Title
Tenzorski račun u prostorima simetrične i nesimetrične afine koneksije i primene u linearnom programiranju i projektovanju fazi regulatora
Creator
Simjanović, Dušan, 1985-
CONOR:
61434889
Copyright date
2023
Object Links
Select license
Autorstvo-Nekomercijalno-Bez prerade 3.0 Srbija (CC BY-NC-ND 3.0)
License description
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Language
Serbian
Cobiss-ID
Theses Type
Doktorska disertacija
description
Datum odbrane: 08.05.2024.
Other responsibilities
Academic Expertise
Tehničko-tehnološke nauke
University
Univerzitet u Nišu
Faculty
Elektronski fakultet
Group
Katedra za automatiku
Alternative title
Tensor calculus at symmetric and non-symetric affine connection in the fields of linear programming and design fuzzy controllers
Publisher
[D. J. Simjanović]
Format
XIII, 205 listova
description
Biografija autora: list 197.
Biobibliografija: listovi 198-202.
description
Applied Mathematics
Abstract (en)
This Ph. D. dissertation is devoted to the study of the general approach
of the shortest distances between two points of a surface, leading
to new approaches in considering the theoretically defined terms
in differential geometry. The importance of the obtained results of
tensor calculus is also reflected in the application in linear programming
techniques, where applying the scalar product generated by a
metric tensor, the objective function is defined in a new way, completing
the concept of the transportation problem. Surface fuzzy sets
are also defined as an important tool in describing indecision, ambiguity,
and indeterminacy, with the aim of designing optimal control
in automatic control systems, as well as improving the performance
of fuzzy controllers. The main contributions of the dissertation concern
the determination of components of the alternation of the double
covariant derivative and the examination of the relationship between
curvature tensors and pseudotensors of a non-symmetric affine connection
space, as well as the generalization of the concept of invariants
for geometric mapping, such as the determination of the family
of these invariants for mappings defined on the space GAN.
v
Also, in this Ph.D. thesis, the application of tensor calculus in linear
programming was observed, where the objective function was defined
in a new way and the concept of the transportation problem was
completed by applying the scalar product generated by the symmetric
contravariant metric tensor. With this procedure, by finding a new
way of determining the extreme values of the functions of a given
system, automatic control can be improved. It is shown that by using
geodesic lines of a surface instead of great circles of the unit sphere to
determine the distance between two fuzzy numbers, spherical fuzzy
numbers are generalized and thus the last coordinate is viewed as a
function instead as as a constant, allowing decision makers a greater
degree of freedom. The use of surface fuzzy sets and other fuzzy
numbers and different methods of fuzzification and defuzzification
provides an opportunity for better and more precise definition of the
input and output values of the fuzzy regulator, shortening the time required
to perform calculation operations, improving the performance
of the fuzzy regulator and the automatic control system.
Authors Key words
tenzorski račun, Ričijev tenzor, linearno programiranje, transportni
problem, fazi brojevi, fazi regulator
Authors Key words
tensor calculus, Ricci tensor, linear programming, transportation
problem, fuzzy numbers, fuzzy controller
Classification
629.113-523.6:514.763.5(043.3)
Type
Tekst
Abstract (en)
This Ph. D. dissertation is devoted to the study of the general approach
of the shortest distances between two points of a surface, leading
to new approaches in considering the theoretically defined terms
in differential geometry. The importance of the obtained results of
tensor calculus is also reflected in the application in linear programming
techniques, where applying the scalar product generated by a
metric tensor, the objective function is defined in a new way, completing
the concept of the transportation problem. Surface fuzzy sets
are also defined as an important tool in describing indecision, ambiguity,
and indeterminacy, with the aim of designing optimal control
in automatic control systems, as well as improving the performance
of fuzzy controllers. The main contributions of the dissertation concern
the determination of components of the alternation of the double
covariant derivative and the examination of the relationship between
curvature tensors and pseudotensors of a non-symmetric affine connection
space, as well as the generalization of the concept of invariants
for geometric mapping, such as the determination of the family
of these invariants for mappings defined on the space GAN.
v
Also, in this Ph.D. thesis, the application of tensor calculus in linear
programming was observed, where the objective function was defined
in a new way and the concept of the transportation problem was
completed by applying the scalar product generated by the symmetric
contravariant metric tensor. With this procedure, by finding a new
way of determining the extreme values of the functions of a given
system, automatic control can be improved. It is shown that by using
geodesic lines of a surface instead of great circles of the unit sphere to
determine the distance between two fuzzy numbers, spherical fuzzy
numbers are generalized and thus the last coordinate is viewed as a
function instead as as a constant, allowing decision makers a greater
degree of freedom. The use of surface fuzzy sets and other fuzzy
numbers and different methods of fuzzification and defuzzification
provides an opportunity for better and more precise definition of the
input and output values of the fuzzy regulator, shortening the time required
to perform calculation operations, improving the performance
of the fuzzy regulator and the automatic control system.
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