scholarly journals The Intuitionistic Fuzzy Linguistic Cosine Similarity Measure and Its Application in Pattern Recognition

Complexity ◽  
2018 ◽  
Vol 2018 ◽  
pp. 1-11 ◽  
Author(s):  
Donghai Liu ◽  
Xiaohong Chen ◽  
Dan Peng
Keyword(s):  
Similarity Measure ◽  
Similarity Measures ◽  
Cosine Similarity ◽  
Intuitionistic Fuzzy ◽  
Linguistic Term ◽  
Cosine Similarity Measure ◽  
Linguistic Scale Function ◽  
Cosine Similarity Measures ◽  
Fuzzy Linguistic ◽  
Interval Valued

We propose the cosine similarity measures for intuitionistic fuzzy linguistic sets (IFLSs) and interval-valued intuitionistic fuzzy linguistic sets (IVIFLSs), which are expressed by the linguistic scale function based on the cosine function. Then, the weighted cosine similarity measure and the ordered weighted cosine similarity measure for IFLSs and IVIFLSs are introduced by taking into account the importance of each element, and the properties of the cosine similarity measures are also given. The main advantage of the proposed cosine similarity measures is that the decision-makers can flexibly select the linguistic scale function depending on the actual semantic situation. Finally, we present the application of the cosine similarity measures for intuitionistic fuzzy linguistic term sets and interval-valued intuitionistic fuzzy linguistic term sets to pattern recognition and medical diagnosis, and the existing cosine similarity measures are compared with the proposed cosine similarity measures by the illustrative example.

scholarly journals Interval-Valued Intuitionistic Fuzzy Ordered Weighted Cosine Similarity Measure and Its Application in Investment Decision-Making

Complexity ◽  
2017 ◽  
Vol 2017 ◽  
pp. 1-11 ◽  
Author(s):  
Donghai Liu ◽  
Xiaohong Chen ◽  
Dan Peng
Keyword(s):  
Decision Making ◽  
Similarity Measure ◽  
Investment Decision ◽  
Similarity Measures ◽  
Cosine Similarity ◽  
Weighted Averaging ◽  
Intuitionistic Fuzzy ◽  
Weighted Arithmetic ◽  
Cosine Similarity Measure ◽  
Interval Valued

We present the interval-valued intuitionistic fuzzy ordered weighted cosine similarity (IVIFOWCS) measure in this paper, which combines the interval-valued intuitionistic fuzzy cosine similarity measure with the generalized ordered weighted averaging operator. The main advantage of the IVIFOWCS measure provides a parameterized family of similarity measures, and the decision maker can use the IVIFOWCS measure to consider a lot of possibilities and select the aggregation operator in accordance with his interests. We have studied some of its main properties and particular cases such as the interval-valued intuitionistic fuzzy ordered weighted arithmetic cosine similarity (IVIFOWACS) measure and the interval-valued intuitionistic fuzzy maximum cosine similarity (IVIFMAXCS) measure. The IVIFOWCS measure not only is a generalization of some similarity measure, but also it can deal with the correlation of different decision matrices for interval-valued intuitionistic fuzzy values. Furthermore, we present an application of IVIFOWCS measure to the group decision-making problem. Finally the existing similarity measures are compared with the IVIFOWCS measure by an illustrative example.

scholarly journals The New Similarity Measure and Distance Measure of a Hesitant Fuzzy Linguistic Term Set Based on a Linguistic Scale Function

Symmetry ◽  
2018 ◽  
Vol 10 (9) ◽  
pp. 367 ◽  
Author(s):  
Donghai Liu ◽  
Yuanyuan Liu ◽  
Xiaohong Chen
Keyword(s):  
Similarity Measure ◽  
Distance Measure ◽  
Cosine Similarity ◽  
Scale Function ◽  
Linguistic Term ◽  
Euclidean Distance Measure ◽  
Order Preference ◽  
Cosine Similarity Measure ◽  
Linguistic Scale Function ◽  
Fuzzy Linguistic

The existing cosine similarity measure for hesitant fuzzy linguistic term sets (HFLTSs) has an impediment as it does not satisfy the axiom of similarity measure. Due to this disadvantage, a new similarity measure combining the existing cosine similarity measure and the Euclidean distance measure of HFLTSs is proposed, which is constructed based on a linguistic scale function; the related properties are also given. According to the relationship between the distance measure and the similarity measure, a corresponding distance measure between HFLTSs is obtained. Furthermore, we generalize the technique for order preference by similarity to an ideal solution (TOPSIS) method to the obtained distance measure of the HFLTSs. The principal advantages of the proposed method are that it cannot only effectively transform linguistic information in different semantic environments, but it can also avoid the shortcomings of existing the cosine similarity measure. Finally, a case study is conducted to illustrate the feasibility and effectiveness of the proposed method, which is compared to the existing methods.

