Extensions of LINMAP model for multi criteria decision making with grey numbers

Abstract The linear programming technique for multidimensional analysis of preference, known as LINMAP is one of the existing well-known ideal seeking methods for multi attribute decision making problems. This method originally is proposed under crisp and deterministic circumstances. However, uncertainty is an indubitable property of decision making problems. In this paper, a new version of LINMAP-G is proposed where the decision maker's judgments are expressed as grey numbers. Like original LINMAP method, the grey ideal solution and attributes weight vector is determined and alternatives are ranked according to their weighted distance from determined ideal point. Application of the proposed method is illustrated in two numerical examples.

[1]  Zeshui Xu,et al.  A method based on linguistic aggregation operators for group decision making with linguistic preference relations , 2004, Inf. Sci..

[2]  Edmundas Kazimieras Zavadskas,et al.  Multiple criteria analysis of foundation instalment alternatives by applying Additive Ratio Assessment (ARAS) method , 2010 .

[3]  Zhongliang Yue,et al.  An extended TOPSIS for determining weights of decision makers with interval numbers , 2011, Knowl. Based Syst..

[4]  Edmundas Kazimieras Zavadskas,et al.  Risk assessment of construction projects , 2010 .

[5]  Ching-Lai Hwang,et al.  Multiple Attribute Decision Making: Methods and Applications - A State-of-the-Art Survey , 1981, Lecture Notes in Economics and Mathematical Systems.

[6]  Tomas Baležentis,et al.  A novel method for group multi-attribute decision making with two-tuple linguistic computing: Supplier evaluation under uncertainty , 2011 .

[7]  Yong-Huang Lin,et al.  Multi-attribute group decision making model under the condition of uncertain information , 2008 .

[8]  Numan Çelebi,et al.  Comparative analysis of multi-criteria decision making methodologies and implementation of a warehouse location selection problem , 2011, Expert Syst. Appl..

[9]  Morteza Yazdani,et al.  Risk Analysis of Critical Infrastructures Using Fuzzy Copras , 2011 .

[10]  Ching-Lai Hwang,et al.  Fuzzy Multiple Attribute Decision Making - Methods and Applications , 1992, Lecture Notes in Economics and Mathematical Systems.

[11]  Dragisa Stanujkic,et al.  Extension of Ratio System Part of MOORA Method for Solving Decision-Making Problems with Interval Data , 2012, Informatica.

[12]  Richard Bellman,et al.  Decision-making in fuzzy environment , 2012 .

[13]  Edmundas Kazimieras Zavadskas,et al.  An integrated model for prioritizing strategies of the iranian mining sector , 2011 .

[14]  Allan D. Shocker,et al.  Linear programming techniques for multidimensional analysis of preferences , 1973 .

[15]  Bertrand Mareschal,et al.  An interval version of PROMETHEE for the comparison of building products' design with ill-defined data on environmental quality , 1998, Eur. J. Oper. Res..

[16]  Edmundas Kazimieras Zavadskas,et al.  Contractor selection for construction works by applying saw‐g and topsis grey techniques , 2010 .

[17]  H. Ishibuchi,et al.  Multiobjective programming in optimization of the interval objective function , 1990 .

[18]  Deng-Feng Li,et al.  Fuzzy LINMAP method for multiattribute decision making under fuzzy environments , 2006, J. Comput. Syst. Sci..

[19]  Reay-Chen Wang,et al.  Group decision-making using a fuzzy linguistic approach for evaluating the flexibility in a manufacturing system , 2004, Eur. J. Oper. Res..

[20]  Tarik Aouam,et al.  Fuzzy MADM: An outranking method , 2003, Eur. J. Oper. Res..

[21]  E. Zavadskas,et al.  Multiple criteria decision making (MCDM) methods in economics: an overview , 2011 .

[22]  Wen Lea Pearn,et al.  Comparative analysis of a randomized N-policy queue: An improved maximum entropy method , 2011, Expert Syst. Appl..

[23]  Jurgita Antucheviciene,et al.  Measuring Congruence of Ranking Results Applying Particular MCDM Methods , 2011, Informatica.

[24]  Zenonas Turskis,et al.  Integrated Fuzzy Multiple Criteria Decision Making Model for Architect Selection , 2012 .

[25]  Lotfi A. Zadeh,et al.  Fuzzy Sets , 1996, Inf. Control..

[26]  Mostafa Zandieh,et al.  Extension of the ELECTRE method for decision-making problems with interval weights and data , 2010 .

[27]  Deng Ju-Long,et al.  Control problems of grey systems , 1982 .

[28]  Ruey-Chyn Tsaur,et al.  Decision risk analysis for an interval TOPSIS method , 2011, Appl. Math. Comput..

[29]  Mohammad Izadikhah,et al.  An algorithmic method to extend TOPSIS for decision-making problems with interval data , 2006, Appl. Math. Comput..

[30]  Yi Peng,et al.  Evaluation of Classification Algorithms Using MCDM and Rank Correlation , 2012, Int. J. Inf. Technol. Decis. Mak..

[31]  Gwo-Hshiung Tzeng,et al.  Combining grey relation and TOPSIS concepts for selecting an expatriate host country , 2004, Math. Comput. Model..

[32]  Yi Peng,et al.  FAMCDM: A fusion approach of MCDM methods to rank multiclass classification algorithms , 2011 .

[33]  Deng-Feng Li,et al.  Extension of the LINMAP for multiattribute decision making under Atanassov’s intuitionistic fuzzy environment , 2008, Fuzzy Optim. Decis. Mak..

[34]  Taho Yang,et al.  The use of grey relational analysis in solving multiple attribute decision-making problems , 2008, Comput. Ind. Eng..

[35]  Tao Sun,et al.  Fuzzy LINMAP Method for multiattribute Group Decision Making with Linguistic Variables and Incomplete Information , 2007, Int. J. Uncertain. Fuzziness Knowl. Based Syst..

[36]  Yi-Chung Hu,et al.  Assessing weights of product attributes from fuzzy knowledge in a dynamic environment , 2004, Eur. J. Oper. Res..

[37]  Jian-Bo Yang,et al.  Fuzzy linear programming technique for multiattribute group decision making in fuzzy environments , 2004, Inf. Sci..

[38]  Edmundas Kazimieras Zavadskas,et al.  A Novel Method for Multiple Criteria Analysis: Grey Additive Ratio Assessment (ARAS-G) Method , 2010, Informatica.

[39]  T. Baležentis,et al.  Multimoora for the EU member states updated with fuzzy number theory , 2011 .

[40]  Edmundas Kazimieras Zavadskas,et al.  FOREST ROADS LOCATING BASED ON AHP AND COPRAS-G METHODS: AN EMPIRICAL STUDY BASED ON IRAN , 2011 .