Evaluations as Sets over Lattices – Application Point of View

2021 ◽  
pp. 91-101
Author(s):  
Rainer Bruggemann ◽  
Adalbert Kerber
Keyword(s):  
Point Of View ◽  
Application Point

Rough Sets and Approximate Reasoning

2014 ◽  
pp. 180-228 ◽  
Author(s):  
B. K. Tripathy
Keyword(s):  
Fuzzy Logic ◽  
Fuzzy Sets ◽  
Rough Sets ◽  
Intuitionistic Fuzzy Sets ◽  
Point Of View ◽  
Approximate Reasoning ◽  
Human Reasoning ◽  
Intuitionistic Fuzzy ◽  
Application Point ◽  
Future Work

Several models have been introduced to capture impreciseness in data. Fuzzy sets introduced by Zadeh and Rough sets introduced by Pawlak are two of the most popular such models. In addition, the notion of intuitionistic fuzzy sets introduced by Atanassov and the hybrid models obtained thereof have been very fruitful from the application point of view. The introduction of fuzzy logic and the approximate reasoning obtained through it are more realistic as they are closer to human reasoning. Equality of sets in crisp mathematics is too restricted from the application point of view. Therefore, extending these concepts, three types of approximate equalities were introduced by Novotny and Pawlak using rough sets. These notions were found to be restrictive in the sense that they again boil down to equality of sets and also the lower approximate equality is artificial. Keeping these points in view, three other types of approximate equalities were introduced by Tripathy in several papers. These approximate equalities were further generalised to cover the approximate equalities of fuzzy sets and intuitionistic fuzzy sets by him. In addition, considering the generalisations of basic rough sets like the covering-based rough sets and multigranular rough sets, the study has been carried out further. In this chapter, the authors provide a comprehensive study of all these forms of approximate equalities and illustrate their applicability through several examples. In addition, they provide some problems for future work.

scholarly journals Implicit max-stable extremal integrals

Extremes ◽  
2020 ◽  
Author(s):  
D. Kremer
Keyword(s):  
Loss Function ◽  
Open Problem ◽  
Stochastic Integral ◽  
Extreme Values ◽  
Stable Distributions ◽  
Extreme Value ◽  
Point Of View ◽  
Extreme Value Distributions ◽  
Application Point ◽  
Deterministic Function

Abstract Recently, the notion of implicit extreme value distributions has been established, which is based on a given loss function f ≥ 0. From an application point of view, one is rather interested in extreme loss events that occur relative to f than in the corresponding extreme values itself. In this context, so-called f -implicit α-Fréchet max-stable distributions arise and have been used to construct independently scattered sup-measures that possess such margins. In this paper we solve an open problem in Goldbach (2016) by developing a stochastic integral of a deterministic function g ≥ 0 with respect to implicit max-stable sup-measures. The resulting theory covers the construction of max-stable extremal integrals (see Stoev and Taqqu Extremes 8, 237–266 (2005)) and, at the same time, reveals striking parallels.

Channeling in 4H-SiC from an Application Point of View

2019 ◽  
Vol 963 ◽  
pp. 386-389 ◽  
Author(s):  
Peter Pichler ◽  
Tomasz Sledziewski ◽  
Volker Häublein ◽  
Anton Bauer ◽  
Tobias Erlbacher
Keyword(s):  
Monte Carlo ◽  
Ion Implantation ◽  
Monte Carlo Simulations ◽  
Electronic Devices ◽  
Point Of View ◽  
Power Electronic ◽  
Application Point ◽  
Doping Profiles

During ion implantation into monocrystalline semiconductors, some of the implanted atoms will be deflected to crystal directions along which they may penetrate deeply into the crystal. We investigate such channeling effects for Al and N implantation into 4H-SiC by Monte Carlo simulations. The focus of the work is on the effects of channeling on doping profiles, the relevance for the net doping of typical power electronic devices, and the influence of scattering oxides.

scholarly journals Growth, Optical and Dielectric Studies on Pure and L-Lysine Doped KDP Crystals

2012 ◽  
Vol 2012 ◽  
pp. 1-6 ◽  
Author(s):  
N. Kanagathara ◽  
G. Anbalagan
Keyword(s):  
Dielectric Constant ◽  
Dielectric Loss ◽  
Single Crystals ◽  
Visible Region ◽  
Point Of View ◽  
Dielectric Study ◽  
Dielectric Studies ◽  
Slow Evaporation ◽  
Application Point ◽  
Kdp Crystals

Optically good quality single crystals of pure and L-lysine monohydrochloride-doped KDP crystals have been grown by a slow evaporation method. The grown crystals have been subjected to optical and dielectric studies. The UV-Vis spectrum shows the transmitting ability of the crystals in the entire visible region and transmittance percentage is increased for the doped KDP crystals. From the dielectric study, it is found that the dielectric constant and the dielectric loss of L-lysine-doped KDP crystals were lower than the pure KDP crystals. Hence L-lysine-doped KDP crystals are found to be more beneficial from an application point of view as compared to pure KDP crystals.

Implementation Mode of Industrial Engineering Projects Based on Project Management

2012 ◽  
Vol 433-440 ◽  
pp. 1660-1665
Author(s):  
Hang Liu
Keyword(s):  
Project Management ◽  
Point Of View ◽  
Industrial Engineering ◽  
Practical Application ◽  
Application System ◽  
Application Point ◽  
Body Of Knowledge ◽  
The Subject ◽  
Engineering Projects ◽  
Investigation And Study

Since the Industrial Engineering (IE) was introduced to China, people have already had much understanding of this cross discipline, and IE has been successfully popularized and applied in some enterprises. In such circumstances, a task we face is to systematically and comprehensively develop a theory and application system of IE from the subject development and practical application point of view, and the industrial engineering body of knowledge is established based on such a need. In this paper, on the basis of investigation and study on the domestic and foreign relevant studies, it establishes the industrial engineering body of knowledge, and proposes the implementation mode of IE projects based on project management, providing a certain reference role in the discipline development of IE and the implementation of IE in enterprises.

scholarly journals The Complex Order Fractional Derivatives and Systems Are Non Hermitian

2021 ◽  
Author(s):  
Manuel Ortigueira
Keyword(s):  
Fractional Derivative ◽  
Fractional Derivatives ◽  
Point Of View ◽  
Logarithmic Phase ◽  
Complex Order ◽  
Application Point ◽  
Allpass Filters

This paper discusses the concept of fractional derivative with complex order from the application point of view. It is shown that a fractional derivative is hermitian, if and only if the order is real. The hermitian part of complex order derivatives behave like allpass filters with almost logarithmic phase.

scholarly journals On A Logarithmic Mittag-Leffler Function, its Properties and Applications

2021 ◽  
Author(s):  
M.A. Pathan ◽  
Hemant Kumar
Keyword(s):  
Infectious Diseases ◽  
Hypergeometric Functions ◽  
Point Of View ◽  
Integral Representations ◽  
Contour Integral ◽  
Application Point

In this paper, we introduce a logarithmic Mittag-Leffler function and discuss some of its properties. The application of these properties become helpful in extension of Pochhammer’s type contour integral representations and Rodrigues formulae of some known hypergeometric functions. On application point of view, some relations are discussed which are useful in interpreting the phenomenon of spread of infectious diseases in terms of Lauricella’s multiple hypergeometric functions. 

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