Novel Correlation Coefficient for Intuitionistic Fuzzy Sets and Its Application to Multi-Criteria Decision-Making Problems

Correlation coefficient is an essential measuring operator in an intuitionistic fuzzy environment use in solving MCDM problems. In this paper, Xu et al.'s correlation coefficient for IFSs is generalized for an improved output. The objectives of this work are to generalize the triparametric correlation coefficient for IFSs proposed by Xu et al. and unravel its applicability in some MCDM problems. The generalized correlation coefficient for IFSs is characterized with some number of results. Some numerical illustrations are supplied to validate the preeminence of the generalized correlation coefficient for IFSs over some existing correlation coefficient measures. In addition, some MCDM problems such as determination of suitable lecturer for course allocation and personnel promotion exercise captured in intuitionistic fuzzy pairs are discussed with the aid of the proposed correlation coefficient.

On Generalized Correlation Coefficients of Picture Fuzzy Sets With Their Applications

Picture fuzzy sets (PFSs) play a crucial role in uncertain/vague environments than intuitionistic fuzzy sets (IFSs) which do not take into consideration the degree of neutrality of an element. In this paper, the authors have proposed generalized correlation coefficients of PFSs along with some properties. The effectiveness and application of the proposed generalized correlation coefficients of PFSs in pattern recognition and multi-attribute decision making (MADM) is also discussed with the help of numerical examples.

Generalized Lévêque Solution for Ducts of Arbitrary Cross-Section

The asymptotic limit for perimeter averaged convection is generalized for short ducts of arbitrary cross-section. A correction factor to Lévêque's original analysis is derived in terms of the state of wall shear stress under conditions of fully developed flows for walls of constant temperature (T) and constant heat flux (H1 and H2). This analysis is performed for four duct geometries: elliptic, rhombic, rectangular, and regular polygons. The importance of this correction is greatest for the H2 wall condition and for ducts having walls with acute corners. The results of this analysis can be incorporated into a generalized correlation for the full Graetz problem in ducts of arbitrary cross-section.

Thermodynamic modeling and correlations of CH4, C2H6, CO2, H2S, and N2 hydrates with cage occupancies

The present work focuses on developing a framework for accurate prediction of thermodynamic conditions for single-component hydrates, namely CH4, CO2, N2, H2S, and C2H6 (coded in MATLAB). For this purpose, an exhaustive approach is adopted by incorporating eight different equations of states, namely Peng–Robinson, van der Waals, Soave–Redlich–Kwong, Virial, Redlich–Kwong, Tsai-Teja, Patel, and Esmaeilzadeh–Roshanfekr, with the well-known van der Waals–Platteeuw model. Overall, for I–H–V phase region, the Virial and van der Waals equation of state gives the most accurate predictions with minimum AAD%. For Lw–H–V phase region, Peng–Robinson equation of state is found to yield the most accurate predictions with overall AAD of 3.36%. Also, genetic programming algorithm is adopted to develop a generalized correlation. Overall, the correlation yields quick estimation with an average deviation of less than 1%. The accurate estimation yields a minimal AAD of 0.32% for CH4, 1.93% for C2H6, 0.77% for CO2, 0.64% for H2S, and 0.72% for N2. The same correlation can be employed for fitting phase equilibrium data for other hydrates too. The tuning parameter, n, is to be used for fine adjustment to the phase equilibrium data. The findings of this study can help for a better understanding of phase equilibrium and cage occupancy behavior of different gas hydrates. The accuracy in phase equilibria is intimately related to industrial applications such as crude oil transportation, solid separation, and gas storage. To date, no single correlation is available in the literature that can accurately predict phase equilibria for multiple hydrate species. The novelty of the present work lies in both the accuracy and generalizability of the proposed correlation in predicting the phase equilibrium data. The genetic programming generalized correlation is convenient for performing quick equilibrium prediction for industrial applications.

Generalized correlation-based dynamical network analysis: a new high-performance approach for identifying allosteric communications in molecular dynamics trajectories

Molecular interactions are essential for regulation of cellular processes, from the formation of multiprotein complexes, to the allosteric activation of enzymes. Identifying the essential residues and molecular features that regulate such interactions is paramount for understanding the biochemical process in question, allowing for suppression of a reaction through drug interventions, or optimization of a chemical process using bioengineered molecules. In order to identify important residues and information pathways within molecular complexes, the Dynamical Network Analysis method was developed and has since been broadly applied in the literature. However, in the dawn of exascale computing, this method is generally limited to relatively small biomolecular systems. In this work we provide an evolution of the method, application and interface. All data processing and analysis is conducted through Jupyter notebooks, providing automatic detection of important solvent and ion residues, an optimized and parallel generalized correlation implementation that is linear with respect to the number of nodes in the system, and subsequent community clustering, calculation of betweenness of contacts, and determination optimal paths. Using the popular visualization program VMD, high-quality renderings of the networks over the biomolecular structures can be produced. Our new implementation was employed to investigate three different systems, with up to 2.5 M atoms, namely the OMP-decarboxylase, the Leucyl-tRNA synthetase complexed with its cognate tRNA and adenylate, and the respiratory complex I in a membrane environment. Our enhanced and updated protocol provides the community with an intuitive and interactive interface, which can be easily applied to large macromolecular complexes.