Recent Fuzzy Generalisations of Rough Sets Theory: A Systematic Review and Methodological Critique of the Literature

Abstract

Rough set theory has been used extensively in fields of complexity, cognitive sciences, and artificial intelligence, especially in numerous fields such as expert systems, knowledge discovery, information system, inductive reasoning, intelligent systems, data mining, pattern recognition, decision-making, and machine learning. Rough sets models, which have been recently proposed, are developed applying the different fuzzy generalisations. Currently, there is not a systematic literature review and classification of these new generalisations about rough set models. Therefore, in this review study, the attempt is made to provide a comprehensive systematic review of methodologies and applications of recent generalisations discussed in the area of fuzzy-rough set theory. On this subject, the Web of Science database has been chosen to select the relevant papers. Accordingly, the systematic and metaanalysis approach, which is called "PRISMA," has been proposed and the selected articles were classified based on the author and year of publication, author nationalities, application field, type of study, study category, study contribution, and journal in which the articles have appeared. Based on the results of this review, we found that there are many challenging issues related to the different application area of fuzzy-rough set theory which can motivate future research studies.

Reliability Evolution of Elevators Based on the Rough Set and the Improved TOPSIS Method

“…Therefore, in the process of evaluating the reliability of elevator equipment, we need to fully consider the interacting factors among indicators, clarify the interrelation among indicators, and build the figure of interrelation among the indicators of the reliability of elevators, which is shown in Figure 1. [6][7][8] Definition 1. Let = ( , , , ) be a knowledge expressing system, where is the universe, is the attribute set, is the attribute-values set, and is the information function.…”

“…The setting of management organization 3 The management of maintenance and use 4 The management regulations for elevators 5 The management of safety and accident emergency treatment 6 The reliability of elevators Environment The environment of equipment operation 7 The condition of routine maintenance 8…”

Civil Engineering and Symmetry

“…Neutrosophic sets, recently introduced by Smarandache, opened up new possibilities for representing the uncertain and inconsistent information encountered in decision-making formulations [6]. Fuzzy-rough sets have been applied in various fields, such as expert systems, knowledge discovery, information system, inductive reasoning, intelligent systems, data mining, pattern recognition, decision-making, and machine learning [7].Additionally, fuzzy sets have been intensively applied in decision-making problems modelled within the aggregation operator framework. Various aggregation operators under different fuzzy sets are reviewed in [8].The methodological aspects of the decision-making problems in civil engineering, concerning the combination and integration of fuzzy and probabilistic models to deal with the uncertainties, were discussed in [9].Research into the development of new MCDM methods has been directed towards hybrid MCDM approaches.…”

“…Neutrosophic sets, recently introduced by Smarandache, opened up new possibilities for representing the uncertain and inconsistent information encountered in decision-making formulations [6]. Fuzzy-rough sets have been applied in various fields, such as expert systems, knowledge discovery, information system, inductive reasoning, intelligent systems, data mining, pattern recognition, decision-making, and machine learning [7].…”

Solution Models Based on Symmetric and Asymmetric Information

“…Insufficient information makes market problems more difficult. However, stakeholders also have incentives to create mechanisms that allow them to form mutually beneficial decisions even in the face of imperfect information [6][7][8][9][10][11][12][13][14][15][16][17]. The degree of asymmetry is different, yielding testable implications for the prevalence of asymmetric learning.…”