The consistency measures of multi-granularity linguistic group decision making

When different experts have different uncertainty degrees on the phenomenon, several linguistic term sets with different granularity of uncertainty are necessary. In this paper, we deal with the consistency problem with multi-granularity linguistic term sets applied to group decision making. Firstly, we develop a transformation model to maintain the uncertainty degrees of different granularity associated with each expert. We use the uncertain linguistic variables as the unified form. Some computational rules about uncertain linguistic variables are given. Then consistency index of linguistic preference relations based on the distance of a multi-granularity linguistic preference relation is defined. Chi-square statistic is used to establish the consistency thresholds. Finally two numerical examples are used to show the process and effects of our new proposed method.

[1]  Jian Ma,et al.  A method for group decision making with multi-granularity linguistic assessment information , 2008, Inf. Sci..

[2]  Da Ruan,et al.  A fuzzy-set approach to treat determinacy and consistency of linguistic terms in multi-criteria decision making , 2007, Int. J. Approx. Reason..

[3]  Francisco Herrera,et al.  A fusion approach for managing multi-granularity linguistic term sets in decision making , 2000, Fuzzy Sets Syst..

[4]  Yucheng Dong,et al.  On consistency measures of linguistic preference relations , 2008, Eur. J. Oper. Res..

[5]  Francisco Herrera,et al.  A 2-tuple fuzzy linguistic representation model for computing with words , 2000, IEEE Trans. Fuzzy Syst..

[6]  Francisco Herrera,et al.  Computing with Words in Decision support Systems: An overview on Models and Applications , 2010, Int. J. Comput. Intell. Syst..

[7]  Francisco Herrera,et al.  Some issues on consistency of fuzzy preference relations , 2004, Eur. J. Oper. Res..

[8]  P. D. Jong.  A statistical approach to Saaty's scaling method for priorities , 1984 .

[9]  T. Tanino.  Fuzzy preference orderings in group decision making , 1984 .

[10]  Zhi-Ping Fan,et al.  A method for group decision-making based on multi-granularity uncertain linguistic information , 2010, Expert Syst. Appl..

[11]  Qi Yue,et al.  An approach to group decision-making with uncertain preference ordinals , 2010, Comput. Ind. Eng..

[12]  HerreraF.,et al.  An overview on the 2-tuple linguistic model for computing with words in decision making , 2012 .

[13]  Zeshui Xu.  Deviation measures of linguistic preference relations in group decision making , 2005 .

[14]  Francisco Herrera,et al.  The 2-Tuple Linguistic Computational Model. Advantages of Its Linguistic Description, Accuracy and Consistency , 2001, Int. J. Uncertain. Fuzziness Knowl. Based Syst..

[15]  Francisco Herrera,et al.  Group Decision-Making Model With Incomplete Fuzzy Preference Relations Based on Additive Consistency , 2007, IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics).

[16]  Francisco Herrera,et al.  A Fuzzy Linguistic Methodology to Deal With Unbalanced Linguistic Term Sets , 2008, IEEE Transactions on Fuzzy Systems.

[17]  Francisco Herrera,et al.  Linguistic decision analysis: steps for solving decision problems under linguistic information , 2000, Fuzzy Sets Syst..

[18]  Francisco Herrera,et al.  An overview on the 2-tuple linguistic model for computing with words in decision making: Extensions, applications and challenges , 2012, Inf. Sci..

[19]  Lotfi A. Zadeh,et al.  From Computing with Numbers to Computing with Words - from Manipulation of Measurements to Manipulation of Perceptions , 2005, Logic, Thought and Action.

[20]  Zeshui Xu,et al.  Uncertain linguistic aggregation operators based approach to multiple attribute group decision making under uncertain linguistic environment , 2004, Inf. Sci..

[21]  Jin-Hsien Wang,et al.  A new version of 2-tuple fuzzy linguistic representation model for computing with words , 2006, IEEE Trans. Fuzzy Syst..

[22]  Zhifeng Chen,et al.  On the fusion of multi-granularity linguistic label sets in group decision making , 2006, Comput. Ind. Eng..

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

[24]  Jonathan Lawry,et al.  An Alternative Approach to Computing with Words , 2001, Int. J. Uncertain. Fuzziness Knowl. Based Syst..

[25]  Yueh-Hsiang Chen,et al.  Applying fuzzy linguistic preference relations to the improvement of consistency of fuzzy AHP , 2008, Inf. Sci..

[26]  J. Kacprzyk.  Group decision making with a fuzzy linguistic majority , 1986 .

[27]  S. Orlovsky.  Decision-making with a fuzzy preference relation , 1978 .