یک مدل رتبه بندی جدید برای مسائل تصمیم گیری گروهی چند شاخصه با داده های فازی شهودی
محورهای موضوعی : آمار
زینب اسلامی نسب
1
(گروه ریاضی کاربردی، دانشگاه آزاد اسلامی، واحد کرمان، کرمان، ایران)
علی حمزه ای
2
(گروه ریاضی کاربردی، دانشگاه آزاد اسلامی، واحد کرمان، کرمان، ایران)
کلید واژه: Weight of attributes, Ranking, Linear Programming, Fuzzy intuitionistic number,
چکیده مقاله :
در جهان امروز پیچیدگی ذاتی بسیاری از محیط های تصمیم گیری، ضرورت استفاده از روش های تصمیم گیری را بیش از پیش مشخص می کند. از طرفی سازمان های مدرن امروزی چنان وسیع و پیچیده شده اند که یک نفر از عهده مدیریت آنها بر نمی آید. لذا موضوع تصمیم گیری گروهی چند شاخصه به عنوان یک مسأله سازمانی مورد بررسی قرار می گیرد. در مدل های تصمیم گیری گروهی چند شاخصه با توجه به اینکه ماتریس تصمیم دارای شاخص های مختلفی می باشد، دانستن ضریب اهمیت یا وزن هر یک از شاخص ها در تصمیم گیری ضروری است. به طوریکه وزن هر شاخص اهمیت نسبی آن را نسبت به شاخص های دیگر بیان می کند و انتخاب آگاهانه و صحیح وزن ها کمک بزرگی در جهت رسیدن به هدف مورد نظر است. هدف از ارائه این مقاله، معرفی یک مدل برنامه ریزی خطی جهت تعیین وزن هر یک از شاخص ها در مسائل تصمیم گیری گروهی چند شاخصه با داده های فازی شهودی می باشد. لذا از خطای احتمالی تصمیم گیرندگان در تعیین وزن شاخص ها جلوگیری به عمل می آید در نهایت با استفاده از وزن های بدست آمده، یک روش جدید جهت رتبه بندی گزینه ها بر اساس روش تسلط تقریبی (الکتره3) معرفی شده است و یک مثال کاربردی عددی برای نشان دادن جزئیات روش پیشنهادی در نظر گرفته شده است.
In today’s world, intrinsic complexity in numerous decision making conditions, decides the need of utilizing decision making methods more than previously. On the other hand, the present modern organization have turned out to be so widespread, which one doesn’t capable to oversee them. In this manner, this issue of multi attribute group decision making is considered as an organizational problem. In multi attribute group decision making problems, according to the different attributes in decision matrix, knowing the coefficient of importance or weight of each attribute in decision making is essential. As the weight of each attribute express its relative importance to the others and the conscious and correct selection of weights is a great help in achieving the desired goal. The purpose of this paper is to introduce a linear programming model to determine the weight of each attribute in multi attribute group decision making problems with intuitionistic fuzzy data. As good as, decision makers are prevented from making eventual mistakes in determining the weight of attributes. Finally, using the obtained weights, a new method for ranking the alternatives based on ELECTRE III method, is presented. A numerical applied example is provided to illustrate the details of the proposed method.
[1] L. A. Zadeh, Fuzzy sets. Information and Control 8 (3) (1965) 338-353.
[2] S. H. Nasseri, A new approach to solve fully fuzzy linear programming with trapezoidal numbers using conversion functions. Journal of New Researches in Mathematics 1(3) (2015) 19-28.
[3] A. Khoshnava, M. R. Mozaffari, Fully fuzzy transporting problem. Journal of New Research in Mathematics 1(3) (2015) 41-54.
[4] A. Ebrahimnejad, S.H. Nasseri, A dual simplex method for bounded linear programmers with fuzzy numbers. International Journal of Mathematics in Operational Research 2 (6) (2010) 762-779.
[5] S.H. Nasseri, O. Gholami, M. Fallah Jelodard, A new approach based on alpha cuts for solving data envelopment analysis model with fuzzy stochastic inputs and outputs. Journal of New Research in Mathematics 2 (5) (2016) 61-70.
[6] H. Naseri, K. khazaei kohpar, A Parametric Approach to Solving the Fuzzy Multi-Objective Linear Fractional Programming Problem. Journal of New Research in Mathematics 4 (14) (2018) 87-102.
[7] A. Ebrahimnejad, A revisit of a mathematical model for solving fully fuzzy linear programming problem with trapezoidal fuzzy numbers. Journal of New Research in Mathematics 5 (18) (2019) 145-156.
