Markov frameworks and stock market decision making
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METHODOLOGIES AND APPLICATION
Markov frameworks and stock market decision making Kavitha Koppula1 · Babushri Srinivas Kedukodi1 · Syam Prasad Kuncham1
© The Author(s) 2020
Abstract In this paper, we present applications of Markov rough approximation framework (MRAF). The concept of MRAF is defined based on rough sets and Markov chains. MRAF is used to obtain the probability distribution function of various reference points in a rough approximation framework. We consider a set to be approximated together with its dynamacity and the effect of dynamacity on rough approximations is stated with the help of Markov chains. An extension to Pawlak’s decision algorithm is presented, and it is used for predictions in a stock market environment. In addition, suitability of the algorithm is illustrated in a multi-criteria medical diagnosis problem. Finally, the definition of fuzzy tolerance relation is extended to higher dimensions using reference points and basic results are established. Keywords Rough set · Markov chain · Rough approximation framework
1 Introduction Pawlak (1982) introduced the notion of rough sets by defining the lower approximation of a set X as the collection of all the elements of the universe whose equivalence classes are contained in X , and the upper approximation of X as the set of all the elements of the universe whose equivalence classes have a non-empty intersection with X . We often consider the universe to be an algebraic structure and study the corresponding algebraic properties of rough approximations. The concept of rough approximation framework was defined by Ciucci (2008), basically as a collection of rough approximations of the set. A rough approximation framework is said to be regular if all the approximations of the set are inscribed in one another. An illustration of rough approximation framework was given by Kedukodi et al. (2010) using reference points. Communicated by V. Loia.
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Babushri Srinivas Kedukodi [email protected] Kavitha Koppula [email protected] Syam Prasad Kuncham [email protected]
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Department of Mathematics, Manipal Institute of Technology, Manipal Academy of Higher Education (MAHE), Manipal, Karnataka 576104, India
In Markov chains, the probabilities which finally decide the stability of a system are represented in terms of a matrix known as transition probability matrix. Markov chains have been used in several applications to predict the future possibilities in dynamic and uncertain systems. One such area that has been the focus of intense research is the prediction of the performance of stock markets. In a typical stock market environment, customer’s either SELL, BUY or HOLD a particular stock by assessing and predicting its performance utilizing previous and current performance of the stock, inputs from rating agencies, etc (Tavana et al. 2017). Such an assessment of past performance of the stock with the available empirical data of a stock and predicting the future performance or value of the stock is a challenging task due to
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