Markov analysis of the fuzzy states and its economic applications

Mathematical modeling of a dynamic system in environments characterized by uncertainty, analyzing the possible situations that could occur in the future, determining a strategy and making good decisions in a timely manner is a very challenging and risky process. Markov analysis is a very important model widely used in the modeling of dynamic systems, but is based on exact situations. Fuzzy set theory, which allows the mathematical expression of uncertainty based on fuzzy logic was originally defined by Zadeh in 1965 and has recently contributed significantly to the science of decision-making. Financial investment instruments are instruments that carry high-risk when traded on the stock exchange, which is a dynamic system of uncertainty. In this study, the fuzzy states of the Markov chain analysis method has been applied for analyzing and estimating the future of valuable commodity instruments such as the American Dollar Index, Euro Index, Japanese Yen / Dollar Parity and gold price by using their monthly data. To achieve this, a sufficiently long period was determined and historical data of the proposed investment instruments were used. The monthly change rates in the data obtained were divided into fuzzy situations and fuzzy classification was made. Then, the probability transition matrices of fuzzy states was obtained. Finally, using the randomly determined data and probability transition matrix as in the classical Markov process, the situation that will occur in the next step has been estimated and the reliability of the model has been tested by comparing the results with the actual situation. Furthermore, the stable status of the probability transition matrix of the financial instruments has been obtained and examined. The relation of these investment instruments has also been analyzed. The results of the classical Markov chain and the fuzzy states of the Markov chain have been obtained and evaluated in order to obtain the best strategy of the applications and the differences and similarities of these two models have been discussed. Keywords:Fuzzy logic, Markov analysis, Markov chains of the fuzzy states, economic index estimation