A method of ranking interval numbers based on degrees for multiple attribute decision making

In order to deal with the difficulty of ranking interval numbers in the multiple attribute decision making process, interval numbers are expressed in the Rectangular Coordinate System. On the basis of this, two-dimensional relations of interval numbers are analyzed. For interval numbers, their advantage degree functions of the symmetry axis and the length are deduced after an information mining process, and then the advantage degree function of interval numbers is defined. Procedures of ranking interval numbers based on degrees for multiple attribute decision making are given. Finally, the feasibility and the effectiveness of this method are verified through an example.

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

[2]  Desheng Dash Wu,et al.  The method of grey related analysis to multiple attribute decision making problems with interval numbers , 2005, Math. Comput. Model..

[3]  Francisco Herrera,et al.  Group decision making with incomplete fuzzy linguistic preference relations , 2009, Int. J. Intell. Syst..

[4]  Jun Ye,et al.  Some aggregation operators of interval neutrosophic linguistic numbers for multiple attribute decision making , 2014, J. Intell. Fuzzy Syst..

[5]  F. Herrera,et al.  Group decision making with incomplete fuzzy linguistic preference relations , 2009 .

[6]  Na Zhao,et al.  Operators and Comparisons of Hesitant Fuzzy Linguistic Term Sets , 2014, IEEE Transactions on Fuzzy Systems.

[7]  Yozo Nakahara,et al.  On the linear programming problems with interval coefficients , 1992 .

[8]  Enrique Herrera-Viedma,et al.  A model of an information retrieval system with unbalanced fuzzy linguistic information , 2007, Int. J. Intell. Syst..

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

[10]  Yang Liu,et al.  An Approach to Solve Group-Decision-Making Problems With Ordinal Interval Numbers , 2010, IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics).

[11]  Shui Yu,et al.  Linguistic Computational Model Based on 2-Tuples and Intervals , 2013, IEEE Transactions on Fuzzy Systems.

[12]  H. Breusers,et al.  Applied Mathematical Modelling , 1976 .

[13]  Tapan Kumar Pal,et al.  On comparing interval numbers , 2000, Eur. J. Oper. Res..

[14]  Zeshui Xu,et al.  An overview of methods for determining OWA weights , 2005, Int. J. Intell. Syst..

[15]  Peng Shi,et al.  Relief supplies allocation and optimization by interval and fuzzy number approaches , 2015, Inf. Sci..

[16]  Lang Liu,et al.  Multi-attributed decision making for mining methods based on grey system and interval numbers , 2013 .

[17]  Xu Ze.  Research on Method for Ranking Interval Numbers , 2001 .

[18]  Zhang Quan,et al.  A Ranking Approach for Interval Numbers in Uncertain Multiple Attribute Decision Making Problems , 1999 .

[19]  Petr Krka.  Exact real arithmetic for interval number systems , 2014 .

[20]  Enrique Herrera-Viedma,et al.  Consistency-Driven Automatic Methodology to Set Interval Numerical Scales of 2-Tuple Linguistic Term Sets and Its Use in the Linguistic GDM With Preference Relation , 2015, IEEE Transactions on Cybernetics.

[21]  Yin-Feng Xu,et al.  Computing the Numerical Scale of the Linguistic Term Set for the 2-Tuple Fuzzy Linguistic Representation Model , 2009, IEEE Transactions on Fuzzy Systems.

[22]  Sukhamay Kundu,et al.  Min-transitivity of fuzzy leftness relationship and its application to decision making , 1997, Fuzzy Sets Syst..

[23]  Petr Kurka.  Exact real arithmetic for interval number systems , 2014, Theor. Comput. Sci..

[24]  Jin Wang,et al.  Application of MADM in a fuzzy environment for selecting the best barrier for offshore wells , 2012, Expert Syst. Appl..

[25]  K. Ganesan,et al.  On Arithmetic Operations of Interval Numbers , 2005, Int. J. Uncertain. Fuzziness Knowl. Based Syst..

[26]  M. Sayadi,et al.  Extension of VIKOR method for decision making problem with interval numbers , 2009 .

[27]  P ? ? ? ? ? ? ? % ? ? ? ? , 1991 .

[28]  Zhang Ji.  Research on Method for Ranking Interval Numbers , 2003 .

[29]  Kamran Shahanaghi,et al.  A multi-criteria decision-making approach to solve the product mix problem with interval parameters based on the theory of constraints , 2014 .

[30]  Ramon E. Moore,et al.  Interval analysis and fuzzy set theory , 2003, Fuzzy Sets Syst..

[31]  Deng-Feng Li,et al.  Multiattribute Group Decision Making Method Using Extended Linguistic Variables , 2009, Int. J. Uncertain. Fuzziness Knowl. Based Syst..

[32]  Louis B. Rall.  Automatic error analysis , 1981 .