A Novel Probabilistic Distance Measure for Picture Fuzzy Sets with its Application in Classification Problems

The notion of picture fuzzy set and distance measures are found to be useful in various models and situations in which the human opinions involve the responses of types: yes, abstain, no and refusal. In the present paper, we propose a novel concept of probabilistic distance measure for picture fuzzy sets where the probability of occurrence of an event with respect to picture fuzzy membership and the probability of non-occurrence of the event with respect to picture fuzzy non-membership have been duly taken into consideration. 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 propose 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 in order to show 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 which reflects the advantage of the introduced approach.