An evolutionary algorithm for solving a unique discounted 0-1 knapsack problem in a random type-2 fuzzy environment
摘要
In this article, a discounted 0-1 Knapsack Problem (DKP) for a shopping mall is taken into consideration. Here, a realistic model with sets of (three) objects has been solved. Our suggested model is based on a shopping mall’s policy. In a mall, we have seen for a set of three things, a buyer receives a discount on the third item when he/she buys those two items more expensive. We can assume that each such group only contains the two most profitable things from the perspective of the merchant or vendor. The suggested discounted Knapsack Problem (KP) is solved using an evolutionary method. The problem is resolved in a fuzzy setting. The proposed KP’s parameters are thought to be random type-2 fuzzy (Ty2F) in nature. In order to achieve crisp equivalence of the proposed model, we have de-fuzzified the objective value and constraints using the CV-reduction method and generalized the credibility measure theory. A few benchmark situations are taken into consideration when evaluating the suggested algorithm’s usefulness. We have also taken a few actual cases from the current market survey into consideration as part of experimental results. In order to solve the benchmark instances, we then redefined them in a random type-2 triangular fuzzy (T2TF) environment.