Multiplicative consistency analysis for q‐rung orthopair fuzzy preference relation

The q‐rung orthopair fuzzy set is characterized by membership and nonmembership functions, and the sum of the qth power of them is less than or equal to one. Since it releases the constraints existed in both intuitionistic fuzzy set and Pythagorean fuzzy set, it has wide applications in real cases. However, so far, there is little research on the multiplicative consistency of q‐rung orthopair fuzzy preference relation (q‐ROFPR). To fill this vacancy, this paper provides a detailed analysis on the multiplicative consistency of q‐ROFPR. First, we investigate the concept of multiplicative consistent q‐ROFPR and its properties. Subsequently, two goal programming models are proposed to derive the priorities from individual and group q‐ROFPRs, respectively. After that, a novel consistency‐improving algorithm for q‐ROFPR and a weight‐generating method for decision‐makers are discussed in detail, based on which, a novel group decision‐making method is proposed. Finally, a case study concerning the evaluation of rehabilitation program selection is given to illustrate the applicability of the proposed method. The effectiveness and superiority of the proposed method are verified by comparing it with some existing methods.

[1]  Enrique Herrera-Viedma,et al.  Hospitality brand management by a score-based q-rung orthopair fuzzy V.I.K.O.R. method integrated with the best worst method , 2019, Economic Research-Ekonomska Istraživanja.

[2]  Zeshui Xu,et al.  Consistency-based risk assessment with probabilistic linguistic preference relation , 2016, Appl. Soft Comput..

[3]  Hui Gao,et al.  Some q‐rung orthopair fuzzy Heronian mean operators in multiple attribute decision making , 2018, Int. J. Intell. Syst..

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

[5]  Zhou-Jing Wang.  Derivation of intuitionistic fuzzy weights based on intuitionistic fuzzy preference relations , 2013 .

[6]  P. London.  Injury , 1969, Definitions.

[7]  Ronald R. Yager,et al.  Generalized Orthopair Fuzzy Sets , 2017, IEEE Transactions on Fuzzy Systems.

[8]  V. Dietz,et al.  Rehabilitation of locomotion after spinal cord injury. , 2010, Restorative neurology and neuroscience.

[9]  Peng Wang,et al.  Some q‐Rung Orthopair Fuzzy Aggregation Operators and their Applications to Multiple‐Attribute Decision Making , 2018, Int. J. Intell. Syst..

[10]  E. Triantaphyllou,et al.  Ranking irregularities when evaluating alternatives by using some ELECTRE methods , 2008 .

[11]  M. Byrnes,et al.  Patient-focused goal planning process and outcome after spinal cord injury rehabilitation: quantitative and qualitative audit , 2012, Clinical rehabilitation.

[12]  Hideo Tanaka,et al.  Interval priorities in AHP by interval regression analysis , 2004, Eur. J. Oper. Res..

[13]  Zeshui Xu,et al.  Priorities of Intuitionistic Fuzzy Preference Relation Based on Multiplicative Consistency , 2014, IEEE Transactions on Fuzzy Systems.

[14]  Zhou-Jing Wang,et al.  Goal programming approaches to deriving interval weights based on interval fuzzy preference relations , 2012, Inf. Sci..

[15]  Harish Garg,et al.  Exponential operation and aggregation operator for q‐rung orthopair fuzzy set and their decision‐making method with a new score function , 2018, Int. J. Intell. Syst..

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

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

[18]  J. Reinhardt,et al.  Evaluation of functional outcomes of physical rehabilitation and medical complications in spinal cord injury victims of the Sichuan earthquake. , 2012, Journal of rehabilitation medicine.

[19]  Huchang Liao,et al.  Additive consistency‐based priority‐generating method of q‐rung orthopair fuzzy preference relation , 2019, Int. J. Intell. Syst..

[20]  Krassimir T. Atanassov,et al.  Intuitionistic fuzzy sets , 1986 .

[21]  Zeshui Xu,et al.  A survey of decision-making methods with probabilistic linguistic information: bibliometrics, preliminaries, methodologies, applications and future directions , 2020, Fuzzy Optim. Decis. Mak..

[22]  A. Curt,et al.  Rehabilitation in Spine and Spinal Cord Trauma , 2010, Spine.

[23]  Peide Liu,et al.  Some q‐Rung Orthopai Fuzzy Bonferroni Mean Operators and Their Application to Multi‐Attribute Group Decision Making , 2018, Int. J. Intell. Syst..

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

[25]  Francisco Herrera,et al.  Overview of Hesitant Linguistic Preference Relations for Representing Cognitive Complex Information: Where We Stand and What Is Next , 2019, Cognitive Computation.

[26]  Wen Sheng Du,et al.  Minkowski‐type distance measures for generalized orthopair fuzzy sets , 2018, Int. J. Intell. Syst..

[27]  Roberto Carone,et al.  Towards personalized care for persons with spinal cord injury: a study on patients' perceptions , 2011, The journal of spinal cord medicine.

[28]  Chunqiao Tan,et al.  Multiplicative consistency analysis for interval fuzzy preference relations: A comparative study , 2017 .

[29]  Cheng Liang,et al.  A Novel Method to Detect Functional microRNA Regulatory Modules by Bicliques Merging , 2016, IEEE/ACM Transactions on Computational Biology and Bioinformatics.

[30]  Peide Liu,et al.  Multiple attribute decision‐making method for dealing with heterogeneous relationship among attributes and unknown attribute weight information under q‐rung orthopair fuzzy environment , 2018, Int. J. Intell. Syst..

[31]  Zeshui Xu,et al.  Intuitionistic preference relations and their application in group decision making , 2007, Inf. Sci..

[32]  Zeshui Xu,et al.  Consistency of interval fuzzy preference relations in group decision making , 2011, Appl. Soft Comput..

[33]  M. G. Maioli,et al.  Evaluation of an occupational therapy program for patients with spinal cord injury , 2008, Spinal Cord.

[34]  P. New,et al.  Survival after rehabilitation for spinal cord injury due to tumor: a 12-year retrospective study , 2011, Journal of Neuro-Oncology.

[35]  Zeshui Xu,et al.  A least deviation method to obtain a priority vector of a fuzzy preference relation , 2005, Eur. J. Oper. Res..

[36]  Ronald R. Yager,et al.  Pythagorean Membership Grades in Multicriteria Decision Making , 2014, IEEE Transactions on Fuzzy Systems.

[37]  Shu-Ping Wan,et al.  Mathematical programming methods for consistency and consensus in group decision making with intuitionistic fuzzy preference relations , 2016, Knowl. Based Syst..