Baoding Liu, Ph.D.
Professor
Uncertainty Theory Laboratory
Department of Mathematical Sciences
Tsinghua University
Beijing 100084, China

liu@tsinghua.edu.cn
http://orsc.edu.cn/liu
Tel: +86.10.6278.7724

Office: Room 1307, New Science Buildings, Tsinghua University

Baoding Liu received his B.S. degree in 1986 from Nankai University, and his M.S. degree in 1989 and Ph.D. degree in 1993 from Chinese Academy of Sciences. He joined Tsinghua University as Associate Professor in 1996, and was appointed Professor of Mathematics in 1998. Dr. Liu is the founder of uncertainty theory that is a branch of axiomatic mathematics for studying the behavior of subjective uncertainty. His research led to the development of uncertain programming, uncertain process, uncertain calculus, uncertain differential equation, uncertain logic and uncertain inference.

1. Academic Career

  1. B.S. (1982-1986), Department of Mathematics, Nankai University, Tianjin
  2. M.S. (1986-1989), Institute of Systems Science, Chinese Academy of Sciences
  3. Ph.D. (1990-1993), Institute of Systems Science, Chinese Academy of Sciences
  4. Postdoctoral Fellow (1993-1996), Ashikaga Institute of Technology, Japan
  5. Associate Professor (1996-1998), Tsinghua University, Beijing
  6. Professor of Mathematics (1998-), Tsinghua University, Beijing

2. Selected Books

  1. Liu B, Uncertainty Theory, 2nd ed., Springer-Verlag, Berlin, 2007.
  2. Liu B, Theory and Practice of Uncertain Programming, 2nd ed., Springer-Verlag, Berlin, 2009.
  3. Liu B, and Esogbue AO, Decision Criteria and Optimal Inventory Processes, Kluwer, Boston, 1999.

3. Survey Papers

  1. Liu B, Toward fuzzy optimization without mathematical ambiguity, Fuzzy Optimization and Decision Making, Vol.1, No.1, 43-63, 2002.
  2. Liu B, A survey of credibility theory, Fuzzy Optimization and Decision Making, Vol.5, No.4, 387-408, 2006.
  3. Liu B, A survey of entropy of fuzzy variables, Journal of Uncertain Systems, Vol.1, No.1, 4-13, 2007.

