Synchronization of Stochastic Modeling with Square Fuzzy Transition Probability Relational Matrix

Abstract

There are number of fields like agriculture, industry, insurance, tourism and others get affected directly or indirectly by a most common phenomenon known as the Rainfall. Till now we are not able to predict rainfall and it is one of the unsolved problems. This paper aims to synchronize stochastic modeling and square fuzzy transition probability relational matrix and it is obtained from the lexical terms along with the help of fuzzy value which in turn calculated form the lexical value. Fuzzy matrices are necessary in modeling uncertain situations in various fields. Here the lexical values are specially assigned heptagonal fuzzy numbers which in turn converted into fuzzy value to measure relation mappings. Along with this, synchronization is done for stochastic models with transition probability matrix and also with square fuzzy transition probability relation matrix to get a clear picture of the result. In this work, the changes in annual rainfall of Tamil Nadu depending on markov chain models are monitored. Statistical technique like Markov chain is applied at metrological stations in order to predict short term precipitation. The annual rainfall from 1901 to 2000 is derived and the frequency distribution table is formed. The class intervals are denoted as states and the transition probability matrix is formed due to the variations in annual rainfall. The uniform random states are formed by generating random number. The available stochastic climate models presently be adapted to form new climatic conditions if the forthcoming conditions is identified with necessary accuracy. Finally, prediction of rainfall based on two categories such as climatic factors and through states is analyzed in this study.