Intuitionistic fuzzy linguistic clustering algorithm based on a new correlation coefficient for intuitionistic fuzzy linguistic information

2018 ◽  
Vol 22 (3) ◽  
pp. 907-918
Author(s):  
Sidong Xian ◽  
Yubo Yin ◽  
Yixin Liu ◽  
Meilin You ◽  
Kun Wang
Keyword(s):  
Correlation Coefficient ◽  
Clustering Algorithm ◽  
Linguistic Information ◽  
Intuitionistic Fuzzy ◽  
New Correlation ◽  
Fuzzy Linguistic

scholarly journals Grey Relational Bidirectional Projection Method for Multicriteria Decision Making with Hesitant Intuitionistic Fuzzy Linguistic Information

2018 ◽  
Vol 2018 ◽  
pp. 1-12 ◽  
Author(s):  
Yuqi Zang ◽  
Xiaodong Zhao ◽  
Shiyong Li ◽  
Adnan Nazir
Keyword(s):  
Decision Making ◽  
Projection Method ◽  
Multicriteria Decision Making ◽  
Comparison Method ◽  
Distance Measures ◽  
Linguistic Information ◽  
Multicriteria Decision ◽  
Intuitionistic Fuzzy ◽  
Grey Relational ◽  
Fuzzy Linguistic

We investigate a novel approach for multicriteria decision making (MCDM) with hesitant intuitionistic fuzzy linguistic information. To compare the hesitant intuitionistic fuzzy linguistic term sets (HIFLTSs), we propose a comparison method of HIFLTSs. A family of distance measures of HIFLTSs is developed. After that, we propose the grey relational bidirectional projection method based on the proposed comparison method and distance measures of IVHFLNs for dealing with MCDM problems. Furthermore, we establish a nonlinear optimization model to obtain the weight vector of criteria. Finally, an illustrative example is given to demonstrate the effectiveness and flexibility of the proposed approach.

INNER PRODUCT BASED ENTROPY IN THE INTUITIONISTIC FUZZY SETTING

2006 ◽  
Vol 14 (03) ◽  
pp. 351-366 ◽  
Author(s):  
IOANNIS K. VLACHOS ◽  
GEORGE D. SERGIADIS
Keyword(s):  
Fuzzy Sets ◽  
Correlation Coefficient ◽  
Intuitionistic Fuzzy Sets ◽  
Inner Product ◽  
Entropy Measure ◽  
Entropy Formula ◽  
Intuitionistic Fuzzy ◽  
New Correlation ◽  
Fuzzy Setting ◽  
Fuzzy Vector

In this paper, an entropy formula for intuitionistic fuzzy sets is presented. The notion of the intuitionistic fuzzy vector is introduced and an entropy measure is derived based on the normalized inner product between intuitionistic fuzzy vectors in the unit intuitionistic fuzzy cube. Some considerations regarding the geometrical representations of intuitionistic fuzzy sets are also stated and a connection between the different notions of entropy in the intuitionistic fuzzy setting is established. Finally, the relation of the proposed entropy measure to the concepts of correlation and informational energy for intuitionistic fuzzy sets is revealed and a new correlation coefficient is introduced.

scholarly journals Hesitant Fuzzy Linguistic Agglomerative Hierarchical Clustering Algorithm and Its Application in Judicial Practice

Mathematics ◽  
2021 ◽  
Vol 9 (4) ◽  
pp. 370
Author(s):  
Shuangsheng Wu ◽  
Jie Lin ◽  
Zhenyu Zhang ◽  
Yushu Yang
Keyword(s):  
Hierarchical Clustering ◽  
Clustering Algorithm ◽  
Clustering Algorithms ◽  
Agglomerative Hierarchical Clustering ◽  
Research Gaps ◽  
Judicial Practice ◽  
Linguistic Term ◽  
Clustering Effect ◽  
Hierarchical Clustering Algorithm ◽  
Fuzzy Linguistic

The fuzzy clustering algorithm has become a research hotspot in many fields because of its better clustering effect and data expression ability. However, little research focuses on the clustering of hesitant fuzzy linguistic term sets (HFLTSs). To fill in the research gaps, we extend the data type of clustering to hesitant fuzzy linguistic information. A kind of hesitant fuzzy linguistic agglomerative hierarchical clustering algorithm is proposed. Furthermore, we propose a hesitant fuzzy linguistic Boole matrix clustering algorithm and compare the two clustering algorithms. The proposed clustering algorithms are applied in the field of judicial execution, which provides decision support for the executive judge to determine the focus of the investigation and the control. A clustering example verifies the clustering algorithm’s effectiveness in the context of hesitant fuzzy linguistic decision information.

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