A MATHEMATICAL MODEL OF PROFIT-LOSS SHARING SCHEME OF SMALL INVESTMENT FOR TRADITIONAL MARKET TRADERS USING THE SEMI-FUZZY LOGIC APPROACH

Abstract

A mathematical model of micro-finance investment using profit-loss sharing scheme are made and implemented to simulated data. Here profits from the venture will be shared in a portion between the investor and the entity running the business. The scheme can be classified as Musharaka type of investment in Sharia economy. The proposed model is theoretically implemented with data from small-scale traders at a local traditional market who have small turnover. They are common target of usurers who lend money with high interest rate and penalties. If the traders are in unfortunate conditions, they are potentially in poorer condition than before committing themselves to the usurer. In the conventional practices of the profit sharing scheme, the investor will get a fixed portion of the trader’s income, which is applied for all kind of small-scale traders. If the traders are diligent and hard worker and have very high turnover, then the investor will gain much more profit whether the contributed capital is small or large. In this paper, the scheme is implemented using Semi-Fuzzy Logic Approach so that the profit-loss sharing scheme can achieve its intended goal, which is to make a profitable investment not only for the investor but also for traders. The approach is not fully using Fuzzy Logic because some variables are still in crisp numbers and the optimization problem is regular in the form of crisp numbers. Based on the existing data, the results show that the optimal profit share is depended on the income of the traders. The higher the income coming from the venture, the lesser the profit share for the investor which is reasonable with the fixed initial contributed capital.