A Projection Method for Multiple Attribute Group Decision Making with Intuitionistic Fuzzy Information

The aim of this paper is to investigate intuitionistic fuzzy multiple attribute group decision making problems where the attribute values provided by experts are expressed in intuitionistic fuzzy numbers, and the weight information about the experts is to be determined. We present a new method to derive the weights of experts and rank the preference order of alternatives based on projection models. We first derive the weights of the decision makers according to the projection of the individual decision on the ideal decision. The expert has a large weight if his evaluation value is close to the ideal decision, and has a small weight if his evaluation value is far from the ideal decision. Then, based on the weighted projection of the alternatives on the intuitionistic fuzzy ideal solution (IFIS), we develop a straightforward and practical algorithm to rank alternatives. Furthermore, we extend the developed model and algorithm to the multiple attribute group decision making problems with interval-valued intuitionistic fuzzy information. Finally, an illustrative example is given to verify the developed approach and to demonstrate its practicality and effectiveness.

[1]  Zun-Quan Xia,et al.  Multicriteria fuzzy decision-making methods based on intuitionistic fuzzy sets , 2007, J. Comput. Syst. Sci..

[2]  Krassimir T. Atanassov,et al.  Intuitionistic Fuzzy Sets - Theory and Applications , 1999, Studies in Fuzziness and Soft Computing.

[3]  Shouzhen Zeng.  Some Intuitionistic Fuzzy Weighted Distance Measures and Their Application to Group Decision Making , 2013 .

[4]  Chunqiao Tan,et al.  A multi-criteria interval-valued intuitionistic fuzzy group decision making with Choquet integral-based TOPSIS , 2011, Expert Syst. Appl..

[5]  H. B. Mitchell.  An Intuitionistic Owa Operator , 2004, Int. J. Uncertain. Fuzziness Knowl. Based Syst..

[6]  Zhou-Jing Wang,et al.  A mathematical programming approach to multi-attribute decision making with interval-valued intuitionistic fuzzy assessment information , 2011, Expert Syst. Appl..

[7]  Zeshui Xu,et al.  Intuitionistic preference relations and their application in group decision making , 2007, Inf. Sci..

[8]  Jun Ye,et al.  Fuzzy decision-making method based on the weighted correlation coefficient under intuitionistic fuzzy environment , 2010, Eur. J. Oper. Res..

[9]  Zeshui Xu,et al.  Some similarity measures of intuitionistic fuzzy sets and their applications to multiple attribute decision making , 2007, Fuzzy Optim. Decis. Mak..

[10]  Zeshui Xu,et al.  Projection Models for Intuitionistic Fuzzy Multiple Attribute Decision Making , 2010, Int. J. Inf. Technol. Decis. Mak..

[11]  Deng-Feng Li,et al.  Some measures of dissimilarity in intuitionistic fuzzy structures , 2004, J. Comput. Syst. Sci..

[12]  Krassimir T. Atanassov,et al.  Intuitionistic fuzzy sets , 1986 .

[13]  Zeshui Xu,et al.  Nonlinear optimization models for multiple attribute group decision making with intuitionistic fuzzy information , 2010, Int. J. Intell. Syst..

[14]  Zaiwu Gong,et al.  Goal programming approaches to obtain the priority vectors from the intuitionistic fuzzy preference relations , 2009, Comput. Ind. Eng..

[15]  Weihua Su,et al.  Intuitionistic fuzzy ordered weighted distance operator , 2011, Knowl. Based Syst..

[16]  Zeshui Xu,et al.  A method based on distance measure for interval-valued intuitionistic fuzzy group decision making , 2010, Inf. Sci..

[17]  Diyar Akay,et al.  A multi-criteria intuitionistic fuzzy group decision making for supplier selection with TOPSIS method , 2009, Expert Syst. Appl..

[18]  Dug Hun Hong,et al.  Multicriteria fuzzy decision-making problems based on vague set theory , 2000, Fuzzy Sets Syst..

[19]  Shyi-Ming Chen,et al.  Handling multicriteria fuzzy decision-making problems based on vague set theory , 1994 .

[20]  Eulalia Szmidt,et al.  Amount of Information and Its Reliability in the Ranking of Atanassov’s Intuitionistic Fuzzy Alternatives , 2009 .

[21]  Jun Ye,et al.  Multicriteria fuzzy decision-making method based on a novel accuracy function under interval-valued intuitionistic fuzzy environment , 2009, Expert Syst. Appl..

[22]  Gwo-Hshiung Tzeng,et al.  Comments on “Multiple criteria decision making (MCDM) methods in economics: an overview” , 2012 .

