The case when the source of information provides precise belief function/mass, within the generalized power space, has been studied by many people. However, in many decision situations, the precise belief structure is...The case when the source of information provides precise belief function/mass, within the generalized power space, has been studied by many people. However, in many decision situations, the precise belief structure is not always available. In this case, an interval-valued belief degree rather than a precise one may be provided. So, the probabilistic transformation of imprecise belief function/mass in the generalized power space including Dezert-Smarandache （DSm） model from scalar transformation to sub-unitary interval transformation and, more generally, to any set of sub-unitary interval transformation is provided. Different from the existing probabilistic transformation algorithms that redistribute an ignorance mass to the singletons involved in that ignorance pro- portionally with respect to the precise belief function or probability function of singleton, the new algorithm provides an optimization idea to transform any type of imprecise belief assignment which may be represented by the union of several sub-unitary （half-） open intervals, （half-） closed intervals and/or sets of points belonging to [0,1]. Numerical examples are provided to illustrate the detailed implementation process of the new probabilistic transformation approach as well as its validity and wide applicability.展开更多
基金supported by the National Natural Science Foundation of China (60572161 60874105)+5 种基金the Excellent Ph.D. Paper Author Foundation of China (200443)the Postdoctoral Science Foundation of China (20070421094)the Program for New Century Excellent Talents in University (NCET-08-0345)the Shanghai Rising-Star Program(09QA1402900)the "Chenxing" Scholarship Youth Found of Shanghai Jiaotong University (T241460612)the Ministry of Education Key Laboratory of Intelligent Computing & Signal Processing (2009ICIP03)
文摘The case when the source of information provides precise belief function/mass, within the generalized power space, has been studied by many people. However, in many decision situations, the precise belief structure is not always available. In this case, an interval-valued belief degree rather than a precise one may be provided. So, the probabilistic transformation of imprecise belief function/mass in the generalized power space including Dezert-Smarandache （DSm） model from scalar transformation to sub-unitary interval transformation and, more generally, to any set of sub-unitary interval transformation is provided. Different from the existing probabilistic transformation algorithms that redistribute an ignorance mass to the singletons involved in that ignorance pro- portionally with respect to the precise belief function or probability function of singleton, the new algorithm provides an optimization idea to transform any type of imprecise belief assignment which may be represented by the union of several sub-unitary （half-） open intervals, （half-） closed intervals and/or sets of points belonging to [0,1]. Numerical examples are provided to illustrate the detailed implementation process of the new probabilistic transformation approach as well as its validity and wide applicability.
