Forty years have passed since Prof. Lotfi A. Zadeh introduced fuzzy set theory in his known article “Fuzzy Sets” in Information and Control, 8, 1965, sparking new development in information technology and automation. This article also formed the roots of the Fuzzy Systems Research Group, an active part of the Laboratory of Applied Mathematics, Lappeenranta University of Technology. Rough set theory, evolutionary computing, and neural computing followed, together with their combinations. This Special Issue presents 10 papers representing these areas. Many of the contributors of this Special Issue belong to the Fuzzy Systems Research Group and others work in close co-operations with this group. The first paper considers the use of linguistically expressed objectives in multicriteria decision-making in selection processes based on topological similarity M-relations between L-sets. The second presents basic ideas and fundamental concepts of rough set theory and considers properties of rough approximations. The third combines Lukasiewicz logics and modifier algebras based on Zadeh algebras, i.e., quasi-Boolean algebras of membership functions. The fourth applies Mö{o}bius transformations, known in complex analysis, to fuzzy subgroups in a topological point of view. The fifth discusses the stability of a classifier based on the Lukasiewicz structure and tests Schweizer and Sklar's implications with an extension to generalized mean to a classification task. The sixth deals with the interpretability problem of first-order Takagi-Sugeno systems and interpolation issues, developing a special two-model configuration. The seventh describes an expert system for defining an athlete's aerobic and anaerobic thresholds that successfully mimics decision-making by sport medicine professionals, with system functionality based on fuzzy comparison measures, generalized means, fuzzy membership functions, and differential evolution. The eighth applies a differential evolution algorithm-based method to training radial basis function networks with variables including centers, weights, and widths. The ninth compares two floating-point-encoded evolutionary algorithms – differential evolution and a generalized generation gap model – using a set of problems with different characteristics. The tenth proposes a new approach for monitoring break tendency of paper webs on modern paper machines, combining linguistic equations and fuzzy logic in a case-based reasoning framework. As the Guest Editor of this Special Issue, I thank the contributors and reviewers for their time and effort in making this special issue possible. I am also grateful to the JACIII editorial board, especially Prof. Kaoru Hirota, the Editors-in-Chief and Managing Editor Kenta Uchino, and the staff of Fuji Technology Press for the opportunity to participate in this work. I also thank Prof. Kaoru Hirota for organizing the reviewing of my paper.
Soft covering based rough graphs and corresponding decision making
