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The experimental procedures of drug design, proven to be time-consuming and costly, are successfully complemented with computer-aided (in silico) approaches nowadays. Virtual ligand screening (VLS) is one of the most promising approaches when searching for new hit compounds. The efficiency of VLS procedures might be improved via post-docking optimization. In the focus of this investigation is AMMOS (Automatic Molecular Mechanics Optimization for in silico Screening) developed as multi-step structure-based procedure for efficient computational refinement of protein-ligand complexes at different levels of protein flexibility. Their performance has been assessed by the recently developed InterCriteria Analysis (ICrA), elaborated as multi-criterion decision-making approach to reveal possible relations in the behavior of pairs of criteria when multiple objects are considered. The capacity of ICrA as a supporting tool to assess the effect of applying different levels of protein flexibility in the post-docking optimization via AMMOS has been investigated and analyzed.

The concept of an Intuitionistic Fuzzy Modal Topological Structure (IFMTS) was introduced previously, and some of its properties were studied. So far, there are two different IFMTSs based on the classical intuitionistic fuzzy operations: “union” (∪) and “intersection” (∩). In the present paper, two new IFMTSs are developed. They are based on new intuitionistic fuzzy topological operators from closure and interior types, introduced here for the first time, and on the two standard intuitionistic fuzzy modal operators □ and ◊. Some basic properties of the new IFMTSs are discussed. The newly presented IFMTSs could be considered as a basis for the next research on the IFMTSs. Some ideas for the future development of the IFMTS theory and open problems are formulated, related to the existence of other intuitionistic fuzzy operations that can generate new intuitionistic fuzzy topological operators and, respectively, new IFMTSs.

The concept of an intuitionistic fuzzy deep neural network (IFDNN) is introduced here as a demonstration of a combined use of artificial neural networks and intuitionistic fuzzy sets, aiming to benefit from the advantages of both methods. The investigation presents in a methodological way the whole process of IFDNN development, starting with the simplest form—an intuitionistic fuzzy neural network (IFNN) with one layer with single-input neuron, passing through IFNN with one layer with one multi-input neuron, further subsequent complication—an IFNN with one layer with many multi-input neurons, and finally—the true IFDNN with many layers with many multi-input neurons. The formulas for strongly optimistic, optimistic, average, pessimistic and strongly pessimistic formulas for NN parameters estimation, represented in the form of intuitionistic fuzzy pairs, are given here for the first time for each one of the presented IFNNs. To demonstrate its workability, an example of an IFDNN application to biomedical data is here presented.

(1) Background: In silico approaches to rational drug design are among the fastest evolving ones. Depending on the available structural information for the biomacromolecule and the small molecule, the in silico methods are classified as ligand- and structure-based. The latter predict ligand–receptor binding using 3D structures of both molecules, whose computational simulation is referred to as molecular docking. It aims at estimating the binding affinity (approximated by scoring function) and the ligand binding pose in the receptor’s active site, which postulates a key role of the scoring functions in molecular docking algorithms. This study focuses on the performance of different types of scoring functions implemented in molecular modelling software packages. (2) Methods: An InterCriteria analysis (ICrA) was applied to assess the performance of the scoring functions available in MOE, GOLD, SeeSAR, and AutoDock Vina software platforms. The InterCriteria analysis was developed to distinguish possible relations between pairs of criteria when multiple objects are considered. All 12 investigated scoring functions were tested by docking a set of protease inhibitors in the binding sites of two protein targets. The dataset consisted of 88 benzamidine-type compounds with experimentally measured inhibitory constants for thrombin and trypsin, which allows for the objective assessment of the scoring functions performance. The results generated by the molecular docking were subjected to ICrA in order to analyze both docking energies as approximations of the binding affinities and RMSDs (root-mean-square deviation) as measures of the experimental binding pose proximity between the compounds and the co-crystalized ligand, based on the atoms in the common scaffold. (3) Results: The results obtained for the best poses, the average of the best 5 or 30 poses retained after docking, were analyzed. A comparison with the experimentally observed inhibitory effects was also performed. The InterCriteria analysis application confirms that the performance of the scoring functions for the same dataset of ligands depends on the studied protein. The analysis reveals that none of the studied scoring functions is a good predictor of the compounds’ binding affinities for the considered protein targets. (4) Conclusion: In terms of this analysis, the investigated scoring functions do not produce equivalent results, which suggests the necessity for their combined use in consensus docking studies.

Intuitionistic fuzzy logic is the main tool in the recently developed step-wise “cross-evaluation” procedure that aims at the assessment of different optimization algorithms. In this investigation, the procedure previously applied to compare the effectiveness of two or three algorithms has been significantly upgraded to evaluate the performance of a set of four algorithms. For the first time, the procedure applied here has been tested in the evaluation of the effectiveness of genetic algorithms (GAs), which are proven as very promising and successful optimization techniques for solving hard non-linear optimization tasks. As a case study exemplified with the parameter identification of a S. cerevisiae fed-batch fermentation process model, the cross-evaluation procedure has been executed to compare four different types of GAs, and more specifically, multi-population genetic algorithms (MGAs), which differ in the order of application of the three genetic operators: Selection, crossover and mutation. The results obtained from the implementation of the upgraded intuitionistic fuzzy logic-based procedure for MGA performance assessment have been analyzed, and the standard MGA has been outlined as the fastest and most reliable one among the four investigated algorithms.

The InterCriteria Analysis (ICrA) is based on the mathematical formalisms of index matrices and intuitionistic fuzzy sets. It has been elaborated to discern possible similarities in the behavior of criteria pairs when multiple objects are considered, allowing also the accounting of information uncertainty. The focus of this study is to validate the applicability of ICrA over a large set of ECG criteria extracted for arrhythmia analysis and to evaluate its ability to support the pre-selection of criteria that could be further involved in decision making procedures. ICrA is applied over 88 ECG criteria (resulting in 3828 criteria pairs) calculated for 8528 ECGs from PhysioNet/CinC Challenge 2017 database. Three criteria pairs show strong positive consonance, another 26—positive consonance, while another 15 are in negative consonance. ICrA also reveals lack of dependencies in 98 criteria pairs. The correspondence between our observations (high degrees of agreement/disagreement and lack of dependencies) and our expectations based on knowledge of the principles involved in the computation of the ECG criteria validates the application of ICrA for reliable evaluation of the relation between different criteria. This potential of ICrA to highlight useful relations between ECG criteria makes it suitable in the ECG pre-processing stage for criteria pre-selection. Thus, optimization of the feature space could be achieved together with minimization of the computations’ complexity.