Numerical scales generated individually for analytic hierarchy process

Because individual interpretations of the analytic hierarchy process (AHP) linguistic scale vary for each user, this study proposes a novel framework that AHP decision makers can use to generate numerical scales individually, based on the 2-tuple linguistic modeling of AHP scale problems. By using the concept of transitive calibration, individual characteristics in understanding the AHP linguistic scale are first defined. An algorithm is then proposed for detecting the individual characteristics from the linguistic pairwise comparison data that is associated with each of the AHP individual decision makers. Finally, a nonlinear programming model is proposed to generate individual numerical scales that optimally match the obtained individual characteristics. Two well-known numerical examples are re-examined using the proposed framework to demonstrate its validity.

[1]  Witold Pedrycz,et al.  Analytic Hierarchy Process (AHP) in Group Decision Making and its Optimization With an Allocation of Information Granularity , 2011, IEEE Transactions on Fuzzy Systems.

[2]  T. L. Saaty.  A Scaling Method for Priorities in Hierarchical Structures , 1977 .

[3]  F. Lootsma.  SCALE SENSITIVITY IN THE MULTIPLICATIVE AHP AND SMART , 1993 .

[4]  Quan Zhang,et al.  Decision consolidation: criteria weight determination using multiple preference formats , 2004, Decis. Support Syst..

[5]  Yin-Feng Xu,et al.  A comparative study of the numerical scales and the prioritization methods in AHP , 2008, Eur. J. Oper. Res..

[6]  José María Moreno-Jiménez,et al.  Consensus Building in AHP-Group Decision Making: A Bayesian Approach , 2010, Oper. Res..

[7]  Witold Pedrycz,et al.  A granulation of linguistic information in AHP decision-making problems , 2014, Inf. Fusion.

[8]  Francisco Herrera,et al.  Integrating three representation models in fuzzy multipurpose decision making based on fuzzy preference relations , 1998, Fuzzy Sets Syst..

[9]  R. Jiang,et al.  Scale transitivity in the AHP , 2003, J. Oper. Res. Soc..

[10]  Francisco Herrera,et al.  Aggregation operators for linguistic weighted information , 1997, IEEE Trans. Syst. Man Cybern. Part A.

[11]  Lidija Zadnik Stirn,et al.  Acceptable consistency of aggregated comparison matrices in analytic hierarchy process , 2012, Eur. J. Oper. Res..

[12]  Francisco Herrera,et al.  A model based on linguistic 2-tuples for dealing with multigranular hierarchical linguistic contexts in multi-expert decision-making , 2001, IEEE Trans. Syst. Man Cybern. Part B.

[13]  Jerry M. Mendel,et al.  Perceptual Computing: Aiding People in Making Subjective Judgments , 2010 .

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

[15]  William J. Hurley,et al.  Transitive calibration of the AHP verbal scale , 1999, Eur. J. Oper. Res..

[16]  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..

[17]  Sushil Kumar,et al.  Analytic hierarchy process: An overview of applications , 2006, Eur. J. Oper. Res..

[18]  John A. Keane,et al.  A heuristic method to rectify intransitive judgments in pairwise comparison matrices , 2012, Eur. J. Oper. Res..

[19]  R. Hämäläinen,et al.  On the measurement of preferences in the analytic hierarchy process , 1997 .

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

[21]  Yin-Feng Xu,et al.  Selecting the Individual Numerical Scale and Prioritization Method in the Analytic Hierarchy Process: A 2-Tuple Fuzzy Linguistic Approach , 2011, IEEE Transactions on Fuzzy Systems.

[22]  Alessio Ishizaka,et al.  Does AHP help us make a choice? An experimental evaluation , 2011, J. Oper. Res. Soc..

[23]  John T. Rickard.  Perceptual Computing: Aiding People in Making Subjective Judgments (Mendel, J.M. and Wu, D.; 2010) [Book Review] , 2011, IEEE Computational Intelligence Magazine.

[24]  Francisco Herrera,et al.  A consensus model for multiperson decision making with different preference structures , 2002, IEEE Trans. Syst. Man Cybern. Part A.

[25]  John A. Keane,et al.  Preference elicitation from inconsistent judgments using multi-objective optimization , 2012, Eur. J. Oper. Res..

[26]  Eelko Huizingh,et al.  A comparison of verbal and numerical judgments in the analytic hierarchy process , 1997 .

[27]  Luis G. Vargas,et al.  The theory of ratio scale estimation: Saaty's analytic hierarchy process , 1987 .

[28]  Bojan Srdjevic,et al.  Combining different prioritization methods in the analytic hierarchy process synthesis , 2005, Comput. Oper. Res..

[29]  F. Herrera,et al.  A consistency-based procedure to estimate missing pairwise preference values , 2008 .

[30]  T. Saaty,et al.  The Analytic Hierarchy Process , 1985 .

[31]  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.

[32]  Gang Kou,et al.  A simple method to improve the consistency ratio of the pair-wise comparison matrix in ANP , 2011, Eur. J. Oper. Res..

[33]  T. Saaty.  Decision making — the Analytic Hierarchy and Network Processes (AHP/ANP) , 2004 .

[34]  Francisco Herrera,et al.  A consistency‐based procedure to estimate missing pairwise preference values , 2008, Int. J. Intell. Syst..

[35]  Alessio Ishizaka,et al.  Influence of aggregation and measurement scale on ranking a compromise alternative in AHP , 2009, J. Oper. Res. Soc..

[36]  Thomas L. Saaty,et al.  Marketing Applications of the Analytic Hierarchy Process , 1980 .

[37]  Yin-Feng Xu,et al.  Consensus models for AHP group decision making under row geometric mean prioritization method , 2010, Decis. Support Syst..

[38]  G. A. Miller.  THE PSYCHOLOGICAL REVIEW THE MAGICAL NUMBER SEVEN, PLUS OR MINUS TWO: SOME LIMITS ON OUR CAPACITY FOR PROCESSING INFORMATION 1 , 1956 .

[39]  R. Hämäläinen,et al.  An Experiment on the Numerical Modelling of Verbal Ratio Statements , 1997 .

[40]  Bojan Srdjevic,et al.  Linking analytic hierarchy process and social choice methods to support group decision-making in water management , 2007, Decis. Support Syst..