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Intuitionistic linguistic fuzzy information (ILFI), characterized by linguistic terms and intuitionistic fuzzy sets (IFSs), can easily express the fuzzy information in the process of muticriteria decision making (MCDM) and muticriteria group decision making (MCGDM) problems. The purpose of this paper is to provide an overview of aggregation operators (AOs) and applications of ILFI.

First, some meaningful AOs for ILFI are summarized, and some extended MCDM approaches for intuitionistic uncertain linguistic variables (IULVs), such as extended TOPSIS, extended TODIM, extended VIKOR, are discussed. Then, the authors summarize and analyze the applications about the AOs of IULVs.

IULVs, characterized by linguistic terms and IFSs, can more detailed and comprehensively express the criteria values in the process of MCDM and MCGDM. Therefore, lots of researchers pay more and more attention to the MCDM or MCGDM methods with IULVs.

The authors summarize and analyze the applications about the AOs of IULVs Finally, the authors point out some possible directions for future research.

The purpose of this paper is to investigate the design method of partial observer canonical form (POCF), which is one of the important research tools for industrial plants.

Motivated by the two-steps method proposed in Xu et al. (2020), this paper extends this method to the case of Multi-Input Multi-Output (MIMO) nonlinear system. It decomposes the original system into two subsystems by observable decomposition theorem first and then transforms the observable subsystem into OCF. Furthermore, the necessary and sufficient conditions for the existing of POCF are proved.

The proposed method has a wide range of applications including completely observable nonlinear system, noncompletely observable nonlinear system, autonomous nonlinear system and forced nonlinear system. Besides, comparing to the existing results (Saadi et al., 2016), the method requires less verified conditions.

The new method concerning design POCF has better plants compatibility and less validation conditions.

The purposes of this research are to study the theory and method of multi-attribute index system design and establish a set of systematic, standardized, scientific index systems for the design optimization and inspection process. The research may form the basis for a rational, comprehensive evaluation and provide the most effective way of improving the quality of management decision-making. It is of practical significance to improve the rationality and reliability of the index system and provide standardized, scientific reference standards and theoretical guidance for the design and construction of the index system.

Using modern methods such as complex networks and machine learning, a system for the quality diagnosis of index data and the classification and stratification of index systems is designed. This guarantees the quality of the index data, realizes the scientific classification and stratification of the index system, reduces the subjectivity and randomness of the design of the index system, enhances its objectivity and rationality and lays a solid foundation for the optimal design of the index system.

Based on the ideas of statistics, system theory, machine learning and data mining, the focus in the present research is on “data quality diagnosis” and “index classification and stratification” and clarifying the classification standards and data quality characteristics of index data; a data-quality diagnosis system of “data review – data cleaning – data conversion – data inspection” is established. Using a decision tree, explanatory structural model, cluster analysis, K-means clustering and other methods, classification and hierarchical method system of indicators is designed to reduce the redundancy of indicator data and improve the quality of the data used. Finally, the scientific and standardized classification and hierarchical design of the index system can be realized.

The innovative contributions and research value of the paper are reflected in three aspects. First, a method system for index data quality diagnosis is designed, and multi-source data fusion technology is adopted to ensure the quality of multi-source, heterogeneous and mixed-frequency data of the index system. The second is to design a systematic quality-inspection process for missing data based on the systematic thinking of the whole and the individual. Aiming at the accuracy, reliability, and feasibility of the patched data, a quality-inspection method of patched data based on inversion thought and a unified representation method of data fusion based on a tensor model are proposed. The third is to use the modern method of unsupervised learning to classify and stratify the index system, which reduces the subjectivity and randomness of the design of the index system and enhances its objectivity and rationality.