Maximal confidence intervals of the interval-valued belief structure and applications

  • Authors:

  • Zhi-gang Su;Pei-hong Wang;Xiang-jun Yu;Zhen-zhong Lv

  • Affiliations:

  • School of Energy & Environment, Southeast University, Nanjing, Jiangsu Province 210096, China;School of Energy & Environment, Southeast University, Nanjing, Jiangsu Province 210096, China;School of Energy & Environment, Southeast University, Nanjing, Jiangsu Province 210096, China;School of Energy & Environment, Southeast University, Nanjing, Jiangsu Province 210096, China

  • Venue:
  • Information Sciences: an International Journal
  • Year:
  • 2011

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Abstract

An unsolved problem in the interval-valued belief structure is the existence of maximal confidence intervals, referring to the credible and maximal interval-valued beliefs assigned to focal elements, in which every point can be reached by a combination rule. In this study, the existence of maximal confidence intervals of the interval-valued belief structure was investigated and validated. In addition, some applications of the maximal confidence interval in constructing valid and normalized interval-valued belief structures are discussed. A numerical experiment was conducted to illustrate the existence of maximal confidence intervals. Several propositions and a theorem were further proposed to demonstrate the validity of the maximal confidence interval. By using the concept of the maximal confidence interval, a procedure was proposed to construct valid and normalized interval-valued belief structures, and some meaningful guidance for assigning interval-valued beliefs was also suggested to the experts. Finally, a series of well-designed examples was presented as applications of the maximal confidence interval, the proposed procedure and the suggestions. They indicated that valid and normalized interval-valued belief structures can be achieved accurately and efficiently in practical applications with the proposed procedure and guidance on the basis of the concept of the maximal confidence interval.