The Multi-objective Solid Transportation Problem with Preservation Technology Using Pythagorean Fuzzy Sets

This study’s motive is to vindicate the result of the preservation of a transportation system for transporting perishable items. We introduce a certain preservation technology (PT) with preservation cost to reduce the rate of deterioration, and then simultaneously to increase the lifetime of such items. Here we initiate a multi-objective solid transportation problem with a connection of PT. To make the problem realistic, we consider various criteria, such as transportation cost, preservation cost, time, and deterioration under a Pythagorean fuzzy environment. Pythagorean fuzzy sets are the extension of intuitionistic fuzzy sets and more flexible than the fuzzy sets, intuitionistic fuzzy sets, or other uncertainty. We introduce two numerical examples to elaborate the appropriateness of our approach, which is then solved in three ways: by the ε\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\varepsilon $$\end{document}-constraint method, by neutrosophic linear programming, and by the fuzzy TOPSIS approach.