Abstract
Fuzzy sets and fuzzy variables have undergone several different extensions overtime. One of them involved including a “bifuzzy variable” as a fuzzy element for describing the more complete systems. The properties of bifuzzy variable were obtained by introducing the concept of “chance distribution”. In this paper, we will present a sufficient and necessary condition for chance distribution of bifuzzy variable. Here we present a constructive proof base on credibility theory for the sufficient part.
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Acknowledgments
This work were supported by the National Natural Science Foundation of China Grant (No. 60874067) and China Postdoctoral Science Foundation (No. 20090450024). The authors would like to thank the editor and the referees for their valuable suggestions and comments.
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Qin, Z., Li, X. The sufficient and necessary condition for chance distribution of bifuzzy variable. Soft Comput 15, 595–599 (2011). https://doi.org/10.1007/s00500-010-0567-1
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DOI: https://doi.org/10.1007/s00500-010-0567-1