*Article* **Similarity Measures of q-Rung Orthopair Fuzzy Sets Based on Cosine Function and Their Applications**

**Ping Wang 1, Jie Wang 2, Guiwu Wei 2,\* and Cun Wei 2,3**


Received: 23 March 2019; Accepted: 4 April 2019; Published: 9 April 2019

**Abstract:** In this article, we propose another form of ten similarity measures by considering the function of membership degree, non-membership degree, and indeterminacy membership degree between the q-ROFSs on the basis of the traditional cosine similarity measures and cotangent similarity measures. Then, we utilize our presented ten similarity measures and ten weighted similarity measures between q-ROFSs to deal with multiple attribute decision-making (MADM) problems including pattern recognition and scheme selection. Finally, two numerical examples are provided to illustrate the scientific and e ffective of the similarity measures for pattern recognition and scheme selection.

**Keywords:** multiple attribute decision-making (MADM); q-rung orthopair fuzzy sets (q-ROFSs); cosine function; cosine similarity measure; pattern recognition; scheme selection
