Correlation Coefficients of Hesitant Fuzzy Sets and Their Application Based on Fuzzy Measures

Abstract In this paper, several new correlation coefficients of hesitant fuzzy sets are defined, not taking into account the length of hesitant fuzzy elements and the arrangement of their possible values. To address the situations where the elements in a set are correlative, several Shapley weighted correlation coefficients are presented. It is worth noting that the Shapley weighted correlation coefficient can be seen as an extension of the correlation coefficient based on additive measures. When the weight information of attributes is partly known, models for the optimal fuzzy measure on an attribute set are constructed. After that, an approach to clustering analysis and decision making under hesitant fuzzy environment with incomplete weight information and interactive conditions is developed. Meanwhile, corresponding examples are provided to verify the practicality and feasibility of the new approaches.

[1]  Yi-Chung Hu,et al.  Constructing a Corporate Social Responsibility Fund Using Fuzzy Multiple Criteria Decision Making , 2011 .

[2]  Patryk A. Laurent.  A Neural Mechanism for Reward Discounting: Insights from Modeling Hippocampal–Striatal Interactions , 2012, Cognitive Computation.

[3]  Hamid R. Ronagh,et al.  Correlation between seismic parameters of far-fault motions and damage indices of low-rise reinforced concrete frames , 2014 .

[4]  Shyi-Ming Chen,et al.  Autocratic decision making using group recommendations based on the OWA operator and correlation coefficients , 2015, Inf. Sci..

[5]  Guiwu Wei,et al.  Hesitant Fuzzy Choquet Integral Aggregation Operators and Their Applications to Multiple Attribute Decision Making , 2012 .

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

[7]  S. S. Melnik,et al.  Entropy and long-range correlations in DNA sequences , 2014, Comput. Biol. Chem..

[8]  Fanyong Meng,et al.  Interval-valued intuitionistic fuzzy multi-criteria group decision making based on cross entropy and 2-additive measures , 2015, Soft Comput..

[9]  Zeshui Xu,et al.  Choquet integrals of weighted intuitionistic fuzzy information , 2010, Inf. Sci..

[10]  Petr Ekel,et al.  A flexible consensus scheme for multicriteria group decision making under linguistic assessments , 2010, Inf. Sci..

[11]  Fanyong Meng,et al.  Entropy and similarity measure of Atanassov’s intuitionistic fuzzy sets and their application to pattern recognition based on fuzzy measures , 2014, Pattern Analysis and Applications.

[12]  Qiang Zhang,et al.  The induced generalized interval-valued intuitionistic fuzzy hybrid Shapley averaging operator and its application in decision making , 2013, Knowl. Based Syst..

[13]  Lotfi A. Zadeh,et al.  Outline of a New Approach to the Analysis of Complex Systems and Decision Processes , 1973, IEEE Trans. Syst. Man Cybern..

[14]  Na Chen,et al.  Some Hesitant Fuzzy Aggregation Operators with Their Application in Group Decision Making , 2011, Group Decision and Negotiation.

[15]  Zeshui Xu,et al.  Hesitant fuzzy entropy and cross‐entropy and their use in multiattribute decision‐making , 2012, Int. J. Intell. Syst..

[16]  Andrzej Cichocki,et al.  L1-Regularized Multiway Canonical Correlation Analysis for SSVEP-Based BCI , 2013, IEEE Transactions on Neural Systems and Rehabilitation Engineering.

[17]  Cengiz Kahraman,et al.  Fuzzy multiple criteria forestry decision making based on an integrated VIKOR and AHP approach , 2011, Expert Syst. Appl..

[18]  Zeshui Xu,et al.  Distance and similarity measures for hesitant fuzzy sets , 2011, Inf. Sci..

[19]  M. Grabisch.  Fuzzy integral in multicriteria decision making , 1995 .

[20]  Qiang Zhang,et al.  Approaches to multiple-criteria group decision making based on interval-valued intuitionistic fuzzy Choquet integral with respect to the generalized λ-Shapley index , 2013, Knowl. Based Syst..

[21]  Qiang Zhang,et al.  Some uncertain generalized Shapley aggregation operators for multi-attribute group decision making , 2015, J. Intell. Fuzzy Syst..

