Determination of Pattern Recognition Problems based on a Pythagorean Fuzzy Correlation Measure from Statistical Viewpoint

By considering all the three parameters describing Pythagorean fuzzy set, we introduce a new technique of computing correlation coefficient between Pythagorean fuzzy sets from statistical perspective. The correlation coefficient value obtain via this technique shows strength of correlation between the Pythagorean fuzzy sets and indicates whether the Pythagorean fuzzy sets under consideration are related negatively or positively in contrast to other existing correlation coefficient approaches in Pythagorean fuzzy context, which only assess the strength of relationship. Certain numerical examples are considered to ascertain the authenticity of this method over similar techniques studied in intuitionistic/Pythagorean fuzzy contexts. Some pattern recognition problems are resolved with the aid of the new technique. For higher productivity sake, this technique could be approached from an object-oriented perspective.

[1]  Yuming Feng,et al.  Pattern Recognition Based on an Improved Szmidt and Kacprzyk's Correlation Coefficient in Pythagorean Fuzzy Environment , 2020, ISNN.

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

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

[4]  P. A. Ejegwa,et al.  Improved intuitionistic fuzzy composite relation and its application to medical diagnostic process , 2019, Notes on Intuitionistic Fuzzy Sets.

[5]  Harish Garg,et al.  A robust correlation coefficient measure of complex intuitionistic fuzzy sets and their applications in decision-making , 2018, Applied Intelligence.

[6]  Ranjit Biswas,et al.  An application of intuitionistic fuzzy sets in medical diagnosis , 2001, Fuzzy Sets Syst..

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

[8]  P. A. Ejegwa,et al.  New similarity measures for Pythagorean fuzzy sets with applications , 2020, International Journal of Fuzzy Computation and Modelling.

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

[10]  Chunhai Yu.  Correlation of fuzzy numbers , 1993 .

[11]  Harish Garg,et al.  A novel correlation coefficient of intuitionistic fuzzysets based on the connection number of set pair analysis and its application , 2017 .

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

[13]  Nguyen Xuan Thao,et al.  A new correlation coefficient of the Pythagorean fuzzy sets and its applications , 2019, Soft Computing.

[14]  P. A. Ejegwa.  Improved composite relation for pythagorean fuzzy sets and its application to medical diagnosis , 2019, Granular Computing.

[15]  Surender Singh,et al.  On some correlation coefficients in Pythagorean fuzzy environment with applications , 2020, Int. J. Intell. Syst..

[16]  P. A. Ejegwa.  Pythagorean fuzzy set and its application in career placements based on academic performance using max–min–max composition , 2019, Complex & Intelligent Systems.

[17]  Nguyen Xuan Thao,et al.  A new correlation coefficient of the intuitionistic fuzzy sets and its application , 2018, J. Intell. Fuzzy Syst..

[18]  Jin-Han Park,et al.  Correlation Coefficient between Intuitionistic Fuzzy Sets , 2009, ICFIE.

[19]  Weiqiong Wang,et al.  Distance measure between intuitionistic fuzzy sets , 2005, Pattern Recognit. Lett..

[20]  P. A. Ejegwa.  Distance and similarity measures for Pythagorean fuzzy sets , 2018, Granular Computing.

[21]  Janusz Kacprzyk,et al.  Medical Diagnostic Reasoning Using a Similarity Measure for Intuitionistic Fuzzy Sets , 2004 .

[22]  P. A. Ejegwa,et al.  Distances between intuitionistic fuzzy sets of second type with application to diagnostic medicine , 2019, Notes on Intuitionistic Fuzzy Sets.

[23]  P. A. Ejegwa,et al.  Intuitionistic fuzzy statistical correlation algorithm with applications to multicriteria‐based decision‐making processes , 2020, Int. J. Intell. Syst..

[24]  Shyi-Ming Chen,et al.  Group Decision Making Based on Heronian Aggregation Operators of Intuitionistic Fuzzy Numbers , 2017, IEEE Transactions on Cybernetics.

[25]  Harish Garg,et al.  Novel correlation coefficients under the intuitionistic multiplicative environment and their applications to decision-making process , 2017 .

[26]  Janusz Kacprzyk,et al.  Intuitionistic Fuzzy Sets in some Medical Applications , 2001, Fuzzy Days.

[27]  Diyar Akay,et al.  A biparametric similarity measure on intuitionistic fuzzy sets with applications to pattern recognition , 2014, Inf. Sci..

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

[29]  P. A. Ejegwa,et al.  A pythagorean fuzzy algorithm embedded with a new correlation measure and its application in diagnostic processes , 2020 .

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

[31]  Lingling Mu,et al.  A new correlation measure of the intuitionistic fuzzy sets , 2016, J. Intell. Fuzzy Syst..

[32]  Ronald R. Yager,et al.  Properties and Applications of Pythagorean Fuzzy Sets , 2016, Imprecision and Uncertainty in Information Representation and Processing.

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

[34]  P. A. Ejegwa.  Modified Zhang and Xu’s distance measure for Pythagorean fuzzy sets and its application to pattern recognition problems , 2019, Neural Computing and Applications.

[35]  P. A. Ejegwa.  Generalized triparametric correlation coefficient for Pythagorean fuzzy sets with application to MCDM problems , 2020, Granular Computing.

[36]  C. A. Murthy,et al.  Correlation between two fuzzy membership functions , 1985 .

[37]  Harish Garg,et al.  TOPSIS method based on correlation coefficient for solving decision-making problems with intuitionistic fuzzy soft set information , 2020 .

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

[39]  Xiaolu Zhang,et al.  A Novel Approach Based on Similarity Measure for Pythagorean Fuzzy Multiple Criteria Group Decision Making , 2016, Int. J. Intell. Syst..

[40]  Shiping Wen,et al.  Some new Pythagorean fuzzy correlation techniques via statistical viewpoint with applications to decision-making problems , 2021, J. Intell. Fuzzy Syst..

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

[42]  Florentin Smarandache,et al.  An intuitionistic fuzzy clustering algorithm based on a new correlation coefficient with application in medical diagnosis , 2019, J. Intell. Fuzzy Syst..

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

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

[45]  P. A. Ejegwa,et al.  Novel distance measures for Pythagorean fuzzy sets with applications to pattern recognition problems , 2019, Granular Computing.

[46]  Wenyi Zeng,et al.  Distance and similarity measures of Pythagorean fuzzy sets and their applications to multiple criteria group decision making , 2018, Int. J. Intell. Syst..

[47]  George A. Papakostas,et al.  A novel distance measure of intuitionistic fuzzy sets and its application to pattern recognition problems , 2012, Int. J. Intell. Syst..