A novel probabilistic distance measure for picture fuzzy sets with its application in classification problems

Source abstract

In the present communication, we propose the probabilistic distance measure for picture fuzzy sets where the probability of occurrence/non-occurrence of the picture fuzzy event have been incorporated. This framework has been clearly addressed through outline of a formulated problem and its probable solution structure along with its proof of validity. Further, the proposed probabilistic distance measure has been utilized to present an algorithm for solving some classification decision making problems in a more generalized way. Some important illustrative examples related to the problem of classification - building material classification, mineral classification and a decision making problem of financial investment risk have been worked out to exhibit the implementation of the proposed methodology. The obtained results have also been compared with the existing approaches of solving the classification problems. The uncertainty feature of the problem has been handled in a more broader sense reflecting the advantage of the introduced approach.