scholarly journals Martingale Convergence Theorem for the Conditional Intuitionistic Fuzzy Probability

Mathematics ◽  
2020 ◽  
Vol 8 (10) ◽  
pp. 1707
Author(s):  
Katarína Čunderlíková
Keyword(s):  
Fuzzy Sets ◽  
Conditional Probability ◽  
Convergence Theorem ◽  
Intuitionistic Fuzzy Sets ◽  
Fuzzy Probability ◽  
Martingale Convergence Theorem ◽  
Intuitionistic Fuzzy ◽  
Mv Algebra ◽  
Fuzzy State ◽  
Martingale Convergence

For the first time, the concept of conditional probability on intuitionistic fuzzy sets was introduced by K. Lendelová. She defined the conditional intuitionistic fuzzy probability using a separating intuitionistic fuzzy probability. Later in 2009, V. Valenčáková generalized this result and defined the conditional probability for the MV-algebra of inuitionistic fuzzy sets using the state and probability on this MV-algebra. She also proved the properties of conditional intuitionistic fuzzy probability on this MV-algebra. B. Riečan formulated the notion of conditional probability for intuitionistic fuzzy sets using an intuitionistic fuzzy state. We use this definition in our paper. Since the convergence theorems play an important role in classical theory of probability and statistics, we study the martingale convergence theorem for the conditional intuitionistic fuzzy probability. The aim of this contribution is to formulate a version of the martingale convergence theorem for a conditional intuitionistic fuzzy probability induced by an intuitionistic fuzzy state m. We work in the family of intuitionistic fuzzy sets introduced by K. T. Atanassov as an extension of fuzzy sets introduced by L. Zadeh. We proved the properties of the conditional intuitionistic fuzzy probability.

scholarly journals Conditional intuitionistic fuzzy probability and martingale convergence theorem using IF-probability

2020 ◽  
Vol 26 (3) ◽  
pp. 13-21
Author(s):  
Katarína Čunderlíková ◽  
Keyword(s):  
Convergence Theorem ◽  
Fuzzy Probability ◽  
Martingale Convergence Theorem ◽  
Intuitionistic Fuzzy ◽  
Martingale Convergence

The aim of this paper is to formulate the conditional intuitionistic fuzzy probability and a version of martingale convergence theorem with respect an intuitionistic fuzzy probability. Since the intuitionistic fuzzy probability can be decomposed to two intuitionistic fuzzy states, we can use the results holding for intuitionistic fuzzy states.

scholarly journals Martingale convergence theorem for a conditional intuitionistic fuzzy mean value

2021 ◽  
Vol 27 (2) ◽  
pp. 94-102
Author(s):  
Katarína Čunderlíková ◽  
Keyword(s):  
Convergence Theorem ◽  
Random Variables ◽  
Mean Value ◽  
Martingale Convergence Theorem ◽  
Conditional Mean ◽  
Intuitionistic Fuzzy ◽  
Fuzzy Mean ◽  
Martingale Convergence

The aim of this contribution is to show a representation of a conditional intuitionistic fuzzy mean value of intuitionistic fuzzy observables by a conditional mean value of random variables. We formulate a martingale convergence theorem for a conditional intuitionistic fuzzy mean value, too.

scholarly journals Conditional Intuitionistic Fuzzy Mean Value

Axioms ◽  
2021 ◽  
Vol 10 (2) ◽  
pp. 97
Author(s):  
Katarína Čunderlíková
Keyword(s):  
Fuzzy Sets ◽  
Mean Value ◽  
Financial Mathematics ◽  
Fuzzy Probability ◽  
Classical Probability ◽  
Conditional Mean ◽  
Intuitionistic Fuzzy ◽  
Special Cases ◽  
Fuzzy Mean ◽  
Fuzzy State

The conditional mean value has applications in regression analysis and in financial mathematics, because they are used in it. We can find papers from recent years that use the conditional mean value in fuzzy cases. As the intuitionstic fuzzy sets are an extension of fuzzy sets, we will try to define a conditional mean value for the intuitionistic fuzzy case. The conditional mean value in crisp intuitionistic fuzzy events was first studied by V. Valenčáková in 2009. She used Gödel connectives. Her approach can only be used for special cases of intuitionistic fuzzy events, therefore, we want to define a conditional mean value for all elements of a family of intuitionistic fuzzy events. In this paper, we define the conditional mean value for intuitionistic fuzzy events using Lukasiewicz connectives. We use a Kolmogorov approach and the notions from a classical probability theory for construction. B. Riečan formulated a conditional intuitionistic fuzzy probability for intuitionistic fuzzy events using an intuitionistic fuzzy state in 2012. In classical cases, there exists a connection between the conditional probability and the conditional mean value, therefore we show a connection between the conditional intuitionistic fuzzy probability induced by the intuitionistic fuzzy state and the conditional intuitionistic fuzzy mean value.

One Hundredth of Intuitionistic Fuzzy Sets

2019 ◽  
Vol 10 (3) ◽  
pp. 445-453
Author(s):  
R. Nagalingam ◽  
S. Rajaram
Keyword(s):  
Fuzzy Sets ◽  
Intuitionistic Fuzzy Sets ◽  
Intuitionistic Fuzzy

Probability Theory for Fuzzy Quantum Spaces with Statistical Applications

2017 ◽  
Author(s):  
Renáta Bartková ◽  
Beloslav Riečan ◽  
Anna Tirpáková
Keyword(s):  
Probability Theory ◽  
Fuzzy Sets ◽  
Ergodic Theorem ◽  
Intuitionistic Fuzzy Sets ◽  
Mathematics Students ◽  
Intuitionistic Fuzzy ◽  
Individual Ergodic Theorem ◽  
Recurrence Theorem ◽  
The Individual ◽  
Atanassov Intuitionistic Fuzzy Sets

The reference considers probability theory in two main domains: fuzzy set theory, and quantum models. Readers will learn about the Kolmogorov probability theory and its implications in these two areas. Other topics covered include intuitionistic fuzzy sets (IF-set) limit theorems, individual ergodic theorem and relevant statistical applications (examples from correlation theory and factor analysis in Atanassov intuitionistic fuzzy sets systems, the individual ergodic theorem and the Poincaré recurrence theorem). This book is a useful resource for mathematics students and researchers seeking information about fuzzy sets in quantum spaces.

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