol.13, no.4, pp.381-413, 2005.
13. Liu, YK, Convergent results about the use of fuzzy simulation in fuzzy optimization problems, IEEE Transactions on Fuzzy Systems, vol.14, no.2, pp.295-304, 2006.
14. Feng, X, Liu, YK, Measurability criteria for fuzzy random vectors, Fuzzy Optimization and Decision Making, vol.5, no.3, pp.245-253, 2006.
15. Liu, YK, Gao, J, The independence of fuzzy variables with applications to fuzzy random optimization, International Journal of Uncertainty, Fuzziness & Knowledge-Based Systems, vol.15, suppl.2, pp.1-20, 2007.
16. Liu, YK, The approximation method for two-stage fuzzy random programming with recourse, IEEE Transactions on Fuzzy Systems, vol.15, no.6, pp.1197-1208, 2007.
17. Liu, YK, Zhu, X, Capacitated fuzzy two-stage location-allocation problem, International Journal of Innovative Computing, Information and Control, vol.3, no.4, pp.987-999, 2007.
18. Liu, YK, Dai, X, The convergence modes in random fuzzy theory, Thai Journal of Mathematics, vol.6, no.1, 2008.
19. Liu, YK, The convergent results about approximating fuzzy random minimum risk problems, Applied Mathematics and Computation, to be published.
20. Liu, YK, Liu, ZQ, Gao, J, The modes of convergence in the approximation of fuzzy random optimization problems, Soft Computing, to be published.
21. Liu, YK, Tian, M, Convergence of optimal solutions about approximation scheme for fuzzy programming with minimum-risk criteria, Computers & Mathematics with Applications, to be published.

6. Research Projects

1. "Metaheuristics for Solving Large-Scale Uncertain Programming Models", Ministry of Science and Technology of China (PRA SI 00-01), 2001-2002.
2. "Random Fuzzy Programming and Hybrid Intelligent Algorithms", National Natural Science Foundation of China (No.60174049), 2002-2004.
3. "Systems Reliability Models in Various Uncertain Environments", Specialized Research Fund for the Doctoral Program of Higher Education, Ministry of Education of China (No.20020003009), 2003-2005.
4. "Programming under Uncertainty and its Intelligent Algorithms", Doctoral Research Fund of Hebei University (No.Y2004022), 2004-2006. (PI)
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5. "Theory and Practice of Two-Stage Fuzzy Random Optimization", Natural Science Foundation of Hebei Province (A2005000087), 2005-2007. (PI)
6. "Fuzzy Random Programming with Recourse and Its Applications", National Natural Science Foundation of China (No.70571021), 2006-2008. (PI)
7. "Program for One Hundred Excellent and Innovative Talents in Colleges and Universities of Hebei Province", The Education Department of Hebei Province, 2007-2009. (PI)

7. Editorial Services

1. International Journal of Natural Sciences & Technology, Editorial Board Member (2006-)
2. Journal of Uncertain Systems, Editor-in-Chief (2007-)
   

8. Membership & Activities in Professional Associations

1. Hebei Mathematics Society
2. The Society of Operations Research, Hebei Province
3. Operations Research Society of China (ORSC)
4. Youth Working Committee, Operations Research Society of China
5. Uncertainty Society of China, Operations Research Society of China
6. Associate Editor, Proceedings of the Fourth National Youth Conference on Operations Research and Management, Huairou, China, October 17-20, 2001.
7. Member, Organizing Committee, Second International Conference on Information, Beijing, China, July 24-27, 2002.
8. Member, Organizing Committee, First Annual Conference on Uncertainty, Daqing, China, August 16-19, 2003.
9. Member, Program Committee, Fifth National Youth Conference on Operations Research and Management, Daqing, China, August 16-19, 2003.
10. Member, Organizing Committee, Second International Conference on Information and Management Sciences, Chengdu, China, August 24-30, 2003.
11. Member, Organizing Committee, Third International Conference on Information and Management Sciences, Dunhuang, China, June 5-10, 2004.
12. Co-Chair, Organizing Committee, Second Annual Conference on Uncertainty, Qinhuangdao, China, July 16-20, 2004.
13. Member, Program Committee, Sixth National Youth Conference on Operations Research and Management, Qinghuangdao, China, August 16-20, 2004.
14. Publicity Chair, Fifth International Conference on Information and Management Sciences, Chengdu, China, July 1-8, 2006.
15. Co-Editors, Sixth International Conference on Information and Management Sciences, Lhasa, Tibet, China, July 1-6, 2007.
16. Chair, Fifth Annual Conference on Uncertainty, Wuhan, China, August 20-24, 2007.
17. Co-Guest Editors, Special issue on Uncertainty Analysis and Decision Making, Soft Computing, 2008.