Abstract
The transportation of big species is essential to rescue or relocate them and it requires the optimized cost of transportation. The present study brings out an optimized way to handle a special class of transportation problem called the Pythagorean fuzzy species transportation problem. To deal effectively with uncertain parameters, a new method for finding the initial fuzzy basic feasible solution (IFBFS) has been developed and applied. To test the optimality of the solutions obtained, a new approach named the Pythagorean fuzzy modified distribution method is developed. After reviewing the literature, it has been observed that till now the work done on Pythagorean fuzzy transportation problems is solely based on defuzzification techniques and so the optimal solutions obtained are in crisp form only. However, the proposed study is focused to get the optimal solution in its fuzzy form only. Getting results in the fuzzy form will lead to avoid any kind of loss of information during the defuzzification process. A comparative study with other defuzzification-based methods has been done to validate the proposed approach and it confirms the utility of the proposed methodology.
Highlights
The transportation of big species is the deliberate movement of creatures by transport
To obtain the optimal solution of given Pythagorean Species fuzzy transportation problem, Modi method has applied in the initial fuzzy basic feasible solution (IFBFS)
A special class of fuzzy transportation problem named as Pythagorean fuzzy species transportation problem (PFSTP) is optimized
Summary
The transportation of big species is the deliberate movement of creatures by transport. Authors proposed a new technique which is based on classical method to find initial fuzzy basic feasible solution and used generalized trapezoidal fuzzy numbers as parametric values. Authors proposed a new trisectional approach to convert IBTP into FTP and a unique defuzzification method based on incenter of triangle is developed to convert triangular fuzzy numbers into crisp numbers. To the best of author’s knowledge, no optimization model is present in existing literature of Pythagorean fuzzy species transportation problems in which the optimum solution has obtained in fuzzy values. In the proposed methods, PFNs have taken and to obtain the IFBFS of Pythagorean fuzzy species transportation problem (PFSTP), a new technique is developed.
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