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

[23]  Qiang Zhang,et al.  Multi-attribute decision analysis under a linguistic hesitant fuzzy environment , 2014, Inf. Sci..

[24]  Chunqiao Tan,et al.  Group decision making with linguistic preference relations with application to supplier selection , 2011, Expert Syst. Appl..

[25]  Zeshui Xu,et al.  Hesitant fuzzy information aggregation in decision making , 2011, Int. J. Approx. Reason..

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

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

[28]  R. Dorf,et al.  The Balanced Scorecard: Translating Strategy Into Action , 1997, Proceedings of the IEEE.

[29]  Xingyu Wang,et al.  Frequency Recognition in SSVEP-Based BCI using Multiset Canonical Correlation Analysis , 2013, Int. J. Neural Syst..

[30]  Jian Wu,et al.  The extended COWG operators and their application to multiple attributive group decision making problems with interval numbers , 2011 .

[31]  Zeshui Xu,et al.  Clustering algorithm for intuitionistic fuzzy sets , 2008, Inf. Sci..

[32]  Bing Pan,et al.  Speeding up digital image correlation computation using the integral image technique , 2015 .

[33]  Fanyong Meng,et al.  A hesitant fuzzy linguistic multi-granularity decision making model based on distance measures , 2015, J. Intell. Fuzzy Syst..

[34]  Chris J. Hinde,et al.  A new extension of fuzzy sets using rough sets: R-fuzzy sets , 2010, Inf. Sci..

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

[36]  W.-L. Gau,et al.  Vague sets , 1993, IEEE Trans. Syst. Man Cybern..

[37]  Zhang Yong,et al.  High-efficiency and high-accuracy digital image correlation for three-dimensional measurement , 2015 .

[38]  Xiaohong Chen,et al.  Intuitionistic fuzzy Choquet integral operator for multi-criteria decision making , 2010, Expert Syst. Appl..

[39]  Robert C. Wolpert,et al.  A Review of the , 1985 .

[40]  Guiwu Wei,et al.  Hesitant fuzzy prioritized operators and their application to multiple attribute decision making , 2012, Knowl. Based Syst..

[41]  Chunqiao Tan,et al.  Some interval-valued intuitionistic uncertain linguistic hybrid Shapley operators , 2014 .

[42]  Hans-Jürgen Zimmermann,et al.  Fuzzy Set Theory - and Its Applications , 1985 .

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

[44]  Zhong-Zhong Jiang,et al.  Atanassov’s intuitionistic fuzzy Quasi-Choquet geometric operators and their applications to multicriteria decision making , 2014, Fuzzy Optimization and Decision Making.

[45]  L. S. Shapley,et al.  17. A Value for n-Person Games , 1953 .

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

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

[48]  Luis-Felipe Rodríguez,et al.  Development of Computational Models of Emotions for Autonomous Agents: A Review , 2014, Cognitive Computation.

[49]  Zeshui Xu,et al.  Uncertain linguistic aggregation operators based approach to multiple attribute group decision making under uncertain linguistic environment , 2004, Inf. Sci..

[50]  Peide Liu.  Some geometric aggregation operators based on interval intuitionistic uncertain linguistic variables and their application to group decision making , 2013 .

[51]  Amaury Lendasse,et al.  A Two-Stage Methodology Using K-NN and False-Positive Minimizing ELM for Nominal Data Classification , 2014, Cognitive Computation.

[52]  Dejian Yu,et al.  Multi-Criteria Decision Making Based on Choquet Integral under Hesitant Fuzzy Environment , 2011 .

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

[54]  Michael Smithson,et al.  Fuzzy Set Theory and Applications in Psychology , 1999 .

[55]  G. Wei,et al.  Extension of VIKOR method for decision making problem based on hesitant fuzzy set , 2013 .

[56]  Chunqiao Tan,et al.  Generalized intuitionistic fuzzy geometric aggregation operator and its application to multi-criteria group decision making , 2011, Soft Comput..

[57]  Vitaly Kober,et al.  Pattern recognition with composite correlation filters designed with multi-objective combinatorial optimization , 2015 .

[58]  Zeshui Xu,et al.  Hesitant fuzzy geometric Bonferroni means , 2012, Inf. Sci..