Quantum Pythagorean Fuzzy Evidence Theory: A Negation of Quantum Mass Function View

Dempster-Shafer (D-S) evidence theory is an effective methodology to handle unknown and imprecise information,due it can assign the probability into power of set. However, the process of information obtained is a complex procedure, which can consider the rational, conscious, objective evaluation of utility with behavioral effects. Besides, in most cases, information can be obtained form the different angles at the same time. Quantum of mass function (QM) used amplitude and phase angle to easily express the those properties of information, which can extend D-S evidence theory to the unit circle in complex plane. Moreover, everything in nature will have its opposite, which is a kind of universality. The Bayes theorem is essentially the process of negation. However, in most cases, the decisions can be made only fully considering the known information without considering the other side of the information. Hence, considering the negation of information is a question to be investigated deeply, which can analyze information from the another point. The paper proposed negation of QM by using the subtraction of vectors in the unit circle, which can degenerate into negation proposed by Yager in standard probability theory and negation proposed by Yin.et al in D-S evidence theory. Negation can provide us the more information to consider problem from both positive and negative aspects. In this paper, negation can be understood information which is not belong the event A, that is to say, negation can be regarded as the non-membership by using the fuzzy terms. Based above discussion, the paper proposed quantum Pythagorean fuzzy evidence theory (QPFET), which is the novel work to consider QPFET from the point of negation. Besides, there are some numerical examples to explain the proposed method. In order to explore the application of QPFET, the paper discussed the possibility of the VIKOR method under QPFET to handle multi-criteria decision making that enables us to capture two-dimensional data, which considers not only amplitude but also phase angle.