مدل تحلیل پوششی داده های ترکیبی برای حل مسائل تصمیم گیری با اعداد GTHF

محورهای موضوعی : آمار

طیبه رضائی تازیانی ¹ , مهناز برخورداری احمدی ² , محمد رضا بلوچ شهریاری ³

1 - گروه ریاضی، واحد کرمان، دانشگاه آزاد اسلامی، کرمان، ایران
2 - گروه ریاضی، واحد بندرعباس، دانشگاه آزاد اسلامی، بندرعباس، ایران
3 - گروه ریاضی، واحد کرمان، دانشگاه آزاد اسلامی، کرمان، ایران

تاریخ دریافت : 1399/07/25 تاریخ پذیرش : 1400/02/14 تاریخ انتشار : 1401/06/01

کلید واژه: generalized trapezoidal hesitant fuzzy numbers (GTHF), Ranking, Data Envelopment Analysis, hesitant fuzzy sets,

چکیده مقاله :

اصولا عدم قطعیت در ذات و نهاد طبیعت جای دارد. برای مواجهه با عدم قطعیت و ابهام موجود در جهان واقعی، منطق دو ارزشی به تدریج جای خود را به منطق فازی داده است. این دیدگاه جدید، عدم قطعیت ناشی از تردید را مدیریت می کند، و در این نوع تصمیم گیری یکی از مسائل مهم جمع آوری اطلاعات فازی مردد و انتخاب گزینه بهینه است. اعداد فازی مردد ذوزنقه ای تعمیم‌یافته (‏GTHF) که درجه عضویت آن‌ها توسط چندین عدد فازی ذوزنقه ای بیان می‌شود، برای حل مساله تصمیم‌گیری در زندگی واقعی نسبت به اعداد حقیقی مناسب تر است. در این مقاله، به مفهوم جدیدی به نام اعداد فازی مردد ذونقه ای تعمیم یافته و ترکیب آن با تحلیل پوششی داده ها می پردازیم. با استفاده از این اطلاعات مقادیر انحراف و امتیاز را به عنوان ورودی و خروجی مدل تحلیل پوششی داده های دو مرحله ای در نظر می گیریم، سپس از نتایج حاصل جهت ساخت ماتریس مقایسه زوجی استفاده کردیم و در نهایت واحد های تصمیم گیرنده را اولویت بندی نمودیم. برای استفاده از برخی از مفاهیم در روش تصمیم‌گیری پیشنهادی، ابتدا تعاریفی از مفاهیمی مانند تابع امتیاز و تابع انحراف از اعداد فازی مردد ذوزنقه‌ای تعمیم‌یافته را ارائه می‌دهیم. در نهایت، یک مثال عددی برای روش پیشنهادی جهت تایید و کاربردی بودن آن ارائه و نتیجه رتبه بندی را با روش های AP، TOPSIS با اعداد فازی مردد ذوزنقه ای تعمیم یافته و روش تجمع هندسی وزن دار در ]7[ مورد مقایسه قرار می‌دهیم.

چکیده انگلیسی:

To face uncertainty in the real world, the two value logic has gradually replaced the fuzzy logic. In some real world problems, accurate determination of membership value is difficult and decision- making is associated with uncertainty and hesitation. This new perspective manages the uncertainty caused by hesitation. Generalized trapezoidal hesitant fuzzy numbers (GTHFN), whose membership degree is expressed by several trapezoidal fuzzy number, is best suited to solve the decision-making problem in real life than real numbers. In this paper, we refer to a new concept called 'generalized trapezoidal hesitant fuzzy numbers' and its combination with data envelopment analysis. Using this information, we consider the deviation and the score values as input and output of the data envelopment analysis model in two stages respectively; then we used the result to construct a paired comparison matrix and eventually we prioritize the receivers decision making units. To use some concepts in the proposed decision making method, we first present some definitions of concepts such as the score and deviation functions from the generalized trapezoidal hesitant fuzzy numbers. Finally, a numerical example is presented for the proposed method to confirm its applicability, and the ranking result is compared with the methods of AP, TOPSIS with GTHF number and the weighted geometric operator in [7].

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