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 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 Cosine Distance Measure between Neutrosophic Hesitant Fuzzy Linguistic Sets and Its Application in Multiple Criteria Decision Making

Symmetry ◽  
2018 ◽  
Vol 10 (11) ◽  
pp. 602 ◽  
Author(s):  
Donghai Liu ◽  
Xiaohong Chen ◽  
Dan Peng
Keyword(s):  
Distance Measure ◽  
Multiple Criteria Decision Making ◽  
Point Of View ◽  
Scale Function ◽  
Topsis Method ◽  
Linguistic Distance ◽  
Linguistic Term ◽  
Linguistic Scale Function ◽  
Cosine Distance ◽  
Fuzzy Linguistic

This paper proposes a neutrosophic hesitant fuzzy linguistic term set (NHFLTS) based on hesitant fuzzy linguistic term set (HFLTS) and neutrosophic set (NS), which can express the inconsistent and uncertainty information flexibly in multiple criteria decision making problems. The basic operational laws of NHFLTS based on linguistic scale function are also discussed. Then we propose the generalized neutrosophic hesitant fuzzy linguistic distance measure and discuss its properties. Furthermore, a new similarity measure of NHFLTS combines the generalized neutrosophic hesitant fuzzy linguistic distance measure and the cosine function is given. A corresponding cosine distance measure between NHFLTSs is proposed according to the relationship between the similarity measure and the distance measure, and we develop the technique for order preference by similarity to an ideal solution (TOPSIS) method to the obtained cosine distance measure. The main advantages of the proposed NHFLTS is defined on linguistic scale function, the decision makers can flexibly convert the linguistic information to semantic values, and the proposed cosine distance measure between NHFLTSs with TOPSIS method can deal with the related decision information not only from the point of view of algebra, but also from the point of view of geometry. Finally, the reasonableness and effectiveness of the proposed method is demonstrated by the illustrative example, which is also compared to the other existing methods.

Multi-attribute group decision-making method based on time-series q-rung orthopair fuzzy sets

2021 ◽  
pp. 1-10
Author(s):  
Yan Gao ◽  
Chenchen Liu ◽  
Liangyu Zhao ◽  
Kun Zhang
Keyword(s):  
Decision Making ◽  
Time Series ◽  
Similarity Measure ◽  
Distance Measure ◽  
Point Of View ◽  
Cosine Similarity ◽  
Fuzzy Decision Making ◽  
Actual Problem ◽  
Correlation Degree ◽  
Cosine Similarity Measure

The q-rung orthopair fuzzy set is a powerful and useful tool to deal with uncertainty, but in actual decision-making process, decision-makers are usually required to analyze the actual problem dynamically. Therefore in this paper, we consider the time-series q-rung orthopair fuzzy decision making. First, we introduce the new cosine similarity measure of q-ROFS which combines the cosine similarity measure and the Euclidean distance measure. Then, we combine the advantages of projection method and grey correlation degree, establishing the nonlinear programming model to calculate the weights of attributes. Furthermore, we use the exponential decay model to get the weights formulas of q-ROFS at different times. Then we replace the distance function with grey relational projection and extend TOPSIS method. Based on these, we propose a new MAGDM approach to deal with time-series q-rung orthopair fuzzy problem not only from the point of view of geometry but also from the point of view of algebra. Finally, we give a practical example to illustrate effectiveness and feasibility of the new method.

Is it possible to rank universities using fewer indicators? A study on five international university rankings

2019 ◽  
Vol 71 (1) ◽  
pp. 18-37 ◽  
Author(s):  
Güleda Doğan ◽  
Umut Al
Keyword(s):  
Similarity Measure ◽  
Decision Makers ◽  
Cosine Similarity ◽  
University Rankings ◽  
University Ranking ◽  
Data Set ◽  
Content Type ◽  
Research Questions ◽  
Cosine Similarity Measure ◽  
International University

