دانلود مقاله ISI انگلیسی شماره 25209
عنوان فارسی مقاله

# روش برنامه ریزی خطی برای MADM با مجموعه های فازی شهودی با ارزش بازه ای

کد مقاله سال انتشار مقاله انگلیسی ترجمه فارسی تعداد کلمات
25209 2010 7 صفحه PDF سفارش دهید 5330 کلمه
خرید مقاله
پس از پرداخت، فوراً می توانید مقاله را دانلود فرمایید.
عنوان انگلیسی
Linear programming method for MADM with interval-valued intuitionistic fuzzy sets
منبع

Publisher : Elsevier - Science Direct (الزویر - ساینس دایرکت)

Journal : Expert Systems with Applications, Volume 37, Issue 8, August 2010, Pages 5939–5945

کلمات کلیدی
تصمیم گیری ویژگی چند - مجموعه های فازی شهودی - فاصله ارزش مجموعه های فازی شهودی - برنامه ریزی ریاضی - تردید -
پیش نمایش مقاله

#### چکیده انگلیسی

Fuzziness is inherent in decision data and decision making process. In this paper, interval-valued intuitionistic fuzzy (IVIF) sets are used to capture fuzziness in multiattribute decision making (MADM) problems. The purpose of this paper is to develop a methodology for solving MADM problems with both ratings of alternatives on attributes and weights being expressed with IVIF sets. In this methodology, a weighted absolute distance between IF sets is defined using weights of IF sets. Based on the concept of the relative closeness coefficients, we construct a pair of nonlinear fractional programming models which can be transformed into two simpler auxiliary linear programming models being used to calculate the relative closeness coefficient intervals of alternatives to the IVIF positive ideal solution, which can be employed to generate ranking order of alternatives based on the concept of likelihood of interval numbers. The proposed method is illustrated with a real example.

#### مقدمه انگلیسی

The theory of the fuzzy set introduced by Zadeh (1965) has achieved a great success in various fields. Atanassov, 1986 and Atanassov, 1999 introduced the intuitionistic fuzzy (IF) set, which is a generalization of the fuzzy set. Gau and Buehrer (1993) introduced the concept of the vague set, which is another generalization of the fuzzy set. But, it was proven that the vague set is the same as the IF set (Burillo & Bustince, 1996). The IF set has received more and more attention and has been applied to many fields since its appearance. The theory of the IF set has been found to be more useful to deal with vagueness and uncertainty in decision situations than that of the fuzzy set (Atanassov et al., 2005, Deschrijver and Kerre, 2007, Szmidt and Kacprzyk, 1996a, Szmidt and Kacprzyk, 1996b, Szmidt and Kacprzyk, 1996c, Szmidt and Kacprzyk, 1997 and Szmidt and Kacprzyk, 2002). Over the last decades, the IF set theory has been successfully applied to solve decision making problems (Chen and Tan, 1994, Hong and Choi, 2000, Li, 2005, Li, 2008, Liu and Wang, 2007, Li and Wang, 2008, Li et al., 2009, Pankowska and Wygralak, 2006, Szmidt and Kacprzyk, 1996a, Szmidt and Kacprzyk, 1996b, Szmidt and Kacprzyk, 1996c, Szmidt and Kacprzyk, 1997, Szmidt and Kacprzyk, 2002, Xu, 2007a, Xu, 2007b, Xu, 2007c, Xu, 2007d and Xu and Yager, 2006). Atanassov and Gargov (1989) further generalized the IF set in the spirit of ordinary interval-valued fuzzy (IVF) sets and defined the notion of an interval-valued intuitionistic fuzzy (IVIF) set. The relations, operations and operators related to IF sets and IVIF sets have been systematically studied in (Deschrijver & Kerre, 2003). Recently, some researchers proposed several aggregation operators such as the IF weighted averaging operator, the IVIF weighted averaging operator, the IF ordered weighted averaging operator, the IVIF ordered weighted averaging operator and the IF ordered weighted geometric operator as well as the IVIF ordered weighted geometric operator, and employed them to deal with multiattribute decision making (MADM) with IF and IVIF information (Xu, 2007d, Xu, 2007e, Xu and Chen, 2007 and Xu and Yager, 2006). Ye (2009) introduced the IVIF weighted arithmetic average operator, the IVIF weighted geometric average operator and a novel accuracy function of IVIF values. However, there exist little investigation on MADM problems with both ratings of alternatives on attributes and weights being expressed with IVIF sets. In this paper, a weighted absolute distance between IF sets is defined using weights of IF sets. Then, based on the concept of the relative closeness coefficients, a pair of nonlinear fractional programming models is constructed to calculate the relative closeness coefficient intervals of alternatives with respect to the IVIF positive ideal solution (IVIFPIS), which can be used to generate ranking order of the alternatives. The nonlinear fractional programming models can be transformed into two auxiliary linear programming models, respectively. The paper is organized as follows. Section 2 briefly introduces the concept of the IF set and the IVIF set. A weighted absolute distance between IF sets and the definition of likelihood for comparison between two interval numbers are given. The MADM problem with IVIF sets is presented in Section 3. In Section 4, a pair of nonlinear fractional programming models is constructed based on the concept of the relative closeness coefficients and is transformed into two simpler auxiliary linear programming models to solve the MADM problems with IVIF sets. A real example and short remark are given in Sections 5 and 6, respectively.

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