An Analytical Approach to Evaluating Bivariate Functions of Fuzzy Numbers with One Local Extremum

2014 ◽  
Author(s):  
Arthur Seibel ◽  
Josef Schlattmann
Keyword(s):  
Analytical Approach ◽  
Fuzzy Numbers ◽  
Local Extremum ◽  
Bivariate Functions

scholarly journals Generalized Weighted Statistical Convergence for Double Sequences of Fuzzy Numbers and Associated Korovkin-Type Approximation Theorem

2020 ◽  
Vol 2020 ◽  
pp. 1-8
Author(s):  
Abdullah Alotaibi
Keyword(s):  
Statistical Convergence ◽  
Fuzzy Numbers ◽  
Approximation Theorem ◽  
Bernstein Operators ◽  
Double Sequences ◽  
Korovkin Type Approximation Theorem ◽  
Type Approximation ◽  
Functions Of Two Variables ◽  
Sequences Of Fuzzy Numbers ◽  
Bivariate Functions

We define the notions of weighted λ,μ-statistical convergence of order γ1,γ2 and strongly weighted λ,μ-summability of γ1,γ2 for fuzzy double sequences, where 0<γ1,γ2≤1. We establish an inclusion result and a theorem presenting a connection between these concepts. Moreover, we apply our new concept of weighted λ,μ-statistical convergence of order γ1,γ2 to prove Korovkin-type approximation theorem for functions of two variables in a fuzzy sense. Finally, an illustrative example is provided with the help of q-analogue of fuzzy Bernstein operators for bivariate functions which shows the significance of our approximation theorem.

scholarly journals An Extended Analytical Approach to Evaluating Monotonic Functions of Fuzzy Numbers

2014 ◽  
Vol 2014 ◽  
pp. 1-9 ◽  
Author(s):  
Arthur Seibel ◽  
Josef Schlattmann
Keyword(s):  
Mathematical Models ◽  
Analytical Approach ◽  
Fuzzy Numbers ◽  
Parameter Uncertainties ◽  
Monotonic Functions

This paper presents an extended analytical approach to evaluating continuous, monotonic functions of independent fuzzy numbers. The approach is based on a parametricα-cut representation of fuzzy numbers and allows for the inclusion of parameter uncertainties into mathematical models.

scholarly journals An Analytical Approach to Evaluating Nonmonotonic Functions of Fuzzy Numbers

2015 ◽  
Vol 2015 ◽  
pp. 1-6
Author(s):  
Arthur Seibel ◽  
Josef Schlattmann
Keyword(s):  
Mathematical Models ◽  
Analytical Approach ◽  
Fuzzy Numbers ◽  
Parameter Uncertainties

This paper presents a novel analytical approach to evaluating continuous, nonmonotonic functions of independent fuzzy numbers. The approach is based on a parametricα-cut representation of fuzzy numbers and allows for the inclusion of parameter uncertainties into mathematical models.

The Dynamics of TAT Process

2014 ◽  
Vol 35 (2) ◽  
pp. 103-133 ◽  
Author(s):  
Benoît Verdon ◽  
Catherine Chabert ◽  
Catherine Azoulay ◽  
Michèle Emmanuelli ◽  
Françoise Neau ◽  
...  
Keyword(s):  
Defense Mechanisms ◽  
Analytical Approach ◽  
Therapeutic Process ◽  
Practice Research ◽  
Rorschach Test ◽  
Mental Functioning ◽  
Projective Tests ◽  
The Subject ◽  
Latent Content ◽  
Rigorous Method

After many years of clinical practice, research and the teaching of projective tests, Shentoub and her colleagues (Debray, Brelet, Chabert & al.) put forward an original and rigorous method of analysis and interpretation of the TAT protocols in terms of psychoanalysis and clinical psychopathology. They developed the TAT process theory in order to understand how the subject builds a narrative. Our article will emphasize the source of the analytical approach developed by V. Shentoub in the 1950s to current research; the necessity of marking the boundary between the manifest and latent content in the cards; the procedure for analyzing the narrative, supported by an analysis sheet for understanding the stories' structure and identifying the defense mechanisms; and how developing hypotheses about how the mental functions are organized, as well as their potential psychopathological characteristics; and the formulation of a diagnosis in psychodynamic terms. In conjunction with the analysis and interpretation of the Rorschach test, this approach allows us to develop an overview of the subject's mental functioning, taking into account both the psychopathological elements that may threaten the subject and the potential for a therapeutic process. We will illustrate this by comparing neurotic, borderline, and psychotic personalities.

