Fuzzy Time Series Model Based on Intuitionistic Fuzzy Sets for Empirical Research in Stock Market

Intuitionistic fuzzy sets introduced by Atanassov are generalization of fuzzy sets as they also handle the nondeterminacy which is caused by degree of hesitation of decision maker. The present study proposes a computational method of forecasting for fuzzy time series. In the proposed method the notion of intuitionistic fuzzy set is used in fuzzy time series forecasting with simplified computational approach. The developed model has been tested on the movement of share market prices of State Bank of India (SBI) at Bombay Stock Exchange (BSE), India. Further the method has been implemented for forecasting SENSEX of BSE. The suitability of the developed model has also been examined by comparing it with the other existing models to show its superiority. DOI: 10.4018/jaec.2012100105 72 International Journal of Applied Evolutionary Computation, 3(4), 71-84, October-December 2012 Copyright © 2012, IGI Global. Copying or distributing in print or electronic forms without written permission of IGI Global is prohibited. improve the forecast of enrolments and also implemented it for Taiwan Futures Exchange (TAIFEX) forecasting. In most of the real life problems, information about an object provided by fuzzy concept may be incomplete. In that case sum of membership grade and non-membership grade of an object in universe corresponding to fuzzy concept is less than one because of the degree of hesitation of decision maker. Atanassov (1986) extended the concept of fuzzy sets and introduced the intuitionistic fuzzy sets (IFS). A prominent characteristic of IFS is that it assigns each element to a membership degree and a non-membership degree. So it gives us a powerful tool to deal with uncertainty and vagueness in real applications. As a generalization of the fuzzy sets, the intuitionistic fuzzy set has received more and more attention since its appearance. In 1993, Gau and Buehrer (1993) presented the concept of vague set. However, Bustince and Burillo (1996) pointed out those vague sets are intuitionistic fuzzy sets. In this paper, we propose computational model of forecasting for fuzzy time series based on IFS. In proposed method degree of non-determinacy is used to establish fuzzy logical relations. The time series data are fuzzified on the basis of degree of non-determinacy in IFSs. The proposed model is implemented on two empirical databases, share price of State Bank of India (SBI) for the year 2009-10 and sensitive index (SENSEX) of Bombay Stock Exchange (BSE). Rest of the paper is organized as follows. In Section 2, we briefly review the definition of fuzzy time series and IFS. In Section 3, construction method of IFS is presented. In Section 4, we present the proposed algorithm for fuzzy time series forecasting. In order to verify the effectiveness of the proposed method, it is implemented in forecasting market prices of SBI share and sensitive index (SENSEX) of BSE in Section 5. Finally in Section 6, the conclusions are presented. 2. BRIEF IDEAS ABOUT FUZZY TIME SERIES AND IFS The various definitions and properties of fuzzy time series forecasting found, summarized and are presented as: Definition 1: A fuzzy set is a class of objects with a continuum of grade of membership. Let U be the Universe of discourse with U = {u1, u2, u3, . . ., un,}, where ui are possible linguistic values of U, then a fuzzy set of linguistic variables Ai of U is defined by: