Decision making under various types of uncertainty

Due to the incompleteness of the available information, the notion of uncertainty is often used as a general term to describe the existing state or potential outcomes in a variety of fields, such as economics, engineering, information and management science. The real-world uncertainties can be classified into several categories according to their specific attributes, for instance, fuzziness, randomness, roughness and so on. Up to now, fuzzy set theory, probability theory and rough set theory have been well-developed to handle these uncertainties in practice. Additionally, different uncertainties can also appear simultaneously in some complex decision making systems. Then some hybrid models of uncertain theories, including fuzzy random theory, random fuzzy theory, and fuzzy rough theory, are usually employed to handle these mixtures of uncertainties. As an application of uncertainty theory, uncertain decision making has been used in many practical applications such as transportation and logistics, risky project evaluation, financial management, information systems, supply chain management and so on. This special issue aims to bring together researchers to present and discuss new decision making models, algorithms and applications under various types of uncertainty.

After the call for papers was announced in late May 2014, this special issue has attracted tremendous attention. In total, we received 25 manuscripts before the submission deadline. After a rigorous review process, six papers were finally accepted for publication. Ding et al. (2016) considered the complexity and uncertainty of international project, a tripartite game model was formulated to describe the relationship among owner, supervisor and general contractor. In addition, a project schedule selection model was formulated and a new benefit allocation method was proposed by introducing a new modified Shapley value with weighted factor. Wang and Qin (2016) considered the multi-product newsvendor problem with mixed randomness and fuzziness. An expected profit maximization model was formulated by defining the demands as hybrid variables. Du,Yu, and Li (2016) formulated a fuzzy multi-objective chance-constrained programming model for hazardous materials transportation problem that minimizes the transportation risk, travel time and fuel consumption. Zhou et al. (2016) proposed the notion of fuzzy $\mathit{\alpha }$-minimum spanning tree and discussed the solutions of the fuzzy $\mathit{\alpha }$-minimum spanning tree problem under different assumptions. Ke et al. (2016) proposed a general framework of fuzzy bilevel programming including hybrid models (integrated with different modeling methods at different levels). Two of these models were applied to pricing decision problem in a decentralized supply chain with fuzzy coefficients. Hu, Pedrycz, and Wang (2016) developed a roughness measure for fuzzy sets from the perspective of distance, and provided an application of the roughness measure to incomplete information systems with fuzzy decision making.

The guest editors would like to place on record their sincere thanks to Prof. George J. Klir, the Founding Editor of International Journal of General Systems, for this very special opportunity provided to us for contributing to this special issue. The guest editors would also like to thank all the referees for their kind support, and express the gratitude to all authors of submissions in this special issue for their contributions. Without the support of the authors and the referees, it would be impossible to make this special issue for our readers.

The guest editors hope that the papers published in this special issue will be valuable to academic researchers and practitioners, and will provide a clearer sense of further research directions. It is hoped that readers can find some topics of interest and benefit to them. The guest editors also hope that this special issue will inspire researchers in the fields of uncertain decision making to explore more creative contributions in their research fields.

Xiang Li and Lean Yu School of Economics and Management, Beijing University of Chemical Technology, Beijing 100029, China[email protected]