Formation of Surfaces Under Kinetic Displaying

The fuzzy set concept is often used in solution of problems in which the initial data is difficult or impossible to represent in the form of specific numbers or sets. Geo-information objects are distinguished by their uncertainty, their characteristics are often vague and have some error. Therefore, in the study of such objects is introduced the concept of "fuzziness" — fuzzy sets, fuzzy logic, linguistic variables, etc. The fuzzy set concept is given in the form of membership function. An ordinary set is a special case of a fuzzy one. If we consider a fuzzy object on the map, for example, a lake that changes its shape depending on the time of year, we can build up for it a characteristic function from two variables (the object’s points coordinates) and put a certain number in accordance with each point of the object. That is, we can describe a fuzzy set using its two-dimensional graphical image. Thus, we obtain an approximate view of a surface z = μ(x, y) in three-dimensional space. Let us now draw planes parallel to the plane. We’ll obtain intersections of our surface with these planes at 0 ≤ z ≤ 1. Let's call them as isolines. By projecting these isolines on the OXY plane, we’ll obtain an image of our fuzzy set with an indication of intermediate values μ(x, y) linked to the set’s points coordinates. So we’ll construct generalized Euler — Venn diagrams which are a generalization of well-known Euler — Venn diagrams for ordinary sets. Let's consider representations of operations on fuzzy sets A a n d B. Th e y u s u a l l y t a k e : μA B = min (μA,μB ), μA B = max (μA,μB ), μA = 1 − μA. Algebraic operations on fuzzy sets are defined as follows: μ A B x μ A x μ B x ( ) = ( ) + ( ) − −μ A (x)μ B (x), μ A B x μ A x μ B x ( ) = ( ) ( ), μ A (x) = 1 − μ A (x). Let's construct for a particular problem a generalized Euler — Venn diagram corresponding to it, and solve subtasks graphically, using operations on fuzzy sets, operations of intersection and integrating of the diagram’s bars.

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Representation of Engineering Geometry Development in “Geometry and Graphics” Journal

Сальков¹,

Kadykova²

2020

Geometry &Amp; Graphics

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In the paper "On the Increasing Role of Geometry", published in the electronic "Journal of Natural Science Research" in 2017, it was outspoken a hypothesis that now, at the time of innovative technologies, the importance of geometry is constantly increasing. The significance of geometry is also demonstrated by numerous Ph.D. and doctoral dissertations in the specialty No 05.01.01 - “Engineering Geometry and Computer Graphics”. It can be affirmed that all and everyone dissertations of technical and technological profile contain a geometric component to one degree or another. The "Geometry and Graphics" journal turned 8 (it was founded in June 2012). During this time, on its pages have been published numerous scientific papers, developing namely geometry and its branches: from simplest geometric constructions based on new properties of both lines and surfaces, to imaginary elements. Investigations were conducted in the following areas: “New Directions in Geometry”, “Fractal Geometry”, “Multidimensional Geometry”, “Geometric Constructions”, “Construction and Research of Surfaces”, “Imaginary Geometry”, “Practical Application of Geometry”, “Computer Graphics”, “Descriptive Geometry as Basis of other Branches of Geometry” ,”Geometry of Phase Spaces”. The journal publishes both recognized scientists and candidate for Ph.D. and doctor degrees. The considered array of papers clearly confirms the statement of the majority of authors, published in the journal, about geometry continuous development, which knocks out the ground for skeptics who decided that geometry is the science of the past centuries. As long as objects with shapes and surfaces surround us, geometry will be in demand. This, as they say, is unequivocal.

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Formation of Surfaces Under Kinetic Displaying

Cited by 16 publications

References 9 publications

Algorithms of recognizing solid-state objects by dynamic parameters in architectural and construction design

Algorithms of recognizing solid-state objects by dynamic parameters in architectural and construction design

Generalized Euler-Venn Diagrams for Fuzzy Sets

Representation of Engineering Geometry Development in “Geometry and Graphics” Journal

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