Conditional Intuitionistic Fuzzy Mean Value

• Main Author: Katarína Čunderlíková
• Format: Article
• Language: English
• Published: MDPI AG 2021-05-01
• Series: Axioms
• Subjects: intuitionistic fuzzy event; intuitionistic fuzzy observable; intuitionistic fuzzy state; product; conditional intuitionistic fuzzy probability; conditional intuitionistic fuzzy mean value
• Online Access: https://www.mdpi.com/2075-1680/10/2/97

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.