Ostrich farming has been started in Iran since the last decade through imports of ostrich chicks from south Africa and Italy. Fuzzy logic issued in many disciplines of science by different methods but little attention has been paid to the use of this methodology in economics. Hashemi et al. (2012) compared and ranked several economic projects using fuzzy approach and chose the most economical project based on fuzzy outputs. In their study, they proposed a good approach dealing with cash flows using triangular fuzzy numbers, which were applied in the economic analysis of projects. For the first time, Ghasemi and Mahmoudzadeh (2010) provided a fuzzy model to evaluate the economic projects under condition that could be as the unique method in terms of generalization and application compared to conventional procedures. Pochampally et al. (2003) proposed a fuzzy cost-benefit function based on multi-criteria economic analysis to select the most economical products and to process in a closed-loop supply chain. Buckley (1987); Ward (1985); Chiu and Park (1994); Wang and Liang (1995); Kahraman et al. (1995); Kahraman et al. (2000) and Anagnostopoulos and Petalas (2011) are among the authors who deal with the fuzzy present worth analysis, the fuzzy benefit/cost ratio analysis, the fuzzy future value analysis, the fuzzy payback period analysis, and the fuzzy capitalized value analysis. Ostrich production is involved different phases from hatchlings to mature breeders, however, in the present study; we are going to economic evaluation of growing phase of three-month old chicks to slaughter using fuzzy approach.
MATERIALS AND METHODS
Expressions like “not very clear”, “probably so” and “very likely” can be heard very often in daily conversations. The commonality in such terms is that they are all tainted with imprecision. This imprecision or vagueness of human decision-making is called “fuzziness” in the literature. With different decision-making problems of diverse intensity, the results can be misleading if fuzziness is not taken into account. However, since Zadeh (1965) first proposed fuzzy set theory, an increasing number of studies have dealt with imprecision (fuzziness) in problems by applying the fuzzy set theory. Fuzzy set theory presents an alternative to having to use exact numbers or to have a probability distribution of the cash flow. Using the basic concepts of fuzzy logic and also due to its specific mathematics, analysis of engineering economic models can be extended. Therefore, these models are more consistent with the real world. Some of common discounted criteria which were used to assess agricultural projects and also are applied in this study are net present value and benefit-cost ratio (Ghasemi and Mahmoudzadeh, 2010).
Net present value
One of the main indices of project assessment is the method of net present value. This index is calculated based on differential net profit or differential cash flow. Net present value can be defined as the present value of the income generated by the capital. Net present value formula for evaluation of economical projects is as follows:
R: represents the income.
r: interest rate.
i: (1, 2, 3, …).
In the new method, the value of variables cannot be identified exactly; therefore, these variables are represented by asymmetrical triangular fuzzy number using fuzzy mathematics as follows (Ghasemi and Mahmoudzadeh, 2010):
RiFUZZY= (Ri, αi, βi)
rFUZZY= (r, α′, β′) (2)
CiFUZZY= (Ci, αi″, βj″)
In the fuzzy number XFUZZY= (X, α, β).
Fuzzy: shows the fuzziness of number.
X: center of fuzzy number that occurs with most probability.
α, β: respectively left and right side.
Hence, net present value, by using the fuzzy number, can be defined as follows (Ghasemi and Mahmoudzadeh, 2010):
Equation below was calculated for comparing fuzzy value XFUZZY= (X, α, β) with zero.
S= (-α+2X+β) / 4 (5)
If the equation is positive, then it can be said that the obtained value is larger than zero and project will be economically justified.
Benefit-cost analysis is an economic tool to aid social decision-making, and is typically used by governments to evaluate the desirability of a given intervention in markets. The deterministic B/C ratio can be defined as the ratio of the equivalent value of benefits to the equivalent value of costs. The equivalent values can correspond to present, annual or future values. The purpose of benefit cost analysis is to give management a reasonable picture of the costs, benefits and risks associated with a given project so that it can be compared to other investment opportunities (Davis 1999). By use of fuzzy logic, benefit- cost ratio estimated as follows (Ghasemi and Mahmoudzadeh, 2010):
Now the question is; whether the obtained value is considered larger than one or not. If it is larger than one, the project is economically justified and otherwise it does not have economic justification. For comparing fuzzy value XFUZZY= (X, α, β) with one, the following equation is being estimated.
