Correlation and correlation coefficient of generalized orthopair fuzzy sets

Generalized orthopair fuzzy sets are extensions of ordinary fuzzy sets by relaxing restrictions on the degrees of support for and support against. Correlation analysis is to measure the statistical relationships between two samples or variables. In this paper, we propose a function measuring the interrelation of two q ‐rung orthopair fuzzy sets, whose range is the unit interval [ 0 , 1 ] . First, the correlation and correlation coefficient of q ‐rung orthopair membership grades are presented, and their basic properties are investigated. Second, these concepts are extended to q ‐rung orthopair fuzzy sets on discrete universes. Then, we discuss their applications in cluster analysis under generalized orthopair fuzzy environments. And, a real‐world problem involving the evaluation of companies is used to illustrate the detailed processes of the clustering algorithm. Finally, we introduce the correlation and correlation coefficient of q ‐rung orthopair fuzzy sets on both bounded and unbounded continuous universes and provide some numerical examples to substantiate such arguments.

[1]  Dug Hun Hong,et al.  Correlation of intuitionistic fuzzy sets in probability spaces , 1995, Fuzzy Sets Syst..

[2]  Krassimir T. Atanassov,et al.  On Intuitionistic Fuzzy Sets Theory , 2012, Studies in Fuzziness and Soft Computing.

[3]  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..

[4]  S. Tyagi.  Correlation coefficient of dual hesitant fuzzy sets and its applications , 2015 .

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

[6]  Na Chen,et al.  Correlation coefficients of hesitant fuzzy sets and their applications to clustering analysis , 2013 .

[7]  George J. Klir,et al.  Fuzzy sets and fuzzy logic - theory and applications , 1995 .

[8]  Naif Alajlan,et al.  Aspects of generalized orthopair fuzzy sets , 2018, Int. J. Intell. Syst..

[9]  Bidyut Baran Chaudhuri,et al.  On correlation between two fuzzy sets , 2001, Fuzzy Sets Syst..

[10]  Jun Ye,et al.  Cosine similarity measures for intuitionistic fuzzy sets and their applications , 2011, Math. Comput. Model..

[11]  Zeshui Xu,et al.  Correlation coefficients of hesitant multiplicative sets and their applications in decision making and clustering analysis , 2017, Appl. Soft Comput..

[12]  B. Farhadinia,et al.  Correlation for Dual Hesitant Fuzzy Sets and Dual Interval‐Valued Hesitant Fuzzy Sets , 2014, Int. J. Intell. Syst..

[13]  Harish Garg,et al.  A robust correlation coefficient measure of dual hesitant fuzzy soft sets and their application in decision making , 2018, Eng. Appl. Artif. Intell..

[14]  Harish Garg,et al.  A Novel Correlation Coefficients between Pythagorean Fuzzy Sets and Its Applications to Decision‐Making Processes , 2016, Int. J. Intell. Syst..

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

[16]  K. Atanassov,et al.  Interval-Valued Intuitionistic Fuzzy Sets , 2019, Studies in Fuzziness and Soft Computing.

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

[18]  Robert LIN,et al.  NOTE ON FUZZY SETS , 2014 .

[19]  Muhammad Irfan Ali,et al.  Another view on q‐rung orthopair fuzzy sets , 2018, Int. J. Intell. Syst..

[20]  Ding-An Chiang,et al.  Correlation of fuzzy sets , 1999, Fuzzy Sets Syst..

[21]  Zheng Zhou,et al.  Synthetic Correlation Coefficient Between Hesitant Fuzzy Sets with Applications , 2018, International Journal of Fuzzy Systems.

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

[23]  Fanyong Meng,et al.  Correlation Coefficients of Hesitant Fuzzy Sets and Their Application Based on Fuzzy Measures , 2015, Cognitive Computation.

[24]  Wen-Liang Hung,et al.  Using Statistical Viewpoint in Developing Correlation of Intuitionistic Fuzzy Sets , 2001, Int. J. Uncertain. Fuzziness Knowl. Based Syst..