scholarly journals Cosine Similarity Measure of Complex Fuzzy Sets and Robustness of Complex Fuzzy Connectives

2020 ◽  
Vol 2020 ◽  
pp. 1-9
Author(s):  
Wenping Guo ◽  
Lvqing Bi ◽  
Bo Hu ◽  
Songsong Dai
Keyword(s):  
Similarity Measure ◽  
Fuzzy Set ◽  
Fuzzy Inference ◽  
Similarity Measures ◽  
Cosine Similarity ◽  
Invariance Properties ◽  
Cosine Similarity Measure ◽  
Cosine Similarity Measures ◽  
Complex Valued ◽  
Fuzzy Connectives

Complex fuzzy set (CFS), as a generalization of fuzzy set (FS), is characterized by complex-valued membership degrees. By considering the complex-valued membership degree as a vector in the complex unit disk, we introduce the cosine similarity measures between CFSs. Then, we investigate some invariance properties of the cosine similarity measure. Finally, the cosine similarity measure is applied to measure the robustness of complex fuzzy connectives and complex fuzzy inference.

scholarly journals Cosine Similarity Measure between Hybrid Intuitionistic Fuzzy Sets and Its Application in Medical Diagnosis

2018 ◽  
Vol 2018 ◽  
pp. 1-7 ◽  
Author(s):  
Donghai Liu ◽  
Xiaohong Chen ◽  
Dan Peng
Keyword(s):  
Fuzzy Sets ◽  
Similarity Measure ◽  
Medical Diagnosis ◽  
Similarity Measures ◽  
Intuitionistic Fuzzy Sets ◽  
Cosine Similarity ◽  
Individual Decision ◽  
Intuitionistic Fuzzy ◽  
Cosine Similarity Measure ◽  
The Ideal

In this paper, a cosine similarity measure between hybrid intuitionistic fuzzy sets is proposed. The aim of the paper is to investigate the cosine similarity measure with hybrid intuitionistic fuzzy information and apply it to medical diagnosis. Firstly, we construct the cosine similarity measure between hybrid intuitionistic fuzzy sets, and the relevant properties are also discussed. In order to obtain a reasonable evaluation in group decision, the weight of experts under different attributes is determined by the projection of individual decision information on the ideal decision information, where the ideal decision information is the average values of each expert’s evaluation. Furthermore, we propose a decision method for medical diagnosis based on the cosine similarity measure between hybrid intuitionistic fuzzy sets, and the patient can be diagnosed with the disease according to the values of proposed cosine similarity measure. Finally, an example is given to illustrate feasibility and effectiveness of the proposed cosine similarity measure, which is also compared with the existing similarity measures.

scholarly journals Some Similarity and Distance Measures between Complex Interval-Valued q-Rung Orthopair Fuzzy Sets Based on Cosine Function and their Applications

2021 ◽  
Vol 2021 ◽  
pp. 1-25
Author(s):  
Harish Garg ◽  
Zeeshan Ali ◽  
Tahir Mahmood ◽  
Sultan Aljahdali
Keyword(s):  
Decision Making ◽  
Solution Method ◽  
Similarity Measures ◽  
Cosine Similarity ◽  
Distance Measures ◽  
Uncertain Information ◽  
Cosine Similarity Measures ◽  
Complex Valued ◽  
Interval Valued ◽  
The Ideal

The purpose of this paper is to present a new method to solve the decision-making algorithm based on the cosine similarity and distance measures by utilizing the uncertain and vague information. A complex interval-valued q-rung orthopair fuzzy set (CIVQROFS) is a reliable and competent technique for handling the uncertain information with the help of the complex-valued membership grades. To address the degree of discrimination between the pairs of the sets, cosine similarity measures (CSMs) and distance measures (DMs) are an accomplished technique. Driven by these, in this manuscript, we defined some CSMs and DMs for the pairs of CIVQROFSs and investigated their several properties. Choosing that the CSMs do not justify the axiom of the similarity measure (SM), then we investigate a technique to developing other CIVQROFSs-based SMs using the explored CSMs and Euclidean DMs, and it fulfills the axiom of the SMs. In addition, we find the cosine DMs (CDMs) by considering the inter-relationship between the SM and DMs; then, we have modified the procedure for the rank of partiality by similarity to the ideal solution method for the CDMs under investigation, which can deal with the associated decision-making problems not only individually from the argument of the opinion of geometry but also the fact of the opinion of algebra. Finally, we provide a numerical example to demonstrate the practicality and effectiveness of the proposed procedure, which is also in line with existing procedures. Graphical representations of the measures developed are also used in this manuscript.

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