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

1. Introduction

The growth in applications of fuzzy sets and fuzzy logic in modelling various real life problems lies in its power of dealing with imprecise knowledge (linguistic) variables in decision making. The knowledge of forecasting based on the available time series data, is one of the core components in planning and decision making. The concept of fuzzy set theory and fuzzy logic introduced by Zadeh (1965) provides a framework for handling uncertainty and vagueness in information available in linguistic terms. Fuzzy set theory and the concept of linguistic variables and its application to approximate reasoning developed by Zadeh (1975) has been successfully employed by Song and Chissom (1993, 1994) in fuzzy time series forecasting.

Chen (1996, 2002) presented a simplified method for time series forecasting using the arithmetic operations rather than complicated max-min composition operations, there are many researchers used the concept of fuzzy time series in forecasting. Huarng (2001) presented a heuristic model for time series forecasting using heuristic increasing and decreasing relations to 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, . . ., u_n,}, where u_i are possible linguistic values of U, then a fuzzy set of linguistic variables A_i of U is defined by: