Research Article

The Integrated Fuzzy AHP and Goal Programing Model Based on LCA Results for Industrial Waste Management by Using the Nearest Weighted Approximation of FN: Aluminum Industry in Arak, Iran

Table 21

The comparison of various FAHP models [30, 31].

SourcesBasic specificationsPositives (P)/negatives (N)

[15]Direct extension of Saaty’s AHP model with triangular fuzzy numbers(P) The judgments of multiple experts may be modeled in the reciprocal matrix
Lootsma’s logarithmic least square model is used to derive fuzzy weights and fuzzy performance scores(N) Evermore there is no solution to the linear equations
(N) The calculational demand is great, even for a low problem
(N) It permits only triangular FN to be applied

[16] Direct extension of Saaty’s AHP model with trapezoidal fuzzy numbers(P) It is simple to extend to the fuzzy term
Uses the geometric mean model to derive fuzzy weights and performance scores(P) It guarantees an alone solution to the reciprocal comparison matrix
(N) The calculational demand is great

[33] Modifies van Laarhoven and Pedrycz’s model(P) The judgments of multiple experts may be modeled
Shows a more robust method to the normalization of the local priorities (N) The calculational demand is great

[32] Synthetical degree values(P) The calculational demand is partly low
Layer simple sequencing(P) It follows the steps of crisp AHP; it does not involve additional process
Composite total sequencing (N) It permits only triangular FN to be applied

[32] Creates fuzzy standards(P) The calculational demand is not great
Illustrates performance numerals by membership functions (N) Entropy is applied when probability distribution is known. The model is based on both probability and possibility measures
Uses entropy concepts to calculate aggregate weights

Proposed methodUses interval approximation to defuzzification(P) It permits all FN to be applied
(P) It retains uncertainty of fuzzy number in itself
Uses goal programming method to obtain weights(P) It is done, mainly, with a software such as Lingo