[25]  Shyi-Ming Chen,et al.  Multiple-Attribute Group Decision-Making Based on q-Rung Orthopair Fuzzy Power Maclaurin Symmetric Mean Operators , 2020, IEEE Transactions on Systems, Man, and Cybernetics: Systems.

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

[27]  Jin-Han Park,et al.  Correlation coefficient of interval-valued intuitionistic fuzzy sets and its application to multiple attribute group decision making problems , 2009, Math. Comput. Model..

[28]  Lotfi A. Zadeh,et al.  The Concepts of a Linguistic Variable and its Application to Approximate Reasoning , 1975 .

[29]  Janusz Kacprzyk,et al.  Correlation of Intuitionistic Fuzzy Sets , 2010, IPMU.

[30]  Zeshui Xu,et al.  Qualitative decision making with correlation coefficients of hesitant fuzzy linguistic term sets , 2015, Knowl. Based Syst..

[31]  Zeshui Xu,et al.  Extension of TOPSIS to Multiple Criteria Decision Making with Pythagorean Fuzzy Sets , 2014, Int. J. Intell. Syst..

[32]  Chen Wang,et al.  Correlation Coefficients of Interval‐Valued Hesitant Fuzzy Sets and Their Application Based on the Shapley Function , 2016, Int. J. Intell. Syst..

[33]  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..

[34]  Peide Liu,et al.  Correlation coefficient of single-valued neutrosophic hesitant fuzzy sets and its applications in decision making , 2017, Neural Computing and Applications.

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

[36]  Vicenç Torra,et al.  Hesitant fuzzy sets , 2010, Int. J. Intell. Syst..

[37]  Jun Ye.  Correlation coefficient of dual hesitant fuzzy sets and its application to multiple attribute decision making , 2014 .

[38]  Ronald R. Yager,et al.  Pythagorean Membership Grades, Complex Numbers, and Decision Making , 2013, Int. J. Intell. Syst..

[39]  Lotfi A. Zadeh,et al.  The concept of a linguistic variable and its application to approximate reasoning-III , 1975, Inf. Sci..

[40]  Naif Alajlan,et al.  Approximate reasoning with generalized orthopair fuzzy sets , 2017, Inf. Fusion.

[41]  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..

[42]  Zeshui Xu,et al.  Hesitant Fuzzy Sets Theory , 2014, Studies in Fuzziness and Soft Computing.

[43]  Zeshui Xu,et al.  On Correlation Measures of Intuitionistic Fuzzy Sets , 2006, IDEAL.

[44]  Zeshui Xu,et al.  Intuitionistic Fuzzy Aggregation Operators , 2007, IEEE Transactions on Fuzzy Systems.

[45]  Humberto Bustince,et al.  Correlation of interval-valued intuitionistic fuzzy sets , 1995, Fuzzy Sets Syst..

[46]  Tadeusz Gerstaenkorn,et al.  Correlation of intuitionistic fuzzy sets , 1991 .

[47]  Peng Wang,et al.  Multiple-Attribute Decision-Making Based on Archimedean Bonferroni Operators of q-Rung Orthopair Fuzzy Numbers , 2019, IEEE Transactions on Fuzzy Systems.

[48]  H. B. Mitchell.  A correlation coefficient for intuitionistic fuzzy sets , 2004, Int. J. Intell. Syst..

[49]  Jong-Wuu Wu,et al.  Correlation of intuitionistic fuzzy sets by centroid method , 2002, Inf. Sci..

[50]  Zeshui Xu,et al.  On distance and correlation measures of hesitant fuzzy information , 2011, Int. J. Intell. Syst..

[51]  Zeshui Xu,et al.  Novel correlation coefficients between hesitant fuzzy sets and their application in decision making , 2015, Knowl. Based Syst..

[52]  Zeshui Xu,et al.  Some geometric aggregation operators based on intuitionistic fuzzy sets , 2006, Int. J. Gen. Syst..