The following paper presents deductive theories of n-Pythagorean fuzzy sets (n-PFS). N-PFS objects are a generalization of the intuitionistic fuzzy sets (IFSs) and the Yager Pythagorean fuzzy sets (PFSs). Until now, the values of membership and non-membership functions have been described on a one-to-one scale and a quadratic function scale. There is a symmetry between the values of this membership and non-membership functions. The scales of any power functions are used here in order to increase the scope of the decision-making problems. The theory of n-PFS introduces a conceptual apparatus analogous to the classic theory of Zadeh fuzzy sets, consistently striving to correctly define the n-PFS algebra.

The paper presents a certain class of the mathematical models of diagnostic information granules describing the fuzzy symptoms-faults relationship. A certain fuzzy diagnostic information retrieval system is described as an application of an expert diagnostic system. Symptoms and faults are fuzzy, and with some scaling of the symptom-fault concept pair values. These value pairs can be considered as intuitionistic fuzzy sets for the space of diagnosed objects. In this article, for scaling intuitionistic fuzzy sets (n-ScIFS), the deductive theory is formulated. There the intuitionistic fuzzy sets (IFSs) and the Pythagorean fuzzy sets (PFSs) are generalized to the n-ScIFS objects. The membership and non-membership values, as standard, can be described by the 1:1 scale or the quadratic function scale. However, any power scale $n>2$ can be used. In this paper, any n-Sc scaling functions retaining the IFSs properties are considered. The n-ScIFS theory introduces a conceptual apparatus analogous to the classical theory of Zadeh fuzzy sets and Yager PFSs, consistently striving, for the first time, to formulate the relational structure of n-ScIFSs as a model of a certain information granule system called here the diagnostic granule system. In addition, power- and linear-repeatable diagnostic granules are defined in the n-ScIFSs structure for serial or parallel diagnosis processes. The information granule base is determined and a diagnostic granule system model produced by this information granule base is shown. Certain algorithms have been given to establish the semantic language of diagnosis describing the system of diagnostic information granules.

Machine learning (ML) methods are increasingly being applied to analyze biological signals. For example, ML methods have been successfully applied to the human electroencephalogram (EEG) to classify neural signals as pathological or non-pathological and to predict working memory performance in healthy and psychiatric patients. ML approaches can quickly process large volumes of data to reveal patterns that may be missed by humans. This study investigated the accuracy of ML methods at classifying the brain’s electrical activity to cognitive events, i.e., event-related brain potentials (ERPs). ERPs are extracted from the ongoing EEG and represent electrical potentials in response to specific events. ERPs were evoked during a visual Go/NoGo task. The Go/NoGo task requires a button press on Go trials and response withholding on NoGo trials. NoGo trials elicit neural activity associated with inhibitory control processes. We compared the accuracy of six ML algorithms at classifying the ERPs associated with each trial type. The raw electrical signals were fed to all ML algorithms to build predictive models. The same raw data were then truncated in length and fitted to multiple dynamic state space models of order $n_x$ using a continuous-time subspace-based system identification algorithm. The $4n_x$ numerator and denominator parameters of the transfer function of the state space model were then used as substitutes for the data. Dimensionality reduction simplifies classification, reduces noise, and may ultimately improve the predictive power of ML models. Our findings revealed that all ML methods correctly classified the electrical signal associated with each trial type with a high degree of accuracy, and accuracy remained high after parameterization was applied. We discuss the models and the usefulness of the parameterization.

In the Dempster-Shafer's theory of evidence, for incorporating uncertainty, the valuation assigns to the data tables the degrees of belief for these data. Firstly, we are looking for the answers to the following questions. Is there a valuation-based system in which combination and marginalization operate on valuations? Has this system prosperities analogical to the t-norm system? In the t-norm system of the valuation for the specific database attributes configuration can be described the algebra of possible data set in which can be interpreted the Information Retrieval Logic.