On the Negation of discrete Z-numbers
Qing Liu, Huizi Cui, Ye Tian and Bingyi Kang（通讯作者）
The negation of a problem provides a new perspective for information representation. However, existing negation method has limitations since it can only be applied to the accurately expressed knowledge. Real-world information is imperfect and imprecise. It usually describes in natural language. In view of this, Prof. Zadeh suggested the concept of Z-number as a more adequate way for description of real world information. As Z-number involves both fuzzy and probabilistic uncertainty, a novel method for the negation of Z-number in combination of probability and fuzziness is proposed from the reliability of probability transmission in this paper. Moreover, several examples are used to describe the negation process and result. As far as our latest knowledge is concerned, the negation of Z-number has not been covered by researchers, so this may be another door for us to process Z-number-based information.
ZSLF : A new soft likelihood function based on Z-numbers and its application in expert decision system
Ye Tian, Lili Liu, Xiangjun Mi and Bingyi Kang（通讯作者）
IEEE Transactions on Fuzzy Systems（中科院大类1区，CCF推荐国际期刊B类）
Due to the complexity of the real world, effective consideration of the ambiguity and reliability of information is a challenge that must be addressed by the correct decision of the expert system. Z-number provides us with a good idea because it describes the probability of the random variable and the possibility measure. Recently, Yager presented a soft likelihood function that effectively combines probabilistic evidence to deal with the conflict information. This paper generalizes Yager's soft likelihood function based on Z-numbers and proposes a ZSLF decision model. The application examples show the rationality and effectiveness of the method. The comparison and discussion further show the advantages of the ZSLF decision model.
A modified method of generating Z-number based on OWA weights and maximum entropy
Ye Tian and Bingyi Kang（通讯作者）
How to generate Z-number is an important and open issue in the uncertain information processing of Z-number. In Kang et al. (Int J Intell Syst 33(8):1745–1755, 2018), a method of generating Z-number using OWA weight and maximum entropy is investigated. However, the meaning of the method in Kang et al. (2018) is not clear enough according to the definition of Z-number. Inspired by the methodology in Kang et al. (2018), we modify the method of determining Z-number based on OWA weights and maximum entropy, which is more clear about the meaning of Z-number. In addition, the model of generating Z-number under the environment of group decision making is well investigated based the modified model. Some numerical examples are used to illustrate the effectiveness of the proposed methodology.