Managing incomplete preferences and consistency improvement in hesitant fuzzy linguistic preference relations with applications in group decision making

Abstract Incomplete hesitant fuzzy linguistic preference relations (IHFLPRs) are useful in decision making which combine advantages of hesitant fuzzy linguistic term sets and incomplete fuzzy preference relations. The existing researches on IHFLPRs pay little attention to missing elements, and the consistency improvement processes change original information greatly. Inspired by the worst and the best consistency indexes of hesitant fuzzy linguistic preference relations, this paper constructs several optimization models to calculate the missing elements of IHFLPRs. As a result, a complete hesitant fuzzy linguistic preference relation is obtained. Furthermore, an algorithm is introduced to improve the additive consistency of the hesitant fuzzy linguistic preference relation to an acceptable level. Finally a group decision making model based on IHFLPRs is introduced and an example is presented.

[1]  Vicenç Torra,et al.  On hesitant fuzzy sets and decision , 2009, 2009 IEEE International Conference on Fuzzy Systems.

[2]  V. Torra,et al.  A framework for linguistic logic programming , 2010 .

[3]  Enrique Herrera-Viedma,et al.  Average-case consistency measurement and analysis of interval-valued reciprocal preference relations , 2016, Knowl. Based Syst..

[4]  Luis Martínez-López,et al.  Modelling experts’ attitudes in group decision making , 2012, Soft Computing.

[5]  Francisco Herrera,et al.  A position and perspective analysis of hesitant fuzzy sets on information fusion in decision making. Towards high quality progress , 2016, Inf. Fusion.

[6]  Zhiming Zhang,et al.  Deriving the priority weights from incomplete hesitant fuzzy preference relations based on multiplicative consistency , 2016, Appl. Soft Comput..

[7]  Enrique Herrera-Viedma,et al.  Consensus Building for the Heterogeneous Large-Scale GDM With the Individual Concerns and Satisfactions , 2018, IEEE Transactions on Fuzzy Systems.

[8]  Luis Martínez-López,et al.  Integration of a Consistency Control Module within a Consensus Model , 2008, Int. J. Uncertain. Fuzziness Knowl. Based Syst..

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

[10]  Francisco Herrera,et al.  Connecting the linguistic hierarchy and the numerical scale for the 2-tuple linguistic model and its use to deal with hesitant unbalanced linguistic information , 2016, Inf. Sci..

[11]  Yin-Feng Xu,et al.  Consistency and consensus measures for linguistic preference relations based on distribution assessments , 2014, Inf. Fusion.

[12]  Francisco Herrera,et al.  Consistency of hesitant fuzzy linguistic preference relations: An interval consistency index , 2018, Inf. Sci..

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

[14]  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).

[15]  Yejun Xu,et al.  Consistency and Consensus Models with Local Adjustment Strategy for Hesitant Fuzzy Linguistic Preference Relations , 2018, Int. J. Fuzzy Syst..

[16]  Zhibin Wu,et al.  A consensus model for large-scale group decision making with hesitant fuzzy information and changeable clusters , 2018, Inf. Fusion.

[17]  Yin-Feng Xu,et al.  Linear optimization modeling of consistency issues in group decision making based on fuzzy preference relations , 2012, Expert Syst. Appl..

[18]  Yejun Xu,et al.  Logarithmic least squares method to priority for group decision making with incomplete fuzzy preference relations , 2013 .

[19]  Francisco Herrera,et al.  Hesitant Fuzzy Linguistic Term Sets for Decision Making , 2012, IEEE Transactions on Fuzzy Systems.

[20]  Francisco Herrera,et al.  A Consensus Model for Group Decision Making With Incomplete Fuzzy Preference Relations , 2007, IEEE Transactions on Fuzzy Systems.

[21]  Zhibin Wu,et al.  Possibility Distribution-Based Approach for MAGDM With Hesitant Fuzzy Linguistic Information , 2016, IEEE Transactions on Cybernetics.

[22]  Xinwang Liu,et al.  Orness and parameterized RIM quantifier aggregation with OWA operators: A summary , 2008, Int. J. Approx. Reason..

