This paper proposes a new distributed Kalman filtering fusion with random state transition and measurement matrices, i.e., random parameter matrices Kalman filtering. It is proved that under a mild condition the fused state estimate is equivalent to the centralized Kalman filtering using all sensor measurements; therefore, it achieves the best performance. More importantly, this result can be applied to Kalman filtering with uncertain observations including the measurement with a false alarm probability as a special case, as well as, randomly variant dynamic systems with multiple models. Numerical examples are given which support our analysis and show significant performance loss of ignoring the randomness of the parameter matrices.

The single-valued neutrosophic set (SVNS) is considered as an attractive tool for handling highly uncertain and vague information. With this regard, different from the most current distance-based technique for order preference by similarity to ideal solution (TOPSIS) methods, this study proposes a correlation-based TOPSIS model for addressing the single-valued neutrosophic (SVN) multiple attribute decision making (MADM) problems. To achieve this aim, we first develop a novel conception of SVN correlation coefficient, whose significant feature is that it lies in the interval [[Formula: see text],1], which is in accordance with the classical correlation coefficient in statistics, whereas all the existing SVN correlation coefficients in the literature are within unit interval [0,1]. Afterwards, a weighted SVN correlation coefficient is also introduced to infuse the importance of attributes. Moreover, a correlation-based comprehensive index is further proposed to establish the central structure of TOPSIS model, called the SVN correlation-based TOPSIS approach. Finally, a numerical example and relevant comparative analysis are implemented to explain the applicability and effectiveness of the mentioned methodology.

The probabilistic linguistic term set (PLTS) is a newly emerging mathematical tool for handling uncertainties. It is considered a useful extension of linguistic term sets associated with probability information and can improve the effectiveness of multiple attribute decision making (MADM). This paper proposes a new PLTS correlation coefficient and addresses its usefulness in MADM problems. For achieving this aim, some new concepts of mean, variance, and covariance of the PLTS are first proposed. Moreover, a novel PLTS Pearson correlation coefficient is defined to overcome the shortcomings of the existing methods, whose significant feature is that it lies in the interval [−1,1], which makes it more effective in reflecting the negative and positive correlation between PLTSs. A weighted PLTS Pearson correlation coefficient is further defined to consider the importance of attribute weights and expand the scope of application. Then, a relative PLTS closeness coefficient is constructed based on the developed Pearson correlation coefficient, and based on which, a Pearson correlation-based TOPSIS (technique for order of preference by similarity to ideal solution) approach for MADM problems is developed. Finally, the effectiveness as well as the applicability of the developed method are illustrated through numerical examples and comparative analysis.

The aim of this paper is to present a multiple-attribute group decision-making (MAGDM) framework based on a new single-valued neutrosophic linguistic (SVNL) distance measure. By unifying the idea of the weighted average and ordered weighted averaging into a single-valued neutrosophic linguistic distance, we first developed a new SVNL weighted distance measure, namely a SVNL combined and weighted distance (SVNLCWD) measure. The focal characteristics of the devised SVNLCWD are its ability to combine both the decision-makers’ attitudes toward the importance, as well as the weights, of the arguments. Various desirable properties and families of the developed SVNLCWD were contemplated. Moreover, a MAGDM approach based on the SVNLCWD was formulated. Lastly, a real numerical example concerning a low-carbon supplier selection problem was used to describe the superiority and feasibility of the developed approach.

As a generalization of several fuzzy tools, picture fuzzy sets (PFSs) hold a special ability to perfectly portray inherent uncertain and vague decision preferences. The intention of this paper is to present a Pearson’s picture fuzzy correlation-based model for multi-attribute decision-making (MADM) analysis. To this end, we develop a new correlation coefficient for picture fuzzy sets, based on which a Pearson’s picture fuzzy closeness index is introduced to simultaneously calculate the relative proximity to the positive ideal point and the relative distance from the negative ideal point. On the basis of the presented concepts, a Pearson’s correlation-based model is further presented to address picture fuzzy MADM problems. Finally, an illustrative example is provided to examine the usefulness and feasibility of the proposed methodology.

Glaucoma is a progressive disease due to damage in the optic nerve with associated functional losses. Although the relationship between structural and functional progression in glaucoma is well established, there is disagreement on how this association evolves over time. In addressing this issue, we propose a new class of non-Gaussian linear-mixed models to estimate the correlations among subject-specific effects in multivariate longitudinal studies with a skewed distribution of random effects, to be used in a study of glaucoma. This class provides an efficient estimation of subject-specific effects by modeling the skewed random effects through the log-gamma distribution. It also provides more reliable estimates of the correlations between the random effects. To validate the log-gamma assumption against the usual normality assumption of the random effects, we propose a lack-of-fit test using the profile likelihood function of the shape parameter. We apply this method to data from a prospective observation study, the Diagnostic Innovations in Glaucoma Study, to present a statistically significant association between structural and functional change rates that leads to a better understanding of the progression of glaucoma over time.

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