*In the transportation problem, the objective is to minimize the cost of distributing a product from these sources to the destinations, but the demand and supply of the product with the following assumptions and constraints are crisp: In this section, we propose a new algorithm (Main Algorithm) to solve all types of TP under Pythagorean fuzzy environment. The first sub-algorithm (Algorithm 1) presents a method to find an initial basic feasible solution for TP and the second sub-algorithm (Algorithm 2) is an existing optimality method for calculation of the cost of transportation.These algorithms are as follows: represent the maximum degree of the membership (i.e., the degree of acceptance of quantity) and the non-membership (i.e., the degree of rejection of quantity) respectively.Detailed information on how Wiley uses cookies can be found in our Privacy Policy.*

*In the transportation problem, the objective is to minimize the cost of distributing a product from these sources to the destinations, but the demand and supply of the product with the following assumptions and constraints are crisp: In this section, we propose a new algorithm (Main Algorithm) to solve all types of TP under Pythagorean fuzzy environment. The first sub-algorithm (Algorithm 1) presents a method to find an initial basic feasible solution for TP and the second sub-algorithm (Algorithm 2) is an existing optimality method for calculation of the cost of transportation.*These algorithms are as follows: represent the maximum degree of the membership (i.e., the degree of acceptance of quantity) and the non-membership (i.e., the degree of rejection of quantity) respectively.Detailed information on how Wiley uses cookies can be found in our Privacy Policy.

However, these values are generally imprecise or vague. However, the fuzzy set takes only a membership function.

Consequently, various attempts have been made by researchers for different types of transportation problems in the fuzzy environment. Here, the degree of the non-membership function is just a compliment of the degree of the membership function.

However, in most of the cases, the data to be handled are uncertain, imprecise and inconsistence, the obtained results are not consistent, and, therefore, uncertainty theory came into existence.

During the last few decades, the topic of fuzzy optimization has achieved substantial popularity among researchers because of its widespread applications in different branches of network flow problem [Transportation problems play a significant role in many real-life applications.

Therefore, there is a need to establish a new algorithm for Pythagorean fuzzy transportation problem.

To the nice of our facts, there are no optimization models in literature for TP under Pythagorean fuzzy environment.

To design the algorithm, we have described the Pythagorean fuzzy arithmetic and numerical conditions in three different models in Pythagorean fuzzy environment.

To achieve our aim, we have first extended the initial basic feasible solution.

Special properties of transportation problem help us to operate each step of simplex algorithm directly on the transportation tableau.

At last, numerical examples are represented to illustrate our method.

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