[23]  Ronald R. Yager,et al.  Intuitionistic fuzzy interpretations of multi-criteria multi-person and multi-measurement tool decision making , 2005, Int. J. Syst. Sci..

[24]  Gui-Wu Wei,et al.  GRA method for multiple attribute decision making with incomplete weight information in intuitionistic fuzzy setting , 2010, Knowl. Based Syst..

[25]  Yejun Xu,et al.  The induced generalized aggregation operators for intuitionistic fuzzy sets and their application in group decision making , 2012, Appl. Soft Comput..

[26]  Zeshui Xu,et al.  Multi-person multi-attribute decision making models under intuitionistic fuzzy environment , 2007, Fuzzy Optim. Decis. Mak..

[27]  Zeshui Xu,et al.  Intuitionistic Fuzzy Aggregation Operators , 2007, IEEE Transactions on Fuzzy Systems.

[28]  Guiwu Wei,et al.  Some induced geometric aggregation operators with intuitionistic fuzzy information and their application to group decision making , 2010, Appl. Soft Comput..

[29]  Guodong Ye,et al.  An Approach for Multiple Attribute Group Decision Making Based on Intuitionistic Fuzzy Information , 2009, Int. J. Uncertain. Fuzziness Knowl. Based Syst..

[30]  Zhoujing Wang,et al.  Intuitionistic fuzzy multiple attribute group decision making based on projection method , 2009, 2009 Chinese Control and Decision Conference.

[31]  Peide Liu.  An approach to group decision making based on 2-dimension uncertain linguistic information , 2012 .

[32]  Zeshui Xu.  A Deviation-Based Approach to Intuitionistic Fuzzy Multiple Attribute Group Decision Making , 2010 .

[33]  Zhongliang Yue,et al.  Deriving decision maker's weights based on distance measure for interval-valued intuitionistic fuzzy group decision making , 2011, Expert Syst. Appl..

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

[35]  Deng-Feng Li,et al.  Closeness coefficient based nonlinear programming method for interval-valued intuitionistic fuzzy multiattribute decision making with incomplete preference information , 2011, Appl. Soft Comput..

[36]  Eulalia Szmidt,et al.  A NEW APPROACH TO RANKING ALTERNATIVES EXPRESSED VIA INTUITIONISTIC FUZZY SETS , 2008 .

[37]  Mei Gui,et al.  Multi-Attribute Decision Making Method Based on Intuitionistic Fuzzy Grey Sets , 2012 .

[38]  Gui-Wu Wei,et al.  Maximizing deviation method for multiple attribute decision making in intuitionistic fuzzy setting , 2008, Knowl. Based Syst..

[39]  V. Lakshmana Gomathi Nayagam,et al.  Ranking of interval-valued intuitionistic fuzzy sets , 2011, Appl. Soft Comput..

[40]  Przemyslaw Grzegorzewski,et al.  Distances between intuitionistic fuzzy sets and/or interval-valued fuzzy sets based on the Hausdorff metric , 2004, Fuzzy Sets Syst..

[41]  Deng-Feng Li,et al.  Linear programming method for multiattribute group decision making using IF sets , 2010, Inf. Sci..

[42]  Humberto Bustince,et al.  Vague sets are intuitionistic fuzzy sets , 1996, Fuzzy Sets Syst..

[43]  Shu Liu,et al.  Fractional programming methodology for multi-attribute group decision-making using IFS , 2009, Appl. Soft Comput..

[44]  Huawen Liu,et al.  Multi-criteria decision-making methods based on intuitionistic fuzzy sets , 2007, Eur. J. Oper. Res..

[45]  Zeshui Xu,et al.  Intuitionistic and interval-valued intutionistic fuzzy preference relations and their measures of similarity for the evaluation of agreement within a group , 2009, Fuzzy Optim. Decis. Mak..

[46]  Zeshui Xu,et al.  Some geometric aggregation operators based on intuitionistic fuzzy sets , 2006, Int. J. Gen. Syst..

[47]  Z. Yue.  Application of the projection method to determine weights of decision makers for group decision making , 2012 .

[48]  B. Ayvaz,et al.  SUPPLIER SELECTION WITH TOPSIS METHOD IN FUZZY ENVIRONMENT: AN APPLICATION IN BANKING SECTOR , 2015 .

[49]  Zeshui Xu,et al.  Generalized aggregation operators for intuitionistic fuzzy sets , 2010 .

[50]  Zeshui Xu,et al.  Dynamic intuitionistic fuzzy multi-attribute decision making , 2008, Int. J. Approx. Reason..

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

[52]  Z. Yue.  Approach to group decision making based on determining the weights of experts by using projection method , 2012 .

[53]  W.-L. Gau,et al.  Vague sets , 1993, IEEE Trans. Syst. Man Cybern..