A model for the "Fuzzy TOPSIS" based on Zadde's extension principle

Document Type: research paper

Author

Department of Mathematics, Qom Branch, Islamic Azad University, Qom, Iran

Abstract

The TOPSIS process is one of the most comprehensive systems designed for decision making with multiple criteria, since this technique enables formulation of the problem as decision matrix, as well as the possibility of considering different quantitative and qualitative criteria in the problem. Fuzzy TOPSIS methods have been introduced to make fundamental decisions that make decisions decisions in these ways, including the lack of precision in fuzzy calculations, which can be attributed to the lack of use of the principle of "Zadeh” in the definition of operators. For example, the multiplication of two triangular fuzzy numbers will not necessarily be triangular fuzzy. However, in most of the fuzzy TOPSIS methods, this is assumed. In this paper, we attempt to first define the ideal vector of false algebra, then two functions are designed for this purpose, then the optimal of these functions can be found using GA. All steps are based on the principle of "Zadeh”".

Keywords


Article Title [Persian]

ارایه روشی برایTOPSIS فازی با اعمال اصل گسترش"زاده

Author [Persian]

  • رضا کارگر
گروه ریاضی، دانشکده علوم پایه، دانشگاه آزاد اسلامی، واحد قم، قم، ایران
Abstract [Persian]

فرایند TOPSISیکی از جامع ترین سیستم های طراحی شده برای تصمیم گیری با معیارهای چندگانه است زیرا این تکنیک امکان فرموله کردن مساله را به صورت ماتریس تصمیم فراهم میکند و همچنین امکان در نظر گرفتن معیار های مختلف کمی و کیفی را در مساله دارد. به روش‌های TOPSIS فازی موجود ایرادات اساسی وارد است که باعث میشود مفاهیم تصمیم در این روشهاکمرنگ شوند از جمله این اشکالات می توان به عدم دقت لازم در محاسبات فازی اشاره داشت و علت آن عدم استفاده از اصل گسترش "زاده " در تعریف اپراتورها ست.به عنوان مثال ضرب دو عدد فازی مثلثی الزاما فازی مثلثی نخواهد بود.لکن در عمده روشهای TOPSISفازی اینگونه فرض شده است . در این مقاله تلاش می شود ابتدا تعریف بردار ایده آل وضدایده آل فازی بیان گردد سپس برای تحقق این منظور دو تابع طراحی میشود سپس بهینه این توابع به کمک GA یافت می گردد. همه مراحل بر اساس اصل زاده است.

Keywords [Persian]

  • اصل گسترش "زاده"
  • تاپسیس
  • فازی
  • ماکسیمال
  • ایده ال

 

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]17[ رساله دکتری رضا کارگر استاد راهنما فرهاد حسین­زاده و... دانشگاه آزاد اسلامی واحد علوم تحقیقات دانشکده علوم پایه زمستان 92.

 

]18[ محمد جواد اصغر پور، تصمیم­گیری­های چند معیاره انتشارات دانشگاه تهران چاپ ششم 1387.