Solving an EPQ model with doubt fuzzy set: A robust intelligent decision-making approach

Abstract

This article deals with the novel application of complex neutrosophic set in a production inventory model. First of all, we develop a new set named doubt fuzzy set the real and imaginary parts of which are the membership functions of fuzzy variables. The real part of the set is coined as “true or sure” and that for complex part it is defined as “hesitation or suspect” membership functions or it may be defined as “optimism” and “pessimism” respectively in the psychological view point. Then, we give some definitions of doubt fuzzy set in a rectangular complex plane. Subsequently, we give novel defuzzification method by introducing the concept of power of difficulty/ opportunity power which are complementary to each other. Secondly, we develop a backlogging economic production quantity (EPQ) model the demand function of which is disrupted due to the presence of shortages. Assuming the demand function as complex in nature, we develop four types of doubt fuzzy sets namely proper doubt, harmful doubt, depressive doubt and confident doubt respectively and split the model into four sub-models accordingly. Based on new defuzzification method, we have introduced a new solution algorithm named dynamical doubt fuzzy optimization algorithm (DDFOA). By this new approach we have shown that with the application of learning vector by means of opportunity power/ fitness of various test functions the decision maker can achieve and avail the financial benefit as (s)he wishes to adopt. However, the concept of robust intelligent decision making has been discussed extensively through the numerical illustrations. Finally, sensitivity analysis, graphical illustrations are made to justify the proposed approach.