Concept learning consistency under three‑way decision paradigm

Concept Mining is one of the main challenges both in Cognitive Computing and in Machine Learning. The ongoing improvement of solutions to address this issue raises the need to analyze whether the consistency of the learning process is preserved. This paper addresses a particular problem, namely, how the concept mining capability changes under the reconsideration of the hypothesis class. The issue will be raised from the point of view of the so-called Three-Way Decision (3WD) paradigm. The paradigm provides a sound framework to reconsider decision-making processes, including those assisted by Machine Learning. Thus, the paper aims to analyze the influence of 3WD techniques in the Concept Learning Process itself. For this purpose, we introduce new versions of the Vapnik-Chervonenkis dimension. Likewise, to illustrate how the formal approach can be instantiated in a particular model, the case of concept learning in (Fuzzy) Formal Concept Analysis is considered.This work is supported by State Investigation Agency (Agencia Estatal de Investigación), project PID2019-109152GB-100/AEI/10.13039/501100011033. We acknowledge the reviewers for their suggestions and guidance on additional references that have enriched our paper. Open Access funding provided thanks to the CRUE-CSIC agreement with Springer Nature

Fuzzy rough granular neural networks, fuzzy granules, and classification

AbstractWe introduce a fuzzy rough granular neural network (FRGNN) model based on the multilayer perceptron using a back-propagation algorithm for the fuzzy classification of patterns. We provide the development strategy of the network mainly based upon the input vector, initial connection weights determined by fuzzy rough set theoretic concepts, and the target vector. While the input vector is described in terms of fuzzy granules, the target vector is defined in terms of fuzzy class membership values and zeros. Crude domain knowledge about the initial data is represented in the form of a decision table, which is divided into subtables corresponding to different classes. The data in each decision table is converted into granular form. The syntax of these decision tables automatically determines the appropriate number of hidden nodes, while the dependency factors from all the decision tables are used as initial weights. The dependency factor of each attribute and the average degree of the dependency factor of all the attributes with respect to decision classes are considered as initial connection weights between the nodes of the input layer and the hidden layer, and the hidden layer and the output layer, respectively. The effectiveness of the proposed FRGNN is demonstrated on several real-life data sets

Mixed-attitude three-way decision model for aerial targets: Threat assessment based on IF-VIKOR-GRA method

Assessing potential threats typically necessitates the use of a robust mathematical model, a comprehensive evaluation method and universal decision rules. A novel approach is utilized in this study to optimize existing threat assessment (TA) algorithms and three-way decision models (3WDMs) are leveraged that incorporate decision-theoretic rough sets (DTRSs) within dynamic intuitionistic fuzzy (IF) environments to create a mixed-attitude 3WDM based on the IF-VIKOR-GRA method in the context of aviation warfare. The primary objectives of this study include determining conditional probabilities for IF three-way decisions (3WDs) and establishing mixed-attitude decision thresholds. Both the target attribute and loss function are expressed in the form of intuitionistic fuzzy numbers (IFNs). To calculate these conditional probabilities, an IF technique is used to combine the multi-attribute decision-making (MADM) method VIKOR and the grey relational analysis (GRA) method, while also taking into account the risk-related preferences of decision-makers (DMs). Optimistic and pessimistic 3WDMs are developed from the perspectives of membership degree and non-membership degree, then subsequently integrated into the comprehensive mixed-attitude 3WDM. The feasibility and effectiveness of this methodology are demonstrated through a numerical example and by comparison to other existing approaches

A three-way decision-making technique based on Pythagorean double hierarchy linguistic term sets for selecting logistic service provider and sustainable transportation investments

Finding the best transportation project and logistic service provider is one for the most important aspects of the development of a country. This task becomes more complicated from time to time as different criteria are involved. Hence, this paper proposes an approach to the linguistic three-way decision-making (TWDs) problem for selecting sustainable transportation investments and logistic service providers with unknown criteria and expert weight information. To this end, we first propose a new tool, the Pythagorean double hierarchy linguistic term sets (PyDHLTSs), which is a combination of first hierarchy linguistic term sets and second hierarchy linguistic term sets which can describe uncertainty and fuzziness more flexibly in decision-making (DM) problems. In addition, we propose some aggregation operators and basic operational laws for PyDHLTSs. A new decision-making technique for PyDHLTSs based on decision-theoretic rough sets (DTRSs) is proposed in the three-way decisions. Next, the conditional probability is computed using grey relational analysis in a PyDHLTSs environment, which improves decision-making. The loss function is computed by using the proposed aggregation operator, and the decision's results are determined by the minimum-loss principle. Finally, a real-world case study of a transportation project and logistic service provider is considered to demonstrate the efficiency of the proposed methods