As a generation of fuzzy sets, intuitionistic fuzzy sets (IFSs) have a more powerful ability to represent and address the uncertainty of information. Therefore, IFSs have been used in many areas. However, the distance measure between the IFSs indicating the difference or discrepancy grade is still an open question that has attracted considerable attention over the past few decades. Although various measurement methods have been developed, some problems still exist regarding the unsatisfactory axioms of distance measure or that lack discernment and cause counterintuitive cases. To address the above issues, in this article, we propose a new distance measure between IFSs based on the Jensen-Shannon divergence. This new IFS distance measure can not only satisfy the axiomatic definition of distance measure but also has nonlinear characteristics. As a result, it can better discriminate the discrepancies between IFSs, and it generates more reasonable results than do other existing measure methods; these advantages are illustrated by several numerical examples. Based on these qualities, an algorithm for pattern classification is designed that provides a promising solution for addressing inference problems.

In artificial intelligence systems, a question on how to express the uncertainty in knowledge remains an open issue. The negation scheme provides a new perspective to solve this issue. In this paper, we study quantum decisions from the negation perspective. Specifically, complex evidence theory (CET) is considered to be effective to express and handle uncertain information in a complex plane. Therefore, we first express CET in the quantum framework of Hilbert space. On this basis, a generalized negation method is proposed for quantum basic belief assignment (QBBA), called QBBA negation. In addition, a QBBA entropy is revisited to study the QBBA negation process to reveal the variation tendency of negation iteration. Meanwhile, the properties of the QBBA negation function are analyzed and discussed along with special cases. Then, several multisource quantum information fusion (MSQIF) algorithms are designed to support decision making. Finally, these MSQIF algorithms are applied in pattern classification to demonstrate their effectiveness. This is the first work to design MSQIF algorithms to support quantum decision making from a new perspective of “negation”, which provides promising solutions to knowledge representation, uncertainty measure, and fusion of quantum information.

Dempster-Shafer evidence (DSE) theory, which allows combining pieces of evidence from different data sources to derive a degree of belief function that is a type of fuzzy measure, is a general framework for reasoning with uncertainty. In this framework, how to optimally manage the conflicts of multiple pieces of evidence in DSE remains an open issue to support decision making. The existing conflict measurement approaches can achieve acceptable outcomes but do not fully consider the optimization at the decision-making level using the novel measurement of conflicts. In this paper, we proposed a novel evidential correlation coefficient (ECC) for belief functions by measuring the conflict between two pieces of evidence in decision making. Then, we investigated the properties of our proposed evidential correlation and conflict coefficients, which are all proven to satisfy the desirable properties for conflict measurement, including nonnegativity, symmetry, boundedness, extreme consistency, and insensitivity to refinement. We also presented several examples and comparisons to demonstrate the superiority of our proposed ECC method. Finally, we applied the proposed ECC in a decision-making application of motor rotor fault diagnosis, which verified the practicability and effectiveness of our proposed novel measurement.

Multicriteria decision making (MCDM) has become one of the most frequently applied decision-making methodologies in various fields. However, uncertainty is inevitably involved in the process of MCDM due to the subjectivity of humans. To address this issue, a novel evidential fuzzy MCDM method, called EFMCDM, is proposed by integrating Dempster-Shafer theory with belief entropy. In particular, each criterion can be modeled as evidence, and all the alternatives compose the frame of discernment in the framework of Dempster-Shafer theory. To generate more appropriate basic probability assignments (BPAs) of the criteria, the EFMCDM method considers both the subjective and objective weighting of the criteria that are leveraged in MCDM problems. Thereafter, the classic Dempster's rule of combination is leveraged to fuse the multiple pieces of evidence into composite evidence. On this basis, the alternatives are ranked to determine the optimal alternative. In addition, the EFMCDM method can quantitatively model uncertainty and help to decrease the uncertainty caused by subjective human cognition to improve decision making. Finally, the rationality, effectiveness and robustness of the EFMCDM method are demonstrated through experimental evaluations.