Naslov (srp)

Tenzorski račun u prostorima simetrične i nesimetrične afine koneksije i primene u linearnom programiranju i projektovanju fazi regulatora

Autor

Simjanović, Dušan, 1985-

Doprinosi

Milojković, Marko, 1980-
Ignjatović, Jelena, 1973-
Ranđelović, Branislav M., 1970-
Nikolić, Saša, 1982-
Vesić, Nenad O., 1985-

Opis (srp)

This Ph. D. dissertation is devoted to the study of the general approachof the shortest distances between two points of a surface, leadingto new approaches in considering the theoretically defined termsin differential geometry. The importance of the obtained results oftensor calculus is also reflected in the application in linear programmingtechniques, where applying the scalar product generated by ametric tensor, the objective function is defined in a new way, completingthe concept of the transportation problem. Surface fuzzy setsare also defined as an important tool in describing indecision, ambiguity,and indeterminacy, with the aim of designing optimal controlin automatic control systems, as well as improving the performanceof fuzzy controllers. The main contributions of the dissertation concernthe determination of components of the alternation of the doublecovariant derivative and the examination of the relationship betweencurvature tensors and pseudotensors of a non-symmetric affine connectionspace, as well as the generalization of the concept of invariantsfor geometric mapping, such as the determination of the familyof these invariants for mappings defined on the space GAN.vAlso, in this Ph.D. thesis, the application of tensor calculus in linearprogramming was observed, where the objective function was definedin a new way and the concept of the transportation problem wascompleted by applying the scalar product generated by the symmetriccontravariant metric tensor. With this procedure, by finding a newway of determining the extreme values of the functions of a givensystem, automatic control can be improved. It is shown that by usinggeodesic lines of a surface instead of great circles of the unit sphere todetermine the distance between two fuzzy numbers, spherical fuzzynumbers are generalized and thus the last coordinate is viewed as afunction instead as as a constant, allowing decision makers a greaterdegree of freedom. The use of surface fuzzy sets and other fuzzynumbers and different methods of fuzzification and defuzzificationprovides an opportunity for better and more precise definition of theinput and output values of the fuzzy regulator, shortening the time requiredto perform calculation operations, improving the performanceof the fuzzy regulator and the automatic control system.

Opis (srp)

Biografija autora: list 197. Biobibliografija: listovi 198-202. Datum odbrane: 08.05.2024. Applied Mathematics

Jezik

srpski

Datum

2023

Licenca

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