Martingale Convergence Theorem for the Conditional Intuitionistic Fuzzy Probability

Katarína Čunderlíková
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Katarína Čunderlíková: Mathematical Institute, Slovak Academy of Sciences, Štefánikova 49, 814 73 Bratislava, Slovakia

Mathematics, 2020, vol. 8, issue 10, 1-10

Abstract: 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. Valen?áková 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. Rie?an 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.

Keywords: intuitionistic fuzzy event; intuitionistic fuzzy observable; intuitionistic fuzzy state; product; conditional intuitionistic fuzzy probability; martingale convergence theorem (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2020
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