scholarly journals Novel Construction of Copulas Based on ( α , β ) Transformation for Fuzzy Random Variables

2021 ◽  
Vol 2021 ◽  
pp. 1-15
Author(s):  
Stylianos Giakoumakis ◽  
Basil Papadopoulos
Keyword(s):  
Infinite Number ◽  
Random Variables ◽  
Construction Method ◽  
Fuzzy Random Variables ◽  
Unit Square ◽  
Construction Procedure ◽  
Fuzzy Random

The paper introduces a method for the construction of bivariate copulas with the usage of specific values of the parameters α  and  β ( α , β transformation) and the parameters κ  and  λ in their domain. The produced bivariate copulas are defined in four subrectangles of the unit square. The bounds of the produced copulas are investigated, while a novel construction method for fuzzy copulas is introduced, with the usage of the produced copulas via α , β transformation in four subrectangles of the unit square. Following this construction procedure, the production of an infinite number of copulas and fuzzy copulas could be possibly achieved. Some applications of the proposed methods are presented.

scholarly journals Several Limit Theorems on Fuzzy Quantum Space

Mathematics ◽  
2021 ◽  
Vol 9 (4) ◽  
pp. 438
Author(s):  
Viliam Ďuriš ◽  
Renáta Bartková ◽  
Anna Tirpáková
Keyword(s):  
Financial Markets ◽  
Incomplete Data ◽  
Extreme Values ◽  
Random Variables ◽  
Consumer Electronics ◽  
Financial Risks ◽  
Quantum Space ◽  
Fuzzy Random Variables ◽  
Scientific Disciplines ◽  
Fuzzy Random

The probability theory using fuzzy random variables has applications in several scientific disciplines. These are mainly technical in scope, such as in the automotive industry and in consumer electronics, for example, in washing machines, televisions, and microwaves. The theory is gradually entering the domain of finance where people work with incomplete data. We often find that events in the financial markets cannot be described precisely, and this is where we can use fuzzy random variables. By proving the validity of the theorem on extreme values of fuzzy quantum space in our article, we see possible applications for estimating financial risks with incomplete data.

scholarly journals Fuzzy random variables

1986 ◽  
Vol 114 (2) ◽  
pp. 409-422 ◽  
Author(s):  
Madan L Puri ◽  
Dan A Ralescu
Keyword(s):  
Random Variables ◽  
Fuzzy Random Variables ◽  
Fuzzy Random

scholarly journals On Distribution Characteristics of a Fuzzy Random Variable

2018 ◽  
Vol 47 (2) ◽  
pp. 53-67 ◽  
Author(s):  
Jalal Chachi
Keyword(s):  
Probability Theory ◽  
Distribution Function ◽  
Cumulative Distribution Function ◽  
Random Variables ◽  
Fuzzy Random Variable ◽  
Random Variable ◽  
Cumulative Distribution ◽  
Distribution Characteristics ◽  
Fuzzy Random Variables ◽  
Fuzzy Random

In this paper, rst a new notion of fuzzy random variables is introduced. Then, usingclassical techniques in Probability Theory, some aspects and results associated to a randomvariable (including expectation, variance, covariance, correlation coecient, etc.) will beextended to this new environment. Furthermore, within this framework, we can use thetools of general Probability Theory to dene fuzzy cumulative distribution function of afuzzy random variable.

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