Optimizing neutrosophic fractional transportation problem using neutrosophic aspirational approach

Abstract

The transportation problem is significant in real-life scenarios as it can be utilized in diverse practical applications across various industries and sectors. This problem becomes a fractional transportation problem when the ratio of objective functions is maximized or minimized simultaneously. Real-life problems are often imprecise due to some unpredictable factors like road conditions, weather, price variations and so on. The fuzzy set and intuitionistic fuzzy set are useful for dealing the impreciseness, but there exist some hesitations. To overcome such hesitancy of occurrence and non-occurrence in fuzzy and intuitionistic fuzzy, neutrosophic set is very important and suitable to apply for real life problems. For that reason, in this paper to handle the uncertain, unpredictable and insufficient information in the fractional transportation problem we consider all the parameters as single valued trapezoidal neutrosophic numbers. First, convert the neutrosophic problem into its deterministic problem using the weighted possibility mean. During shipment, sometimes the roles of objective functions and constraints in the problem are not predetermined but may need to be adjusted based on factors such as regulatory changes, market conditions, resource availability, customer priorities and so on. These adjustments contribute to better decision-making, increased cost-effectiveness and improved service efficiency in problems. In this point of view, we have proposed the approach namely, neutrosophic aspirational approach to transform the objective functions of deterministic problem into constraints which is a only novelty of this study. The reduced problem is solved using LINGO software to obtain the optimal compromise solution which is the primary focus of this paper. When the decision makers are in need to select the windmill fans, one may prefer more cost-efficient but less efficient in long-term energy generation while another might have a higher initial cost but offer better long-term benefits. In this situation, the optimal compromise solution obtained by the proposed approach provides valuable insights for the decision makers with flexibility to select their preferred windmill fans using the optimal compromise solution from the available choices based on their financial support. Finally