Fuzzy Markov Decision-Making Model for Interference Effects

Abstract

The law of total probability plays an essential role in Bayesian reasoning, which has been used in many fields. However, some experiments show the law of total probability can be violated. In recent years, researchers have tried to explain this paradox with the interference effect in quantum theory, and they think the main reason for interference effects is the uncertain information in the decision-making process. Therefore, how to effectively model and process the uncertain information in the decision-making process is very important to understand and predict the interference effects. Zadeh proposed the fuzzy set by considering the fuzziness of information. Later, Atanassov proposed the intuitionistic fuzzy sets (IFS). IFS better describes the fuzzy information from the view of membership, nonmembership than fuzzy sets, which can also more flexibly simulate human decision making. Hence, the article proposed the fuzzy Markov decision-making model (FDM) under the framework of IFS to explain and predict the interference effects of decision-making process. In FDM, intuitionistic fuzzy number can be generated by using the negation operation of probability. In addition, the transition matrix can be obtained by using the Kolmogorov equation, which can consider the evolution time in the decision-making process. The transition matrix establishes the relationship between different stages to get the fuzzy numbers of final states. Finally, the article used the Dempster–Shafer evidence theory to transform fuzzy number into the probability. In summary, the proposed FDM can provide a novel idea to explore and explain the interference effects in the decision-making process, which is helpful to promote the development of artificial intelligence.