Maxim Berezovsky C-dur symphony in a context of new biographical scenario of artist’s life-creativity

2018 ◽  
pp. 13-25
Author(s):  
Olha Shumilina
Keyword(s):  
Eighteenth Century ◽  
Instrumental Music ◽  
Analytical Approach ◽  
Spiritual Direction ◽  
Theoretical Research ◽  
Orchestral Music ◽  
Musical Life ◽  
Analysis And Synthesis ◽  
Mental Modeling ◽  
Independent Work

Relevance of the study. The article studies recently found symphony of the prominent Ukrainian composer of the second half of the eighteenth century Maxim Berezovsky. He is widely known now as the author of cyclic spiritual concerts written for the Orthodox worship, and is practically unknown as a musician instrumentalist associated with the imperial theater and the court musical life. The work of M. Berezovsky as a secular musician determined the creative interest in composing instrumental music intended for secular chamber and orchestral music. Main objective of the article is a clarification of M.Berezovsky symphony as one of secular field artworks in the light of new summaries about artist’s life-creativity. Methodology. Taking into account peculiarities of the material and the analytical approach to its study, the methods of theoretical research have been chosen(abstraction, analysis and synthesis, induction and deduction, mental modeling, ascension from abstract to concrete, etc.). Conclusions. As a result of a study the symphony analysis in a context of new authentic statements about M.Berezovsky’s life-creativity. It was stated that this artwork was written not accidentally and detects absolute awareness of the artist in all composer’s niceties – how to build a topic and build a homophonic construction based on it, in a technique of orchestral construction, form creations of that time and etc. From the beginning of his creative career, M. Berezovsky was well aware of the possibilities of the orchestra as a performer, attached to the Italian opera and instrumental music. Symphony enriches our imagination about the works of M. Berezovsky in the field of secular instrumental and operatic music and extends the range of works of the artist beyond the spiritual direction. Some signs indicate that the Symphony was not an independent work, but an overture to the opera Demofont.

Maxim Berezovsky C-dur symphony in a context of new biographical scenario of artist’s life-creativity

2018 ◽  
pp. 13-25
Author(s):  
Olha Shumilina
Keyword(s):  
Eighteenth Century ◽  
Instrumental Music ◽  
Analytical Approach ◽  
Spiritual Direction ◽  
Theoretical Research ◽  
Orchestral Music ◽  
Musical Life ◽  
Analysis And Synthesis ◽  
Mental Modeling ◽  
Independent Work

Relevance of the study. The article studies recently found symphony of the prominent Ukrainian composer of the second half of the eighteenth century Maxim Berezovsky. He is widely known now as the author of cyclic spiritual concerts written for the Orthodox worship, and is practically unknown as a musician instrumentalist associated with the imperial theater and the court musical life. The work of M. Berezovsky as a secular musician determined the creative interest in composing instrumental music intended for secular chamber and orchestral music. Main objective of the article is a clarification of M.Berezovsky symphony as one of secular field artworks in the light of new summaries about artist’s life-creativity. Methodology. Taking into account peculiarities of the material and the analytical approach to its study, the methods of theoretical research have been chosen(abstraction, analysis and synthesis, induction and deduction, mental modeling, ascension from abstract to concrete, etc.). Conclusions. As a result of a study the symphony analysis in a context of new authentic statements about M.Berezovsky’s life-creativity. It was stated that this artwork was written not accidentally and detects absolute awareness of the artist in all composer’s niceties – how to build a topic and build a homophonic construction based on it, in a technique of orchestral construction, form creations of that time and etc. From the beginning of his creative career, M. Berezovsky was well aware of the possibilities of the orchestra as a performer, attached to the Italian opera and instrumental music. Symphony enriches our imagination about the works of M. Berezovsky in the field of secular instrumental and operatic music and extends the range of works of the artist beyond the spiritual direction. Some signs indicate that the Symphony was not an independent work, but an overture to the opera Demofont.

Improved five-factor Altman evaluation model credit about the enterprise with economic indicators as fuzzy numbers

2020 ◽  
Vol 7 (1) ◽  
pp. 72-83
Author(s):  
Alevtina Yu. Shatalova ◽  
◽  
Igor V. Shevchenko ◽  
Boureima Bamadio ◽  
Konstantin A. Lebedev ◽  
...  
Keyword(s):  
Fuzzy Numbers ◽  
Evaluation Model ◽  
Economic Indicators
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