Circular Intuitionistic Fuzzy Knapsack Problem

The Knapsack problem is an NP-hard combinatorial optimization problem whose objective is to select those items to put in the knapsack to reach the highest possible total value without exceeding its capacity. Nowadays, there is great uncertainty in the parameters of this problem. Traditional methods for solving this problem cannot account for the uncertainty in the environment. In 2020, Atanassov introduced an extension of the Intuitionistic Fuzzy Set called the Circular Intuitionistic Fuzzy Set (C-IFS) to model the greater uncertainty of the environment. This study suggests an index-matrix approach to a circular intuitionistic fuzzy knapsack problem (C-IFKP) by extending the classical dynamic optimization algorithm. The urgency and duration of request satisfaction are suggested by experts and their ratings are taken into account in the proposed algorithm. Software for performing the proposed C-IFKP is also developed. The efficiency of the algorithm is applied to optimize the execution of the requests that an Ambulance team must satisfy in a certain time, taking into account the urgency of the request and its duration for execution. Three scenarios are proposed to the decision maker for the final choice - pessimistic, optimistic, and average.