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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.

Pythagorean fuzzy set (PFS) is an extension of the Intuitionistic fuzzy set (IFS). It has a more wider space of membership degrees. Thus, it is more capable of expressing and handling the fuzzy information in engineering practice and scientific research. However, Pythagorean fuzzy sets lack a mathematical tool to express stochastic or probability information, rendering it unsuitable for application in many scenarios. In this paper, an ordered number pair is used to describe fuzzy information and stochastic information under uncertain environments, namely constrained Pythagorean fuzzy set (CPFS). The CPFS has two components, CPFS=(A,P), A is the classical Pythagorean fuzzy set, while P is a measurement of reliable for A. For PFS, CPFS is the first unified description of fuzzy information and probabilistic information, which is a more flexible way to describe knowledge or thinking. Furthermore, the similarity measure of constrained Pythagorean fuzzy sets (CPFSs) is presented, which meets the similarity measure theorems and can better indicate the flexibility of CPFSs. Numerical examples are used to demonstrate that the CPFSs similarity measure is reasonable and effective. The method of similarity measure can be degenerated to the similarity measure of PFSs under specific case, and can avoid generating counter-intuitive results. In addition, similarity measure of CPFSs is applied to medical diagnosis and target classification of Iris. These experimental results prove the practicability and effectiveness of our model.

Intuitionistic fuzzy set (IFS) is a classical branch of fuzzy set, which has advantage to deal with uncertain problems. In IFS, similarity measure is an important fundamental concept, it is used to measure consistency between different intuitionistic fuzzy sets (IFSs) and becomes a key parameter in fuzzy decision system. However, the previous methods of similarity measure do not take enough account the effect of hesitancy degree on membership degree and non-membership degree, so that produce counterintuitive results when measuring similarity. Hence, in this paper, a new similarity measure of IFS is presented. The effect of hesitancy degree on similarity measure is fully considered in the proposed method and some properties also haven been discussed to prove the reasonable of proposed method. Meanwhile, some numerical examples are analyzed to illustrate characteristics of proposed similarity measure in detail. Further, the experiments of target classification and clustering problem demonstrate effectiveness and superiority of proposed similarity measure in the environment of expert assessments and data set.

Seventeen Y-STRs (DYS19, DYS389I, DYS389II, DYS390, DYS391, DYS392, DYS393, DYS385a, DYS385b, DYS438, DYS439, DYS437, DYS448, DYS456, DYS458, DYS635 and YGATAH4) were analyzed for 4451 Chinese Han unrelated males from Zhejiang Province, Eastern China, with the AmpFlSTR Yfiler™ PCR Amplification kit. A total of 3389 different haplotypes was identified, of which 2877 were unique and 512 repeatedly found among different individuals. The overall haplotype diversity (HD) and discrimination capacity (DC) were 0.999696 and 0.761402, respectively. Analysis of molecular variance (AMOVA) tests demonstrated that genetic distance between Zhejiang Han and most Chinese Han populations is closer than that between Zhejiang Han and non-Han populations. This study provides information for the application of Y-chromosomal STRs to forensic identification, indicating that the extended genotyping of Y-STRs is needed for forensic practice.