4. Research Papers

  1. Liu B, and Esogbue AO, Fuzzy criterion set and fuzzy criterion dynamic programming, Journal of Mathematical Analysis and Applications, Vol.199, No.1, 293-311, 1996.
  2. Gen M, Liu B, and Ida K, Evolution program for deterministic and stochastic optimizations, European Journal of Operational Research, Vol.94, No.3, 618-625, 1996.
  3. Liu B, Dependent-chance goal programming and its genetic algorithm based approach, Mathematical and Computer Modelling, Vol.24, No.7, 43-52, 1996.
  4. Iwamura K. and Liu B., A genetic algorithm for chance constrained programming, Journal of Information & Optimization Sciences, Vol.17, No.2, 409-422, 1996.
  5. Liu B, and Iwamura K, Modelling stochastic decision systems using dependent-chance programming, European Journal of Operational Research, Vol.101, No.1, 193-203, 1997.
  6. Liu B, Dependent-chance programming: A class of stochastic optimization, Computers & Mathematics with Applications, Vol.34, No.12, 89-104, 1997.
  7. Gen M. and Liu B., Evolution algorithm for optimal capacity expansion, Journal of the Operations Research Society of Japan, Vol.40, No.1, 1-9, 1997.
  8. Liu B, and Iwamura K, Chance constrained programming with fuzzy parameters, Fuzzy Sets and Systems, Vol.94, No.2, 227-237, 1998.
  9. Iwamura K, and Liu B, Chance constrained integer programming models for capital budgeting in fuzzy environments, Journal of the Operational Research Society, Vol.49, No.8, 854-860, 1998.
  10. Liu B, Stackelberg-Nash equilibrium for multilevel programming with multiple followers using genetic algorithms, Computers & Mathematics with Applications, Vol.36, No.7, 79-89, 1998.
  11. Liu B, and Iwamura K, A note on chance constrained programming with fuzzy coefficients, Fuzzy Sets and Systems, Vol.100, Nos.1-3, 229-233, 1998.
  12. Liu B, Minimax chance constrained programming models for fuzzy decision systems, Information Sciences, Vol.112, Nos.1-4, 25-38, 1998.
  13. Liu B, Fuzzy criterion models for inventory systems with partial backorders, Annals of Operations Research, Vol.87, 117-126, 1999.
  14. Liu B, and Odanaka T, Dynamic fuzzy criterion model for reservoir operations and a case study, Computers & Mathematics with Applications, Vol.37, Nos.11-12, 65-75, 1999.
  15. Esogbue AO, and Liu B, Cluster validity for fuzzy criterion clustering, Computers & Mathematics with Applications, Vol.37, Nos.11-12, 95-100, 1999.
  16. Liu B, Dependent-chance programming with fuzzy decisions, IEEE Transactions on Fuzzy Systems, Vol.7, No.3, 354-360, 1999.
  17. Iwamura K, and Liu B, Dependent-chance integer programming applied to capital budgeting, Journal of the Operations Research Society of Japan, Vol.42, No.2, 117-127, 1999.
  18. Liu B, Dependent-chance programming in fuzzy environments, Fuzzy Sets and Systems, Vol.109, No.1, 97-106, 2000.
  19. Liu B, and Iwamura K, Topological optimization models for communication network with multiple reliability goals, Computers & Mathematics with Applications, Vol.39, 59-69, 2000.
  20. Xia Y., Liu B., Wang S., and Lai K.K., A model for portfolio selection with order of expected returns, Computers & Operations Research, Vol.27, 409-422, 2000.
  21. Liu B, Uncertain programming: A unifying optimization theory in various uncertain environments, Applied Mathematics and Computation, Vol.120, Nos.1-3, 227-234, 2001.
  22. Liu YK, and 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, 511-516, 2001.
  23. Liu B, and Iwamura K, Fuzzy programming with fuzzy decisions and fuzzy simulation-based genetic algorithm, Fuzzy Sets and Systems, Vol.122, No.2, 253-262, 2001.
  24. Liu B, Fuzzy random chance-constrained programming, IEEE Transactions on Fuzzy Systems, Vol.9, No.5, 713-720, 2001.
  25. Liu B, Fuzzy random dependent-chance programming, IEEE Transactions on Fuzzy Systems, Vol.9, No.5, 721-726, 2001.
  26. Liu B, Random fuzzy dependent-chance programming and its hybrid intelligent algorithm, Information Sciences, Vol.141, Nos.3-4, 259-271, 2002.
  27. Liu B, and Liu YK, Expected value of fuzzy variable and fuzzy expected value models, IEEE Transactions on Fuzzy Systems, Vol.10, No.4, 445-450, 2002.
  28. Liu YK, and Liu B, Random fuzzy programming with chance measures defined by fuzzy integrals, Mathematical and Computer Modelling, Vol.36, No.4-5, 509-524, 2002.
  29. Liu B, Inequalities and convergence concepts of fuzzy and rough variables, Fuzzy Optimization and Decision Making, Vol.2, No.2, 87-100, 2003.
  30. Liu YK, and Liu B, Fuzzy random variables: A scalar expected value operator, Fuzzy Optimization and Decision Making, Vol.2, No.2, 143-160, 2003.
  31. Liu YK, and 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, 195-215, 2003.
  32. Zhou J, and Liu B, New stochastic models for capacitated location-allocation problem, Computers & Industrial Engineering, Vol.45, No.1, 111-125, 2003.
  33. Zhao R, and Liu B, Stochastic programming models for general redundancy optimization problems, IEEE Transactions on Reliability, Vol.52, No.2, 181-191, 2003.
  34. Liu YK, and Liu B, A class of fuzzy random optimization: Expected value models, Information Sciences, Vol.155, Nos.1-2, 89-102, 2003.
  35. Zhao R, and Liu B, Renewal process with fuzzy interarrival times and rewards, International Journal of Uncertainty, Fuzziness & Knowledge-Based Systems, Vol.11, No.5, 573-586, 2003.
  36. Zhao R, and Liu B, Redundancy optimization problems with uncertainty of combining randomness and fuzziness, European Journal of Operational Research, Vol.157, No.3, 716-735, 2004.
  37. Zhou J, and Liu B, Analysis and algorithms of bifuzzy systems, International Journal of Uncertainty, Fuzziness & Knowledge-Based Systems, Vol.12, No.3, 357-376, 2004.
  38. Zhu Y, and Liu B, Continuity theorems and chance distribution of random fuzzy variable, Proceedings of the Royal Society of London Series A, Vol.460, 2505-2519, 2004.
  39. Peng J, and Liu B, Parallel machine scheduling models with fuzzy processing times, Information Sciences, Vol.166, Nos.1-4, 49-66, 2004.
  40. Liu YK, and Liu B, On minimum-risk problems in fuzzy random decision systems, Computers & Operations Research, Vol.32, No.2, 257-283, 2005.
  41. Liu YK, and Liu B, Fuzzy random programming with equilibrium chance constraints, Information Sciences, Vol.170, 363-395, 2005.
  42. Yang L, and Liu B, On inequalities and critical values of fuzzy random variable, International Journal of Uncertainty, Fuzziness & Knowledge-Based Systems, Vol.13, No.2, 163-175, 2005.
  43. Gao J, and Liu B, Fuzzy multilevel programming with a hybrid intelligent algorithm, Computers & Mathematics with Applications, Vol.49, 1539-1548, 2005.
  44. Ke H, and Liu B, Project scheduling problem with stochastic activity duration times, Applied Mathematics and Computation, Vol.168, No.1, 342-353, 2005.
  45. Zhao R, and Liu B, Standby redundancy optimization problems with fuzzy lifetimes, Computers & Industrial Engineering, Vol.49, No.2, 318-338, 2005.
  46. Zhu Y, and Liu B, Some inequalities of random fuzzy variables with application to moment convergence, Computers & Mathematics with Applications, Vol.50, Nos.5-6, 719-727, 2005.
  47. Esogbue AO, and Liu B, Reservoir operations optimization via fuzzy criterion decision processes, Fuzzy Optimization and Decision Making, Vol.5, No.3, 289-305, 2006.
  48. Zheng Y, and Liu B, Fuzzy vehicle routing model with credibility measure and its hybrid intelligent algorithm, Applied Mathematics and Computation, Vol.176, No.2, 673-683, 2006.
  49. Yang L, and Liu B, On continuity theorem for characteristic function of fuzzy variable, Journal of Intelligent & Fuzzy Systems, Vol.17, No.3, 325-332, 2006.
  50. Li X, and Liu B, A sufficient and necessary condition for credibility measures, International Journal of Uncertainty, Fuzziness & Knowledge-Based Systems, Vol.14, No.5, 527-535, 2006.
  51. Zhu Y, and Liu B, Fourier spectrum of credibility distribution for fuzzy variables, International Journal of General Systems, Vol.36, No.1, 111-123, 2007.
  52. Zhu Y, and Liu B, A sufficient and necessary condition for chance distribution of random fuzzy variables, International Journal of Uncertainty, Fuzziness & Knowledge-Based Systems, Vol.15, Supp.2, 21-28, 2007.
  53. Li X, and Liu B, Maximum entropy principle for fuzzy variables, International Journal of Uncertainty, Fuzziness & Knowledge-Based Systems, Vol.15, Supp.2, 43-52, 2007.
  54. Ke H, and Liu B, Project scheduling problem with mixed uncertainty of randomness and fuzziness, European Journal of Operational Research, Vol.183, No.1, 135-147, 2007.
  55. Peng J, and Liu B, Birandom variables and birandom programming, Computers & Industrial Engineering, Vol.53, No.3, 433-453, 2007.
  56. Zhou J, and Liu B, Modeling capacitated location-allocation problem with fuzzy demands, Computers & Industrial Engineering, Vol.53, No.3, 454-468, 2007.
  57. Liu B, Fuzzy process, hybrid process and uncertain process, Journal of Uncertain Systems, Vol.2, No.1, 3-16, 2008.
  58. Li P, and Liu B, Entropy of credibility distributions for fuzzy variables, IEEE Transactions on Fuzzy Systems, Vol.16, No.1, 123-129, 2008.
  59. Li X, and Liu B, On distance between fuzzy variables, Journal of Intelligent & Fuzzy Systems, Vol.19, No.3, 197-204, 2008.
  60. Liu B, Some research problems in uncertainty theory, Journal of Uncertain Systems, Vol.3, No.1, 3-10, 2009.
  61. Li X, and Liu B, Chance measure for hybrid events with fuzziness and randomness, Soft Computing, Vol.13, No.2, 105-115, 2009.
  62. Li X, and Liu B, Foundation of credibilistic logic, Fuzzy Optimization and Decision Making, to be published.

