Metric Measure on Bipolar Fuzzy Sets: Mathematical Properties and Applications in Sentiment Analysis

The most challenging aspect of a pattern recognition problem is to identify a pattern with the help of its positive and negative features. The bipolar fuzzy sets (BFSs) are the mathematical tools that can express a pattern with the help of positive and negative membership functions, hereby making it possible to be expressed more conveniently than others. In this article, a real-valued function on the set of BFSs over a universe of discourse is proposed that fulfills the axioms of being a metric measure on the set of BFSs. The proposed metric can be formulated for both the discrete and the continuous universes of discourse. The efficacy of the proposed metric is validated through several important mathematical properties. Further, a bipolar fuzzy clustering algorithm for sentiment analysis is discussed in detail to demonstrate the usefulness of the proposed metric.