Fuzzy Optim Decis Making (2013) 12:1–2

DOI 10.1007/s10700-012-9142-9

Uncertainty theory with applications

Jinwu Gao · Jin Peng · Baoding Liu

Published online: 2 October 2012 © Springer Science+Business Media New York 2012

The Eleventh International Conference on Information and Management Sciences was held on August 3–8, 2012 at Dunhuang, China (in Celebration of the 60th birthday of Professor Shu-Cherng Fang). The objective of the conference is to bring scholars and researchers together to enhance the study and practice of global competitiveness.

Over one hundred papers were presented in front of two hundred some participants.

This special issue focuses on a new research area called uncertainty theory. When the sample size is too small to estimate a probability distribution, we have to invite some domain experts to evaluate their belief degree that each event will occur. Since human beings usually overweight unlikely events, the belief degree may have much larger variance than the real frequency. Perhaps some people think that the belief degree is subjective probability or fuzzy set. However, it is inappropriate because they may lead to counterintuitive results in this case. In order to deal with personal belief degree, an uncertainty theory was invented recently. Nowadays uncertainty theory has become a branch of axiomatic mathematics, and has been applied to many areas including uncertain programming, uncertain statistics, uncertain risk analysis, uncertain reliability analysis, uncertain logic, uncertain inference, uncertain process, uncertain calculus, and uncertain differential equation.

J. Gao (B)

Uncertain Systems Lab, School of Information, Renmin University of China, Beijing 100872, China e-mail: jgao@ruc.edu.cn

J. Peng

Institute of Uncertain Systems, Huanggang Normal University, Hubei 438000, China e-mail: peng@hgnu.edu.cn

B. Liu

Uncertainty Theory Lab, Department of Mathematical Sciences, Tsinghua University,

Beijing 100084, China e-mail: liu@tsinghua.edu.cn 123 2 J. Gao et al.

This special issue contains 10 papers that feature recent advances of uncertainty theory and applications. The first paper by Kai Yao et al. gave some conditions that uncertain differential equations are stable. The second paper by Zhiguo Zeng et al. discussed system reliability by using uncertainty theory when there is no observed data. Case studies showed the effectiveness of the new reliability metrics. The third paper by Rui Mu et al. proposed an uncertain contract model for rural migrant worker’s employment problems under the assumption that the enterprise’s assessment of the rural migrant worker’s own income at home is characterized as an uncertain variable.

The fourth paper by Xintong Ge and Yuanguo Zhu derived a condition of optimality for uncertain optimal control problem by using the variational calculus. Meanwhile, a tool of backward uncertain differential equation is proposed. The fifth paper by Jin

Peng presented some risk metrics, which have the potential applications to risk analysis in uncertain environments. The sixth paper by Jinwu Gao introduced uncertainty theory to game theory and produced a new topic called uncertain bimatrix game. The seventh paper by Xingfang Zhang et al. investigated the delayed renewal process with uncertain interarrival times and obtained an elementary delayed renewal theorem. The eighth paper by Xiaohu Yang dealt with comonotonic functions of uncertain variables, and obtained some useful results on the linearity of expected value operator. The ninth paper by Xiaosheng Wang and Minghu Ha studied the quadratic entropy of uncertain sets as well as its properties. The last paper by Xiaowei Chen et al. proposed an uncertain stock model with periodic dividends, based on which some option pricing formulas are investigated.

Finally, we would like to thank all the reviewers who have contributed with their friendly collaboration and rigorous reviews. Our sincere gratitude also goes to all the authors who submitted their papers to the special issue. 123