S= (-α+2X+β) / 4 (8)
If the mentioned equation is positive, therefore obtained value is larger than one and the project is economically justified.
RESULTS AND DISCUSSION
In this study, the fattened ostrich breeding project was economically assessed for 5 units including a one bird, 30 birds, 50 birds, 100 birds and 200 birds. Information was collected by conducting field visit to estimate the costs of production and revenue. Also different manufacturers in Sistan region and experts in the industry were interviewed and the required costs and revenue for each ostrich production unit was calculated using the existing reports. For ease of calculation, the total costs and revenues are expressed in Table 1. To evaluate a project under uncertainty conditions using fuzzy logic, it is necessary to show all the numbers in fuzzy state to insert uncertainty into the model. To determine fuzzy values of each parameter, three values including optimistic, pessimistic, and the most likely value were extracted by referring to investors and experts. For this purpose, all costs in C were considered as (30%, C, 30%). This means that 30 percent of change (variation) is possible for costs. Also revenues are considered as (20%, R, 20%). Interest rate is also considered as (2%, 22%, 2%) that shows the possibility of change in the interest rate from 20 to 24 percent with the centrality of 22 percent. The Table 2 shows the costs and revenues and the range of left and right change for the calculation of the present value. The Table 3 shows the amounts of present value of project with its intervals.
S= (-12750349 + 2 × 39231843 + 16786090) / 4= 82499427
The result shows that obtained value is positive therefore the project would be economically justified if costs and incomes changed. The results of benefit- cost method in fuzzy state are as follows in Table 4. Benefit to cost ratio in the proposed fuzzy method is approximately obtained as (1.27 and 1.48, and 0.80). The results of ranking criterion show if costs and revenues changed in the benefit- cost method, the project would be economically justified. For other units, the same methods are utilized; that for simplicity and conciseness only the final results are listed. The results of using present value and benefit- cost method in fuzzy state for all units show that ranking criterion is positive for all units. The final ranking of the projects is obtained by calculating the crisp value through equation (4) and equation (8).
Table 1 Cost and revenue of breeding ostrich
Table 2 Analysis of fuzzy present value for 1 bird
Table 3 Result analysis of fuzzy present value for 1 bird
Table 4 Fuzzy benefit- cost method for 1 bird
Table 5 Results of benefit cost method for 1 bird unit
Table 6 Results of present value method for 30, 50, 100 and 200 birds units
Table 7 Results of benefit cost method for 30, 50, 100 and 200 birds units
Since the obtained values in Tables 6 and 7 are positive then the projects are economically justified and the mentioned projects by assuming change in costs and revenues are economically justified (Ghasemi and Mahmoudzadeh, 2010).
According to the results obtained from Present Value and Benefit-Cost in fuzzy state, all the suggested units in the study are economically justified. Therefore, construction of fattened ostrich production, from one bird to 200 birds units, is justified in the region of Sistan. If the number of existing components in each unit is larger, the justifiability of the project would be better. However, due to the high degree of uncertainty in the current economic environment, there are several shortcomings in this approach. Thus, an alternative application is proposed that models the uncertainty of critical variables with the aid of fuzzy set theory. Maravas and et al. (2012) used cost benefit analysis with the aid of fuzzy set theory and showed that fuzzy cost benefit analysis is a promising tool for modeling uncertainty. Anagnostopoulos and Petalas (2011) demonstrated that the fuzzy method allows the comparison of different alternatives according to many criteria, in order to guide the decision maker towards a judicious choice. Due to its suitable climatic conditions and climate variability, Sistan has a high potential in breeding various birds, animals, and especially ostrich. Therefore, ostrich breeding is recommended because of their high resistance to diseases, environmental compatibility and not dependent to energy. Ostrich farming brings high economic potential in its products and there is not any dependence on foreign countries in this industry. Therefore, it can be proposed to construct fattened ostrich farms in Sistan as a profitable activity for farmers in the region.