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Fuzzy-Genetic Approach to Epidemiology
Published in Jyoti Mishra, Ritu Agarwal, Abdon Atangana, Mathematical Modeling and Soft Computing in Epidemiology, 2020
Minakshi Biswas Hathiwala, Jignesh Pravin Chauhan, Gautam Suresh Hathiwala
Fuzzy sets can be used in an extensive range of structures such as topological spaces, groups, rings, algebras, ideals, and vector spaces. They can also be applied in quantum particle physics and control theory. C.L. Chang [10] was the first to propose the concept of fuzzy topological spaces. He used fuzzy sets instead of crisp sets in the definition of point set topology and redefined the theory of ordinary topological spaces. Fuzzy topology is defined by extending ordinary topology to fuzzy setting, and the theory of ordinary topology is a special case of it. Although ordinary topology can be generalized to fuzzy topology, fuzzy topology has its own remarkable characteristics. It can magnify our interpretation of some structures in classical mathematics. Besides that, it provides a new way of observing significant results of classical mathematics [5]. For our convenience, we will now term the “topology” based on crisp sets to be crisp topology. Just like crisp topology, it is possible to define fuzzy pretopology by means of operators discussed below.
Exploration of polygons in a STEAM framework: technology and cultural background
Published in International Journal of Mathematical Education in Science and Technology, 2023
Thierry Dana-Picard, Sara Hershkovitz
Now, we wish to remind that in the past, geometric topics were not only a nice topic to learn, but also an important topic to work on, in professional life. Today professionals may enjoy automated tools to plan architectural and design items, as mathematics learners may enjoy the software for dynamic geometry. Modern technologies enable the easy checking of various possibilities (critical thinking), development of new programming skills and creativity. As a whole, they are here to foster new ways of thinking. Lavoie (1994) claimed that electronic calculators initiated a revolution similar to the transition from writing with a feather to writing with an iron quill: some tasks have been transferred from the head to the hand.8 Software as a DGS may make technical tasks easier, providing a nice opportunity to discover again and apply classical mathematics. More experimentations can be performed; more cases can be checked than in a hand-work only session. Different aspects, both purely mathematical and applied to various fields, can be explored. Mathematical thinking is the winner and applied skills are enhanced. As an example, we refer to the building of an octagonal pyramid or a spherical cupola on top of an octagonal tower, as described by Paynter (1921), p. 198 sq. The main mathematical topics in this book, aimed at civil engineers and architects, can be afforded by high school students.
Determining the membership degrees in the range (0, 1) for hypersoft sets independently of the decision-maker
Published in International Journal of Systems Science, 2022
Uncertain data encountered in many fields need to be addressed during data analysis to increase the robustness of the results. Since classical mathematics cannot successfully model uncertain data, researchers have made different efforts. Fuzzy set theory, one of the first results of these efforts, was proposed by Zadeh (1965). This theory, which can express the belonging (i.e. membership degree in the range ) of an element to any set, is a very successful mathematical model. In particular, it is noteworthy that membership degrees, which are only expressed as 0 and 1 in classical mathematics, are generalised. However, fuzzy sets have some difficulties in modelling uncertainty problems, especially in the application phase. Molodtsov (1999), who thinks that the main reason for these difficulties is the lack of a parameterisation tool, introduced the soft set theory to the literature in 1999. Since these sets allow us to express objects associated with a particular parameter set, better mathematical models for uncertainty problems can be developed. Moreover, this theory has been successfully applied in many fields such as the theory of measurement, game theory, Riemann Integration, smoothness of functions and so on. Since this theory proposed by Molodtsov can successfully express uncertain situations, the application areas of soft sets continue to increase rapidly (Bordbar et al., 2021; Dalkılıç, 2021b, 2021d; Dalkılıç & Demirtaş, 2020, 2021a, 2021b; Demirtaş & Dalkılıç, 2020; Hayat et al., 2020; Sarwar et al., 2021).
A novel image segmentation utilizing FUZZY-based LBP and active contour model
Published in The Imaging Science Journal, 2022
Mojtaba Sajadi, Mohammad Bagher Tavakoli, Farbod Setoudeh, Amir Hossein Salemi
Fuzzy systems are currently used in many applications such as automated control, pattern recognition, decision support, and more. These systems use fuzzy logic which is based on the basic concept of fuzzy sets proposed by Lotfizadeh (1965) [22]. The unique feature of this theory, unlike classical mathematics, is its performance in different membership functions (MF) instead of the definite true values of these variables. This heuristic allows fuzzy theory to be a powerful tool whenever it controls accurate data or ambiguous nonlinear relationships between variables. Fuzzy logic seems to be effective in controlling dynamic, nonlinear, and noisy data, especially when the underlying physical relationships are not fully understood. Since the last decade, there have been some early applications of fuzzy logic in modelling [21], which shows that fuzzy systems can be used effectively in engineering applications.