A parametric similarity measure between picture fuzzy sets and its applications in multi-attribute decision- making

Picture fuzzy set is an extension of intuitionistic fuzzy set, which can deal with inconsistent and uncertain information more accurately. Similarity measure, as an important mathematical tool to evaluate the degree of similarity between picture fuzzy sets, has been widely used to deal with multi-attribute decision-making problems. But there are unreasonable and counter-intuitive cases due to a few undesirable properties. In order to handle these unreasonable cases, this paper proposes a parametric similarity measure based on three parameters m1;m2 and m3, in which decision makers with different decision styles can obtain the appropriate similarity measure by adjusting parameters m1;m2 and m3. Moreover, we analyze some existing similarity measures from the perspective of mathematics and show that the proposed similarity measure is effective by numerical examples. In the end, we use the proposed similarity measure to solve the problems of multi-attribute decision-making. Through the comparison and analysis, we find that the proposed similarity measure is more effective than some existing similarity measures between picture fuzzy sets.