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

[24]  Yejun Xu,et al.  A consensus model for hesitant fuzzy preference relations and its application in water allocation management , 2017, Appl. Soft Comput..

[25]  Zeshui Xu,et al.  Consistency Measures for Hesitant Fuzzy Linguistic Preference Relations , 2014, IEEE Transactions on Fuzzy Systems.

[26]  Francisco Herrera,et al.  A web based consensus support system for group decision making problems and incomplete preferences , 2010, Inf. Sci..

[27]  R. Yager.  Quantifier guided aggregation using OWA operators , 1996, Int. J. Intell. Syst..

[28]  Yejun Xu,et al.  A chi-square method for priority derivation in group decision making with incomplete reciprocal preference relations , 2015, Inf. Sci..

[29]  Luis Martínez-López,et al.  An attitude-driven web consensus support system for heterogeneous group decision making , 2013, Expert systems with applications.

[30]  Yejun Xu,et al.  Missing values estimation and consensus building for incomplete hesitant fuzzy preference relations with multiplicative consistency , 2018, Int. J. Comput. Intell. Syst..

[31]  Francisco Herrera,et al.  Personalized individual semantics based on consistency in hesitant linguistic group decision making with comparative linguistic expressions , 2018, Knowl. Based Syst..

[32]  Zaiwu Gong,et al.  Least-square method to priority of the fuzzy preference relations with incomplete information , 2008, Int. J. Approx. Reason..

[33]  Bowen Zhang,et al.  Reaching a consensus with minimum adjustment in MAGDM with hesitant fuzzy linguistic term sets , 2018, Inf. Fusion.

[34]  Zhiming Zhang,et al.  On the use of multiplicative consistency in hesitant fuzzy linguistic preference relations , 2014, Knowl. Based Syst..

[35]  Yejun Xu,et al.  Deriving the priority weights from incomplete hesitant fuzzy preference relations in group decision making , 2016, Knowl. Based Syst..

[36]  Francisco Herrera,et al.  Hesitant Fuzzy Sets: State of the Art and Future Directions , 2014, Int. J. Intell. Syst..

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

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

[39]  Luis Martínez-López,et al.  Personalized individual semantics in computing with words for supporting linguistic group decision making. An application on consensus reaching , 2017, Inf. Fusion.

[40]  Jun Hu,et al.  A group decision-making model based on incomplete comparative expressions with hesitant linguistic terms , 2017, Appl. Soft Comput..

[41]  Hongbin Liu,et al.  On Improving the Additive Consistency of the Fuzzy Preference Relations Based on Comparative Linguistic Expressions , 2014, Int. J. Intell. Syst..

[42]  Ronald R. Yager,et al.  On ordered weighted averaging aggregation operators in multicriteria decisionmaking , 1988, IEEE Trans. Syst. Man Cybern..

[43]  Xin Chen,et al.  Group decision making based on linguistic distributions and hesitant assessments: Maximizing the support degree with an accuracy constraint , 2018, Inf. Fusion.

[44]  Zhibin Wu,et al.  Managing consistency and consensus in group decision making with hesitant fuzzy linguistic preference relations , 2016 .

[45]  Francisco Herrera,et al.  A rational consensus model in group decision making using linguistic assessments , 1997, Fuzzy Sets Syst..

[46]  Wei Zhou,et al.  Probability Calculation and Element Optimization of Probabilistic Hesitant Fuzzy Preference Relations Based on Expected Consistency , 2018, IEEE Transactions on Fuzzy Systems.

[47]  Yejun Xu,et al.  Eigenvector method, consistency test and inconsistency repairing for an incomplete fuzzy preference relation , 2013 .

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

[49]  Chonghui Guo,et al.  On priority weights and consistency for incomplete hesitant fuzzy preference relations , 2017, Knowl. Based Syst..

[50]  Zhen Zhang,et al.  Additive consistency analysis and improvement for hesitant fuzzy preference relations , 2018, Expert Syst. Appl..