A comparative study for consistency-based decision making with interval multiplicative preference relations

ABSTRACT To ensure the reasonable application and perfect the theory of decision making with interval multiplicative preference relations (IMPRs), this paper continues to discuss decision making with IMPRs. After reviewing previous consistency concepts for IMPRs, we find that Krejčí’s consistency concept is more flexible and natural than others. However, it is insufficient to address IMPRs only using this concept. Considering this fact, this paper researches inconsistent and incomplete IMPRs that are usually encountered. First, programming models for addressing inconsistent and incomplete IMPRs are constructed. Then, this paper studies the consensus of individual IMPRs and defines a consensus index using the defined correlation coefficient. When the consensus requirement does not satisfy requirement, a programming model for improving consensus level is built, which can ensure the consistency. Subsequently, a procedure for group decision making with IMPRs is offered, and associated examples are provided to specifically show the application of main theoretical results.

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

[2]  Fang Liu,et al.  A group decision-making model with interval multiplicative reciprocal matrices based on the geometric consistency index , 2016, Comput. Ind. Eng..

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

[4]  Fanyong Meng,et al.  An approach to incomplete multiplicative preference relations and its application in group decision making , 2015, Inf. Sci..

[5]  Jana Krejčí,et al.  On multiplicative consistency of interval and fuzzy reciprocal preference relations , 2017, Comput. Ind. Eng..

[6]  Kazutomo Nishizawa.  A method to find elements of cycles in an incomplete directed graph and its applications—Binary AHP and petri nets , 1997 .

[7]  Dong Cao,et al.  Modifying inconsistent comparison matrix in analytic hierarchy process: A heuristic approach , 2008, Decis. Support Syst..

[8]  Fanyong Meng,et al.  A consistency and consensus-based method to group decision making with interval linguistic preference relations , 2016, J. Oper. Res. Soc..

[9]  M. Bohanec,et al.  The Analytic Hierarchy Process , 2004 .

[10]  M. P. Biswal,et al.  Preference programming and inconsistent interval judgments , 1997 .

[11]  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..

[12]  Xu Ze.  A Practical Method for Priority of Interval Number Complementary Judgement Matrix , 2001 .

[13]  Xiao-hong Chen,et al.  Two new methods for deriving the priority vector from interval comparison matrices , 2015 .

[14]  X. Zeshui,et al.  A consistency improving method in the analytic hierarchy process , 1999, Eur. J. Oper. Res..

[15]  Zeshui Xu,et al.  Exploiting the priority weights from interval linguistic fuzzy preference relations , 2019, Soft Comput..

[16]  Luis G. Vargas,et al.  Comparison of eigenvalue, logarithmic least squares and least squares methods in estimating ratios , 1984 .

[17]  Chonghui Guo,et al.  Deriving priority weights from intuitionistic multiplicative preference relations under group decision-making settings , 2017, J. Oper. Res. Soc..

[18]  Feng Wang,et al.  A group decision making method with interval valued fuzzy preference relations based on the geometric consistency , 2018, Inf. Fusion.

[19]  F. Liu,et al.  An approach to group decision making based on interval multiplicative and fuzzy preference relations by using projection , 2013 .

[20]  Fang Liu,et al.  A group decision making model based on a generalized ordered weighted geometric average operator with interval preference matrices , 2014, Fuzzy Sets Syst..

[21]  Witold Pedrycz,et al.  A group decision making model based on an inconsistency index of interval multiplicative reciprocal matrices , 2018, Knowl. Based Syst..

[22]  Jana Krej.  On additive consistency of interval fuzzy preference relations , 2017 .

[23]  Fang Liu,et al.  A goal programming model for incomplete interval multiplicative preference relations and its application in group decision-making , 2012, Eur. J. Oper. Res..

[24]  Jian-Bo Yang,et al.  A two-stage logarithmic goal programming method for generating weights from interval comparison matrices , 2005, Fuzzy Sets Syst..

[25]  Luis G. Vargas,et al.  Uncertainty and rank order in the analytic hierarchy process , 1987 .

[26]  Fang Liu,et al.  Acceptable consistency analysis of interval reciprocal comparison matrices , 2009, Fuzzy Sets Syst..

[27]  Weldon A. Lodwick,et al.  Constrained intervals and interval spaces , 2013, Soft Comput..

[28]  Shanlin Yang,et al.  Distributed preference relations for multiple attribute decision analysis , 2016, J. Oper. Res. Soc..

[29]  Luis G. Vargas,et al.  Preference simulation and preference programming: robustness issues in priority derivation , 1993 .

[30]  M. Brunelli.  Introduction to the Analytic Hierarchy Process , 2014 .

[31]  Fanyong Meng,et al.  Decision making with multiplicative hesitant fuzzy linguistic preference relations , 2017, Neural Computing and Applications.

[32]  Zhou-Jing Wang.  Comments on "A group decision-making model with interval multiplicative reciprocal matrices based on the geometric consistency index" , 2018, Comput. Ind. Eng..

[33]  Fanyong Meng,et al.  A new consistency concept for interval multiplicative preference relations , 2017, Appl. Soft Comput..

[34]  Vladislav V. Podinovski,et al.  Interval articulation of superiority and precise elicitation of priorities , 2007, Eur. J. Oper. Res..

[35]  Jana Krejcí,et al.  On additive consistency of interval fuzzy preference relations , 2017, Comput. Ind. Eng..

[36]  Fanyong Meng,et al.  Decision making with intuitionistic linguistic preference relations , 2019, Int. Trans. Oper. Res..

[37]  Bruce L. Golden,et al.  Linear programming models for estimating weights in the analytic hierarchy process , 2005, Comput. Oper. Res..

[38]  Jian Lin,et al.  Two new methods for deriving the priority vector from interval multiplicative preference relations , 2015, Inf. Fusion.

[39]  Zhou-Jing Wang,et al.  A note on "A goal programming model for incomplete interval multiplicative preference relations and its application in group decision-making" , 2015, Eur. J. Oper. Res..

[40]  M. T. Lamata,et al.  A new measure of consistency for positive reciprocal matrices , 2003 .