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 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 Generalized Ordered Weighted Simplified Neutrosophic Cosine Similarity Measure for Multiple Attribute Group Decision Making

2020 ◽  
Vol 14 (1) ◽  
pp. 51-62 ◽  
Author(s):  
Jun Ye
Keyword(s):  
Decision Making ◽  
Similarity Measure ◽  
Group Decision Making ◽  
Group Decision ◽  
Information Aggregation ◽  
Cosine Similarity ◽  
Weighted Averaging ◽  
Multiple Attribute ◽  
Special Cases ◽  
Cosine Similarity Measure

The paper proposes a generalized ordered weighted simplified neutrosophic cosine similarity (GOWSNCS) measure by combining the cosine similarity measure of simplified neutrosophic sets (SNSs) with the generalized ordered weighted averaging (GOWA) operator and investigates its properties and special cases. Then, the author develops a simplified neutrosophic group decision-making method based on the GOWSNCS measure to handle multiple attribute group decision-making problems with simplified neutrosophic information. The prominent characteristics of the GOWSNCS measure are that it not only is a generalization of the cosine similarity measure but also considers the associated weights for attributes and decision makers in the aggregation of the cosine similarity measures of SNSs to alleviate the influence of unduly large or small similarities in the process of information aggregation. Finally, an illustrative example of investment alternatives is provided to demonstrate the application and effectiveness of the developed approach.

Generalized Entropy and Similarity Measure for Interval-Valued Intuitionistic Fuzzy Sets With Application in Decision Making

2021 ◽  
Vol 10 (1) ◽  
pp. 64-93
Author(s):  
Pratiksha Tiwari
Keyword(s):  
Decision Making ◽  
Fuzzy Sets ◽  
Similarity Measure ◽  
Extended Family ◽  
Similarity Measures ◽  
Intuitionistic Fuzzy Sets ◽  
Optimal Point ◽  
Generalized Entropy ◽  
Intuitionistic Fuzzy ◽  
Interval Valued

Interval-valued intuitionistic fuzzy environment is appropriate for most of the practical scenarios involving uncertainty, vagueness, and insufficient information. Entropy, similarity, distance, inclusion, and cross entropy measures are a few methods used for measuring uncertainty and classifying fuzzy sets and its generalizations. Entropy of a fuzzy set describes fuzziness degree of the set and similarity measure measures similarity between two fuzzy or members of its extended family. This paper presents generalized entropy and similarity measures for interval-valued intuitionistic fuzzy sets. Further, the proposed similarity measure is compared with some existing measure of similarity with the help of an illustrative example, and a method is used to define optimal point using the existing information. Finally, entropy and similarity measures are used to identify best alternatives to solve multi-attribute decision making.

Multi-criteria decision making method based on improved cosine similarity measure with interval neutrosophic sets

2019 ◽  
Vol 12 (3) ◽  
pp. 414-423 ◽  
Author(s):  
Lunyan Wang ◽  
Qing Xia ◽  
Huimin Li ◽  
Yongchao Cao
Keyword(s):  
Decision Making ◽  
Similarity Measure ◽  
Interval Number ◽  
Cosine Similarity ◽  
Weighted Averaging ◽  
Multi Criteria Decision Making ◽  
Neutrosophic Sets ◽  
Content Type ◽  
Cosine Similarity Measure ◽  
Interval Neutrosophic Sets

Purpose The fuzziness and complexity of evaluation information are common phenomenon in practical decision-making problem, interval neutrosophic sets (INSs) is a power tool to deal with ambiguous information. Similarity measure plays an important role in judging the degree between ideal and each alternative in decision-making process, the purpose of this paper is to establish a multi-criteria decision-making method based on similarity measure under INSs. Design/methodology/approach Based on an extension of existing cosine similarity, this paper first introduces an improved cosine similarity measure between interval neutosophic numbers, which considers the degrees of the truth membership, the indeterminacy membership and the falsity membership of the evaluation values. And then a multi-criteria decision-making method is established based on the improved cosine similarity measure, in which the ordered weighted averaging (OWA) is adopted to aggregate the neutrosophic information related to each alternative. Finally, an example on supplier selection is given to illustrate the feasibility and practicality of the presented decision-making method. Findings In the whole process of research and practice, it was realized that the application field of the proposed similarity measure theory still should be expanded, and the development of interval number theory is one of further research direction. Originality/value The main contributions of this paper are as follows: this study presents an improved cosine similarity measure under INSs, in which the weights of the three independent components of an interval number are taken into account; OWA are adopted to aggregate the neutrosophic information related to each alternative; and a multi-criteria decision-making method using the proposed similarity is developed under INSs.

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 Cosine Similarity Measure of Interval Valued Bipolar Neutrosophic Hesitant Fuzzy Set and Their Applications to Multi-Attribute Decision-Making Process

2021 ◽  
Vol 2 (5) ◽  
pp. 9-16
Author(s):  
Hans Eric Ramaroson ◽  
René Rakotomanana ◽  
Hery Zo Andriamanohisoa
Keyword(s):  
Decision Making ◽  
Similarity Measure ◽  
Cosine Similarity ◽  
Hesitant Fuzzy Set ◽  
Illustrative Case ◽  
New Approach ◽  
Future Opportunity ◽  
Multi Attribute Decision Making ◽  
Cosine Similarity Measure ◽  
Interval Valued

Cosine similarity measure plays a significant role in various fields. Literature consultation confirms that the theory of cosine similarity measure has received a great interest and attention from the researchers in the world. The concept of Interval Valued Bipolar Neutrosophic Hesitant Fuzzy Sets (IVBNHFS) is recently presented and very interesting. Every element in IVBNHFS is characterized by six independent membership functions (three positive and three negative). There is no investigation on the Cosine Similarity Measure (CSM) of IVBNHFS. In this study, we firstly define a CSM and a weighted CSM between two IVBNHFS and their applications to Multi-Attribute Decision Making (MADM) process in the Interval Valued Bipolar Neutrosophic Hesitant Fuzzy (IVBNHF) setting. And, we establish some properties of CSM and a weighted CSM. We use this strategy to find out the best alternative in MADM case. Then, the new approach to clarify MADM problems in IVBNHF setting is presented in algorithmic form. And, we solve an illustrative case of MADM to demonstrate the effectiveness, workability, and appropriateness of the proposed approach. Finally, the main conclusion and future opportunity of research paper are overviewed and compiled.

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