بررسي روش تحليل فراخ و ارايه‌ي روشي جديد براي به دست آوردن بردار وزن قطعي از ماتريس‌هاي مقايسات زوجي فازي

Evaluating the Extent Analysis Method and Proposing a New Method to Derive a Crisp Priority Vector from Fuzzy Comparison Matrices

چالش اصلي در حل مسايل فرايند تحليل سلسله‌مراتبي فازي، محاسبات فازي و رتبه‌بندي اعداد فازي با استفاده از روش‌هاي مختلفي است كه براي اين كار وجود دارد. از آنجا كه در روش تحليل فراخ وزن‌هاي دقيق عناصر استخراج مي‌شود، نياز به محاسبات اضافي فازي و رتبه‌بندي اعداد فازي از بين مي‌رود. اين روش تاكنون در تحقيقات بسيار زيادي كاربرد داشته است اما در نوشتار حاضر نشان داده مي‌شود كه وزن‌هاي اين روش صحيح نيست. به‌منظور رفع نقص روش تحليل فراخ، در اين نوشتار يك روش جديد مبتني بر الگوريتم‌هاي فراابتكاري براي استخراج وزن‌هاي دقيق از ماتريس‌هاي مقايسات زوجي فازي معرفي مي‌شود. همچنين براي نشان‌دادن اعتبار روش پيشنهادي، اين روش با چهار روش موجود در ادبيات موضوع مقايسه شده كه نتايج حاصله نشان‌دهنده‌ي اعتبار بالاي روش پيشنهادي است.

Different methods are provided to deal with imprecise judgments of decision makers for the analytical hierarchy process. Most previous methods, which allow consideration of imprecise judgments as fuzzy numbers, provide the local and global weights of elements as fuzzy numbers too. Local and global fuzzy numbers need additional aggregation, computation and ranking procedures. The global weights may overlap each other and make the ranking of alternatives difficult. As a result, since there are different methods of fuzzy computation and fuzzy ranking, in some problems, we cannot have a unique ranking of fuzzy numbers. In order to overcome this deficiency, one method for solving fuzzy analytical hierarchy process problems and obtaining the crisp priority vector is called extent analysis. As mentioned, the main challenges of solving such problems are the fuzzy computations and ranking of fuzzy numbers, because different computation and ranking of fuzzy numbers may result in the different ranking of alternatives. Since the extent analysis method derives the crisp priority vector from fuzzy comparison matrices, it eliminates the need for additional computation and ranking of fuzzy numbers. This method is used in much research, but, in this paper, it is indicated that the priority vector of this method is not appropriate. To overcome this defect, in this paper, a new meta-heuristic based algorithm is proposed to derive the crisp priority vector from fuzzy comparison matrices. Furthermore, in order to illustrate the proposed method of this paper, it is compared with four methods available in the literature. The computational results indicate that the proposed method is appropriate for deriving the crisp priority vector from fuzzy comparison matrices.