Aggregating crisp values into intuitionistic fuzzy number for group decision making

Abstract This paper presents a multiple attribute group decision making model based on aggregating crisp values into intuitionistic fuzzy numbers. First, each alternative is evaluated with respect to their attributes, whose values are provided by decision maker as crisp numbers. Second, to make a reasonable normalization of attribute values in the group decision making environment, a maximum grade and a minimum grade are added to the attribute values. These normalized attribute values are then aggregated (per attribute) into an induced intuitionistic fuzzy number. Each alternative is then evaluated according to the induced intuitionistic fuzzy number. To show the major technical advances in this paper, comparisons with other methods are also made. Finally, an experimental analysis for supplier selection is given to illustrate the reasonableness and efficiency of the introduced method.

[1]  Francisco Herrera,et al.  A group decision making model dealing with comparative linguistic expressions based on hesitant fuzzy linguistic term sets , 2013, Inf. Sci..

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

[3]  Soung Hie Kim,et al.  Interactive group decision making procedure under incomplete information , 1999, Eur. J. Oper. Res..

[4]  E. Stanley Lee,et al.  An extension of TOPSIS for group decision making , 2007, Math. Comput. Model..

[5]  Yuying Jia,et al.  Interval Multiple Attribute Decision Making Based on Interval-Valued Intuitionistic Fuzzy Set , 2008, 2008 Congress on Image and Signal Processing.

[6]  Yuying Jia,et al.  A method to aggregate crisp values into interval-valued intuitionistic fuzzy information for group decision making , 2013, Appl. Soft Comput..

[7]  Zeshui Xu,et al.  Projection Method For Uncertain Multi-Attribute Decision Making With Preference Information On Alternatives , 2004, Int. J. Inf. Technol. Decis. Mak..

[8]  Z. Srdjevic,et al.  A two-phase algorithm for consensus building in AHP-group decision making , 2013 .

[9]  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..

[10]  Shady Aly,et al.  Fuzzy aggregation and averaging for group decision making: A generalization and survey , 2009, Knowl. Based Syst..

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

[12]  Ting-Yu Chen Multiple criteria group decision-making with generalized interval-valued fuzzy numbers based on signed distances and incomplete weights , 2012 .

[13]  Shyi-Ming Chen,et al.  Fuzzy group decision making for evaluating the rate of aggregative risk in software development , 2001, Fuzzy Sets Syst..

[14]  Yue Zhong-liang,et al.  The Comprehensive Evaluation of Urban Environmental Quality Based on Intuitionistic Fuzzy Set , 2008 .

[15]  Petr Ekel,et al.  A flexible consensus scheme for multicriteria group decision making under linguistic assessments , 2010, Inf. Sci..

[16]  Shian-Jong Chuu,et al.  Group decision-making model using fuzzy multiple attributes analysis for the evaluation of advanced manufacturing technology , 2009, Fuzzy Sets Syst..

[17]  Zhongliang Yue,et al.  An approach to aggregating interval numbers into interval-valued intuitionistic fuzzy information for group decision making , 2011, Expert Syst. Appl..

[18]  A. I. Ölçer,et al.  A new fuzzy multiple attributive group decision making methodology and its application to propulsion/manoeuvring system selection problem , 2005, Eur. J. Oper. Res..

[19]  S. M. Mousavi,et al.  A new design of the elimination and choice translating reality method for multi-criteria group decision-making in an intuitionistic fuzzy environment , 2013 .

[20]  Ting-Yu Chen,et al.  A multicriteria group decision-making approach based on interval-valued intuitionistic fuzzy sets: A comparative perspective , 2011, Expert Syst. Appl..

[21]  J. Kacprzyk,et al.  Multiperson decision making models using fuzzy sets and possibility theory , 1990 .

[22]  Z. Yue An intuitionistic fuzzy projection-based approach for partner selection , 2013 .

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

[24]  James J. H. Liou,et al.  Developing a hybrid multi-criteria model for selection of outsourcing providers , 2010, Expert Syst. Appl..

[25]  Peide Liu,et al.  Method for Multiple Attribute Decision-Making with Continuous Random Variable under Risk Based on Projection Model , 2010 .

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

[27]  C. Hwang,et al.  Group Decision Making Under Multiple Criteria: Methods and Applications , 1986 .

[28]  Ching-Hsue Cheng,et al.  Using intuitionistic fuzzy sets for fault-tree analysis on printed circuit board assembly , 2006, Microelectron. Reliab..

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

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

[31]  Reza Tavakkoli-Moghaddam,et al.  Group decision making based on novel fuzzy modified TOPSIS method , 2011 .

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

[33]  Zhou-Jing Wang,et al.  An approach to multiattribute decision making with interval-valued intuitionistic fuzzy assessments and incomplete weights , 2009, Inf. Sci..

[34]  Lu Yan-li,et al.  Multiple attribute decision making method based on intuitionistic fuzzy sets , 2007 .

[35]  Krassimir T. Atanassov,et al.  Answer to D. Dubois, S. Gottwald, P. Hajek, J. Kacprzyk and H. Prade's paper "Terminological difficulties in fuzzy set theory - the case of "Intuitionistic Fuzzy Sets" , 2005, Fuzzy Sets Syst..

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

[37]  Zhongliang Yue,et al.  A group decision making approach based on aggregating interval data into interval-valued intuitionistic fuzzy information , 2014 .

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

[39]  Chen-Tung Chen,et al.  Extensions of the TOPSIS for group decision-making under fuzzy environment , 2000, Fuzzy Sets Syst..

[40]  Youyin Jing,et al.  Application of improved grey relational projection method to evaluate sustainable building envelope performance , 2010 .

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

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

[43]  Roberta Parreiras,et al.  Fuzzy set based models and methods of multicriteria group decision making , 2009 .

[44]  Humberto Bustince,et al.  Intuitionistic fuzzy generators Application to intuitionistic fuzzy complementation , 2000, Fuzzy Sets Syst..