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.

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 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 A note on mean value and dispersion of intuitionistic fuzzy events

2020 ◽  
Vol 26 (4) ◽  
pp. 1-8
Author(s):  
Katarína Čunderlíková ◽  
Keyword(s):  
Mean Value ◽  
Fuzzy Probability ◽  
Mean Values ◽  
Intuitionistic Fuzzy ◽  
Fuzzy State

In this paper, we compare two definitions of mean value and dispersion for intuitionistic fuzzy events. We show the connection between these two definitions and we introduce some types of mean values induced by intuitionistic fuzzy state and by intuitionistic fuzzy probability.

A Class of New Interval-Valued Intuitionistic Fuzzy Distance Measures and their Applications in Discriminant Analysis

2012 ◽  
Vol 182-183 ◽  
pp. 1743-1745 ◽  
Author(s):  
Hua Zhao ◽  
Ming Fang Ni ◽  
Hai Feng Liu
Keyword(s):  
Discriminant Analysis ◽  
Fuzzy Sets ◽  
Intuitionistic Fuzzy Sets ◽  
Distance Measures ◽  
Fuzzy Information ◽  
Fuzzy Distance ◽  
Intuitionistic Fuzzy ◽  
Special Cases ◽  
Interval Valued

In this paper we develop a class of new distance measures for interval-valued intuitionistic fuzzy sets. Then we discuss some of the special cases of it by taking different parameters. Finally we apply them for discriminant analysis with interval-valued intuitionistic fuzzy information.

On D-posets of fuzzy sets

2014 ◽  
Vol 64 (3) ◽  
Author(s):  
Roman Frič
Keyword(s):  
Probability Theory ◽  
Fuzzy Sets ◽  
Mathematical Structure ◽  
Fuzzy Probability ◽  
Classical Probability ◽  
Classical Probability Theory ◽  
Epireflective Subcategory ◽  
Generalized Probability ◽  
Fuzzy Probability Theory

AbstractD-posets of fuzzy sets constitute a natural simple mathematical structure in which relevant notions of generalized probability theory can be formalized. We present a classification of D-posets leading to a hierarchy of distinguished subcategories of D-posets related to probability and study their relationships. This contributes to a better understanding of the transition from classical probability theory to fuzzy probability theory. In particular, we describe the transition from the Boolean cogenerator {0, 1} to the fuzzy cogenerator [0, 1] and prove that the generated Łukasiewicz tribes form an epireflective subcategory of the bold algebras.

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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