Purpose The purpose of this paper is to analyze the similarity of intra-indicators used in research-focused international university rankings (Academic Ranking of World Universities (ARWU), NTU, University Ranking by Academic Performance (URAP), Quacquarelli Symonds (QS) and Round University Ranking (RUR)) over years, and show the effect of similar indicators on overall rankings for 2015. The research questions addressed in this study in accordance with these purposes are as follows: At what level are the intra-indicators used in international university rankings similar? Is it possible to group intra-indicators according to their similarities? What is the effect of similar intra-indicators on overall rankings? Design/methodology/approach Indicator-based scores of all universities in five research-focused international university rankings for all years they ranked form the data set of this study for the first and second research questions. The authors used a multidimensional scaling (MDS) and cosine similarity measure to analyze similarity of indicators and to answer these two research questions. Indicator-based scores and overall ranking scores for 2015 are used as data and Spearman correlation test is applied to answer the third research question. Findings Results of the analyses show that the intra-indicators used in ARWU, NTU and URAP are highly similar and that they can be grouped according to their similarities. The authors also examined the effect of similar indicators on 2015 overall ranking lists for these three rankings. NTU and URAP are affected least from the omitted similar indicators, which means it is possible for these two rankings to create very similar overall ranking lists to the existing overall ranking using fewer indicators. Research limitations/implications CWTS, Mapping Scientific Excellence, Nature Index, and SCImago Institutions Rankings (until 2015) are not included in the scope of this paper, since they do not create overall ranking lists. Likewise, Times Higher Education, CWUR and US are not included because of not presenting indicator-based scores. Required data were not accessible for QS for 2010 and 2011. Moreover, although QS ranks more than 700 universities, only first 400 universities in 2012–2015 rankings were able to be analyzed. Although QS’s and RUR’s data were analyzed in this study, it was statistically not possible to reach any conclusion for these two rankings. Practical implications The results of this study may be considered mainly by ranking bodies, policy- and decision-makers. The ranking bodies may use the results to review the indicators they use, to decide on which indicators to use in their rankings, and to question if it is necessary to continue overall rankings. Policy- and decision-makers may also benefit from the results of this study by thinking of giving up using overall ranking results as an important input in their decisions and policies. Originality/value This study is the first to use a MDS and cosine similarity measure for revealing the similarity of indicators. Ranking data is skewed that require conducting nonparametric statistical analysis; therefore, MDS is used. The study covers all ranking years and all universities in the ranking lists, and is different from the similar studies in the literature that analyze data for shorter time intervals and top-ranked universities in the ranking lists. It can be said that the similarity of intra-indicators for URAP, NTU and RUR is analyzed for the first time in this study, based on the literature review.

scholarly journals Consistency Fuzzy Sets and a Cosine Similarity Measure in Fuzzy Multiset Setting and Application to Medical Diagnosis

2021 ◽  
Vol 2021 ◽  
pp. 1-9
Author(s):  
Ezgi Türkarslan ◽  
Jun Ye ◽  
Mehmet Ünver ◽  
Murat Olgun
Keyword(s):  
Correlation Coefficient ◽  
Similarity Measure ◽  
Fuzzy Set ◽  
Medical Diagnosis ◽  
Uncertain Data ◽  
Cosine Similarity ◽  
Comparison Analysis ◽  
Average Value ◽  
Truth Function ◽  
Cosine Similarity Measure

The main purpose of this study is to construct a base for a new fuzzy set concept that is called consistency fuzzy set (CFS) which expresses the multidimensional uncertain data quite successfully. Our motive is to reduce the complexity and difficulty caused by the information contained in the truth sequence in a fuzzy multiset (FMS) and to present the data of the truth sequence in a more understandable and compact manner. Therefore, this paper introduces the concept of CFS that is characterized with a truth function defined on a universal set 0,1 2 . The first component of the truth pair of a CFS is the average value of the truth sequence of a FMS and the second component is the consistency degree, that is, the fuzzy complement of the standard deviation of the truth sequence of the same FMS. The main contribution of a CFS is the reflection of both the level of the average of the data that can be expressed with the different sequence lengths and the degree of the reasonable information in data via consistency degree. To develop this new concept, this paper also presents a correlation coefficient and a cosine similarity measure between CFSs. Furthermore, the proposed correlation coefficient and cosine similarity measure are applied to a multiperiod medical diagnosis problem. Finally, a comparison analysis is given between the obtained results and the existing results in literature to show the efficiency and rationality of the proposed correlation coefficient and cosine similarity measure.

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