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Abstract
In this paper, a new uncertainty modelling concept called strait fuzzy set is introduced, which brings new perspectives to both theoretical and practical advances in fuzzy mathematics. This set type allows objects/points to be graded with fuzzy membership intervals that are partitions of [0,1] (so that the union of these partitions is [0,1] and their intersection is empty) instead of fuzzy membership degrees represented as exact values in [0,1]. Moreover, some basic operations and properties of strait fuzzy sets are studied in detail. The concept of strait fuzzy rough set is put forward and its theoretical aspects are discussed. In addition, two different similarity approaches are proposed for strait fuzzy sets and strait fuzzy rough sets, and applied to measure the similarity rates of vaccines against influenza viruses.
Disclosure statement
No potential conflict of interest was reported by the author(s).
Data availability statement
The data used the support the findings of this study are included within the article.
Additional information
Notes on contributors
Akın Osman Atagün
Akın Osman Atagün is a Professor at the Department of Mathematics, Faculty of Science and Arts, Kırşehir Ahi Evran University in Turkey. He received his MSc degree in Mathematics from Kırıkkale University, Turkey in 2001 and PhD degree in Mathematics from Erciyes University, Turkey in 2006. His research interests are in the areas of fuzzy set theory, soft set theory, soft matrix theory, rough set theory, algebraic structures, operational research, soft computing and decision making. He has published many valuable articles on these scientific topics in international academic journals. He has been on the referee lists of many scientific journals.
Hüseyin Kamacı
Hüseyin Kamacı is an Associate Professor at the Mathematics Department in the Science and Arts Faculty of Yozgat Bozok University, Turkey. He received his MSc and PhD degrees in Mathematics from Bozok University, Yozgat, Turkey in 2014 and 2018, respectively. His research interests include mathematical logic, fuzzy set, rough set, soft set, soft matrix, operational research, computational intelligence, decision making and game theory. He has many valuable publications on these issues in different scientific journals. He is a member of the editorial board of Journal of Fuzzy Logic and Modeling in Engineering, Frontiers in Artificial Intelligence, Modern Intelligent Times, Digital Technologies Research and Applications, Decision Making and Analysis, and Journal of AppliedMath. He is one of top 2% researchers included in the global list released by Stanford University in various disciplines on October 10, 2022.