The minimum cost flow finding under fuzzy intuitionistic conditions

Abstract

Present paper deals with the minimum cost flow finding task with fuzzy trapezoidal intuitionistic values of arc capacities and costs. Nowadays, flow tasks in networks are leading tasks in flow modelling and urban logistics. Peculiarity of the problem is in optimal paths finding, which allows decreasing the total cost of transportation and choosing the best paths for transportation. Fuzzy logic as a powerful tool for dealing with uncertainty, vagueness and inaccurate data influenced the way of presenting characteristics of networks. Arc capacities and costs can be presented as fuzzy numbers of the different form enabling researchers to get more reliable solutions. However, during the simulation a researcher is often faced with difficulties in exact specifying of arc capacities and costs. It is a commonplace that experts hesitate or have doubts choosing a specific value for parameters of the network. In such circumstances arc capacities and costs can be presented in a fuzzy intuitionistic form, in particular, as fuzzy intuitionistic triangular or trapezoidal numbers. A fuzzy intuitionistic number allows taking into account a level of hesitation by including degree of membership, non-membership and indeterminacy margin. Incorporating fuzzy intuitionistic sets into conventional flow patterns enables researchers to solve tasks in fuzzy, vague conditions even when there is a lack of necessary data for problem statement. The main contribution to the paper is the proposal for the fuzzy intuitionistic minimum cost flow algorithm using fuzzy intuitionistic flow patterns based on the ranking technique and arithmetic operations with fuzzy intuitionistic trapezoidal numbers. A case study numerical is presented to illustrate the proposed algorithm.