IJE TRANSACTIONS B: Applications Vol. 28, No. 2 (February 2015) 214-223   

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H. Gitinavard, S. M. Mousavi and B. Vahdani
( Received: June 24, 2014 – Accepted: November 13, 2014 )

Abstract    The purpose of this paper is to extend a new balancing and ranking method to handle uncertainty for a multiple attribute analysis under a hesitant fuzzy environment. The presented hesitant fuzzy balancing and ranking (HF-BR) method does not require attributes’ weights through the process of multiple attribute decision making (MADM) under hesitant conditions. For the rating of possible alternatives, firstly, they are defined as hesitant fuzzy terms and then converted into hesitant fuzzy sets. Second, an outranking matrix indicates that a possible alternative overcomes the other alternatives regarding to each chosen attribute. Third, the outranking matrix is triangularized; this means that we prepare provisional order of possible alternatives or implicit preordering under hesitant conditions. Eventually, the empirical order of alternatives goes through variant operations of balancing and screening that needs continuous application of a balancing axiom to the advantages–disadvantages table. It links incompatible attributes with pair-wise comparisons of the possible alternatives for the multiple attribute analysis. Finally, we present an application example for the supplier selection to show the applicability and feasibility of the proposed HF-BR method in the hesitant fuzzy setting.


Keywords    Ranking and Balancing Method, Multiple Attribute Decision Making, Advantage and Disadvantage Matrix, Outranking Matrix, Hesitant Fuzzy Set.


چکیده    هدف از این مقاله، توسعه­ی یک روش جدید متعادل­سازی و رتبه بندی برای تجزیه و تحلیل چند معیاره در محیط فازی تردیدی است. روش ارائه شده نیازمند وزن معیارها در فرآیند تصمیم­گیری چند معیاره در محیط تردیدی نیست. برای ارزیابی گزینه های ممکن، ابتدا آنها با متغیرهای زبانی تعریف می شوند و سپس به مجموعه­ی فازی تردیدی تبدیل می­شوند. همچنین با تشکیل ماتریس برتری نشان داده می شود که کدام گزینه بر دیگر گزینه ها با توجه به معیارها برتری دارد. سپس ماتریس برتری مثلثی می­شود؛ این بدان معناست که گزینه های ممکن به طور موقت مرتب شده و یا به عبارت دیگر به طور تلویحی در شرایط تردیدی از قبل مرتب­سازی می گردند. در نهایت، این رتبه بندی تجربی گزینه ها باید در عملیات­های متفاوت متعادل­سازی و غربال­گری روش مذکور قرار گیرد که از اینرو نیازمند یک برنامه­ی مستمر از اصل متعادل­سازی بنام جدول مزایا-معایب است. این جدول، با مقایسه ی دو­به­دو گزینه­های ممکن با توجه به معیارها، میزان برتری آنها را می­سنجد. در آخر با استفاده از یک مطالعه­ی کاربردی در زمینه­ی انتخاب تامین کنندگان، کاربردپذیری و امکانپذیر بودن روش در شرایط فازی تردیدی نشان داده می شود.


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