Abstract
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.
Highlights
The fuzzy set was proposed by Zadeh [1] and has achieved a great success in various fields, which is considered to be an effective tool to solve the decision-making problems, pattern recognition, and fuzzy inference [2,3,4]
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
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
Summary
The fuzzy set was proposed by Zadeh [1] and has achieved a great success in various fields, which is considered to be an effective tool to solve the decision-making problems, pattern recognition, and fuzzy inference [2,3,4]. Due to the fuzziness and uncertainty in the multiple criteria decision-making problems, it is difficult to use the exact values to present qualitative evaluation At this time, people often provide their opinions in linguistic term sets. We will propose the cosine similarity measures of IFLSs and IVIFLSs. The main characteristics of the cosine similarity measures that we can calculate are based on linguistic term set by the linguistic scale function. Linguistic scale function between IFLSs and IVIFLSs was introduced by Wang et al [23], which was used to calculate the Hausdorff distance between hesitant fuzzy linguistic numbers (HFLNs); it can assign different semantic values to the linguistic terms under different circumstances and improve the flexibility of the proposed cosine similarity measures.
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