[8] B. Vahdani, M. Salimi, T. Allahviranloo, A Compromise Decision-Making Model Based on TOPSIS and VIKOR for Multi-Objective Large- Scale Nonlinear Programming Problems with A Block Angular Structure under Fuzzy Environment. Journal of New Research in Mathematics 2 (6) (2016) 81-100.
[9] K. T. Atanassov, Intuitionistic fuzzy sets, Fuzzy Sets and Systems 20(1) (1986), 87-96.
[10] B. Roy, The outranking approach and the foundations of ELECTRE methods. Theory and Decision 31 (1991) 49-73.
[11] R. Roostaee, M. Izadikhah, F. H. Lotfi, M. Rostamy Malkhalifeh, A multi-criteria intuitionistic fuzzy group decision making method for supplier selection with VIKOR method. International Journal of Fuzzy System Applications 2 (1) (2012) 1-17.
[12] R. Duan, Q. Han, Z. Wang, Multi attribute group decision making models under intuitionistic fuzzy environment. Applied Mechanics and Materials 263 (2012) 3225-3229.
[13] Z. S. Xu, Multi-person multi-attribute decision making models under intuitionistic fuzzy environment. Fuzzy Optimization and Decision Making 6 (2007) 221-236.
[14] Z. S. Xu, A deviation-based approach to intuitionistic fuzzy multiple attribute group decision making. Group Decision and Negotiation 19 (2010) 57-76.
[15] S. M. Chen, J. M. Tan, Handling multi criteria fuzzy decision making problems based on vague set theory. Fuzzy Sets and Systems 67 (2) (1994)163-172.
[16] F. Shen, J. Xu, Z. Xu, An automatic ranking approach for multi-criteria group decision making under intuitionistic fuzzy environment. Fuzzy Optimization and Decision Making 14 (2015) 311-334.
[17] F. Shen, J. Xu, Z. Xu, An outranking sorting method for multi-criteria group decision making using intuitionistic fuzzy sets. Information Sciences 334 (2016) 338-353.
[18] Z. Wang, J. Xu, W. Wang, Intuitionistic fuzzy multiple attribute group decision making based on projection method, Control and Decision Conference, Chinese, 2009.
[19] Z. Yue, TOPSIS-based group decision making methodology in intuitionistic fuzzy setting. Information Sciences 227 (2014), 141-153.
[20] Z. Yue, Developing a straightforward approach for group decision making based on determining weights of decision makers. Applied Mathematical Modelling 36 (9) (2012), 4106-4117.
[21] F. Ghaemi-Nasab, M. Rostamy-Malkhalifeh, R. Mehrjoo, Decision-Makers Weighting in Fuzzy Multiple Attributes Group Decision-Making. Journal of Communication and Computer 8 (2011) 247-251
[22] S. S. Hashemi, S. H. Razavi Hajiagha, E. K. Zavadskas, H. Amoozad Mahdiraji, Multi criteria group decision making with ELECTRE III method based on interval-valued intuitionistic fuzzy information. Applied Mathematical Modelling 40 (2016) 1554-1564.
[23] S. Xian, W. Sun, S. Xu, Y. Gao, Fuzzy linguistic induced OWA Minkowski distance operator and its application in group decision making. Pattern Anal Applic 19 (2016) 325-335.
[24] S. M. Chen, S. H. Cheng, C. H. Chiou, Fuzzy multi attribute group decision making based on intuitionistic fuzzy sets and evidential reasoning methodology. Information Fusion 27 (2016) 215-227.
[25] Z. Wu, J. Ahmad, J. Xu, A group decision making framework based on fuzzy VIKOR approach for machine tool selection with linguistic information. Applied Soft Computing 42 (2016) 314-324.
[26] P. Sevastjanov, L. Dymova, Generalised operations on hesitant fuzzy values in the framework of Dempster-Shafer theory. Information Sciences 311 (2015) 39-58.
[27] Z. Eslaminasab, A. Hamzehee, Determining appropriate weight for criteria in multi criteria group decision making problems using an Lp model and similarity measure. Iranian Journal of Fuzzy Systems 16 (3) (2019) 35-46.
[28] Z. S. Xu, Intuitionistic fuzzy aggregation and clustering. Berlin, Heidelberg: Springer, 2012.
[29] D. H. Hong, C. H. Choi, Multi criteria fuzzy decision-making problems based on vague set theory. Fuzzy Sets and Systems 114 (1) (2000) 103-113.
[30] A. A. Goshtasby, Similarity and dissimilarity measures. In: Image Registration. Advances in Computer Vision and Pattern Recognition. Springer, London, 2012.
[31] F. Mata, L. Mart´ınez, E. Herrera-Viedma, An Adaptive Consensus Support Model for Group Decision-Making Problems in a Multi granular Fuzzy Linguistic Context. IEEE Transactions on fuzzy Systems 17 (2) (2009) 279-290.