5. Service

  1. IEEE Transactions on Fuzzy Systems, Associate Editor (1999-2007)
  2. Information: An International Journal, Editorial Board Member (1999-)
  3. Fuzzy Optimization and Decision Making, Associate Editor (2001-) and Book Review Editor (2006-)
  4. Asian Information-Science-Life, Associate Editor (2001-2003)
  5. International Journal of Internet and Enterprise Management, Editorial Board Member (2002-)
  6. Uncertainty Society of China (USC), Founding President£¨2003-2011£©
  7. International Journal of Operations Research, Associate Editor (2004-)
  8. International Consortium for Electronic Business (ICEB), Vice President (2004-2006)
  9. World Journal of Modelling and Simulation, Area Editor (2005-)
  10. International Association for Information and Management Sciences (IMS), Vice President (2005-2009)
  11. International Journal of Natural Sciences & Technology, Editorial Board Member (2006-)
  12. Journal of Uncertain Systems, Advisory Editor (2006-)
  13. Far East Journal of Experimental and Theoretical Artificial Intelligence, Editorial Board Member (2007-)

6. Research Projects

  1. "Fuzzy Criterion Decision Processes and Applications", Ministry of Education of China, 1997-1998.
  2. "Uncertain Programming Theory", Outstanding Young Teacher Fund, Ministry of Education of China, 1998-1999.
  3. "Uncertain Programming: Modelling, Evolutionary Algorithms and Applications", National Natural Science Foundation of China (No.69804006), 1999-2001.
  4. "Metaheuristics for Solving Large-Scale Uncertain Programming Models", Ministry of Science and Technology of China (PRA SI 00-01), 2001-2002.
  5. "Random Fuzzy Programming and Hybrid Intelligent Algorithms", National Natural Science Foundation of China (No.60174049), 2002-2004.
  6. "Systems Reliability Models in Various Uncertain Environments", Specialized Research Fund for the Doctoral Program of Higher Education (No.20020003009), Ministry of Education of China, 2003-2005.
  7. "Uncertainty Theory", Distinguished Young Scholar Fund, National Natural Science Foundation of China (No.60425309), 2005-2008.
  8. "Chance Theory and Hybrid Programming", National Natural Science Foundation of China (No.60874067), 2009-2011.