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

Abstract

Dempster–Shafer (D-S) evidence theory is an effective methodology to handle unknown and imprecise information because it can assign probability into the power set. However, the process of obtaining information is a complex task, which can consider the rational, conscious, objective evaluation of utility with behavioral effects. Besides, in most cases, information can be obtained from different angles at the same time. The quantum model of mass function (QM) uses amplitude and phase angle to easily express those properties of information that can extend D-S evidence theory to the unit circle in a 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, decisions can be made by 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 other point. This article proposes 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 <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">et al.</i> in D-S evidence theory. Negation can provide us more information to consider the problem from both positive and negative aspects. In this article, negation can be understood information, which does not belong to event <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$A$</tex-math></inline-formula> , that is to say, negation can be regarded as nonmembership by using the fuzzy terms. Based on the above discussion, this article proposes the 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 applications of QPFET, this article discusses the possibility of the VI <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\check{s}$</tex-math></inline-formula> ekriterijumsko Kompromisno Rangiranje method under QPFET to handle multicriteria decision-making that enables us to capture 2-D data, considering not only amplitude but also phase angle.