Abstract
Fuzzy methods are widely used in the study of trustworthiness. Based on this fact, the paper researches the trustworthiness system (T-System) and probability distribution theory based on bounded product (B-P) implication and Larsen square (L-S) implication. Firstly, we convert a group of single-input and single-output data into fuzzy inference rules and generate fuzzy relation by selecting the appropriate fuzzy implication operator, then calculate joint probability density function of two-dimensional random variables by using of this fuzzy relation. Two specific probability density functions can be obtained by selecting the fuzzy implication as bounded product implication or Larsen square implication. Secondly, we study of the center-of-gravity trustworthiness system based on these two probability distributions. Finally, we gave the sufficient conditions of universal approximations for those trustworthiness systems.
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Acknowledgments
This research was supported by Information and Computing Science Outstanding Talent Training project of Guangdong province (No.20153324).
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Zhong, YB., Deng, Yz., Liu, Zl., Yuan, Xh. (2016). Probability Distribution of T-System Based on B-P and L-S Implication. In: Cao, BY., Wang, PZ., Liu, ZL., Zhong, YB. (eds) International Conference on Oriental Thinking and Fuzzy Logic. Advances in Intelligent Systems and Computing, vol 443. Springer, Cham. https://doi.org/10.1007/978-3-319-30874-6_37
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DOI: https://doi.org/10.1007/978-3-319-30874-6_37
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