ON INEQUALITIES AND CRITICAL VALUES OF FUZZY RANDOM VARIABLES

2005 ◽  
Vol 13 (02) ◽  
pp. 163-175 ◽  
Author(s):  
LIXING YANG ◽  
BAODING LIU
Keyword(s):  
Probability Theory ◽  
Intelligent Systems ◽  
Random Sequence ◽  
Random Variables ◽  
Critical Values ◽  
Fuzzy Random Variables ◽  
Chance Measure ◽  
Mathematical Properties ◽  
Expected Value Operator ◽  
Fuzzy Random

It is well-known that Hölder, Minkowski, Markov, Chebyshev and Jensen's inequalities are important and useful results in probability theory. This paper proposes to extend the usefulness of the above inequalities to the context of uncertainty analysis in intelligent systems. In order to further discuss the mathematical properties of fuzzy random variables, the analogous inequalities for fuzzy random variables are first proved based on the chance measure and expected value operator. After that, monotonicity and continuity of critical values of fuzzy random variables are also investigated. Finally, a convergence theorem of critical values for fuzzy random sequence is obtained.

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.

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
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