This paper introduces a simplified presentation of a new computing procedure for solving the fuzzy Pythagorean transportation problem. 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. Then an existing optimality method is used to obtain the cost of transportation. To justify the proposed method, few numerical experiments are given to show the effectiveness of the new model. Finally, some conclusion and future work are discussed.

Data envelopment analysis (DEA) is a linear programming approach used to determine the relative efficiencies of multiple decision-making units (DMUs). A transportation problem (TP) is a special type of linear programming problem (LPP) which is used to minimize the total transportation cost or maximize the total transportation profit of transporting a product from multiple sources to multiple destinations. Because of the connection between the multi-objective TP (MOTP) and DEA, DEA-based techniques are more often used to handle practical TPs. The objective of this work is to investigate the TP with Fermatean fuzzy costs in the presence of numerous conflicting objectives. In particular, a Fermatean fuzzy DEA (FFDEA) method is proposed to solve the Fermatean fuzzy MOTP (FFMOTP). In this regard, every arc in FFMOTP is considered a DMU. Additionally, those objective functions that should be maximized will be used to define the outputs of DMUs, while those that should be minimized will be used to define the inputs of DMUs. As a consequence, two different Fermatean fuzzy effciency scores (FFESs) will be obtained for every arc by solving the FFDEA models. Therefore, unique FFESs will be obtained for every arc by finding the mean of these FFESs. Finally, the FFMOTP will be transformed into a single objective Fermatean fuzzy TP (FFTP) that can be solved by applying standard algorithms. A numerical example is illustrated to support the proposed method, and the results obtained by using the proposed method are compared to those of existing techniques. Moreover, the advantages of the proposed method are also discussed.

The concept of an interval-valued Fermatean fuzzy set (IVFFS), an extension of Fermatean fuzzy sets, is a more resilient and reliable tool for dealing with uncertain and incomplete data in practical applications. The purpose of this paper is to define a triangular interval-valued Fermatean fuzzy number (TIVFFN) and its arithmetic operations. Fractional transportation problems (FTPs) have important implications for cost reduction and service improvement in logistics and supply management. However, in practical problems, the parameters in the model are not precise due to some unpredictable factors, including diesel prices, road conditions, weather conditions and traffic conditions. Therefore, decision makers encounter uncertainty when estimating transportation costs and profits. To address these challenges, we consider a FTP with TIVFFN as its parameter and call it an interval-valued Fermatean fuzzy fractional transportation problem (IVFFFTP). A new method for solving this IVFFFTP is proposed without re-transforming the original problem into an equivalent crisp problem. Illustrative examples are discussed to evaluate the precision and accuracy of the proposed method. Finally, the results of the proposed method are compared with those of existing methods.

In the past, investors used their own or others’ experiences to achieve their goals. With the development of financial management, investors’ choices became more scientific. They could select the optimal choice by using different models and combining the results with their experiences. In portfolio optimization, the main issue is the optimal selection of the assets and securities that can be provided with a certain amount of capital. In the present study, the problem of optimization, i.e., maximizing stock portfolio returns and minimizing risk, has been studied. Therefore, this study discussed comprehensive modeling for the optimal selection of stock portfolios using multi-criteria decision-making methods in companies listed on the Tehran Stock Exchange. A sample of 79 companies listed on the Tehran Stock Exchange was used to conduct this research. After simulating the data and programming them with MATLAB software, the cumulative data analysis model was performed, and 24 companies were selected. This research data were collected from the financial statements of companies listed on the Tehran Stock Exchange in 2020. The primary purpose of this study was a comprehensive modeling for the optimal selection of stock portfolios using multi-criteria decision-making methods in companies listed on the Tehran Stock Exchange. The index in the Tehran Stock Exchange can be used to provide a comprehensive and optimal model for the stock portfolio; different multi-index decision-making methods (TOPSIS method), the taxonomy method (Taxonomy), ARAS method, VIKOR method, The COPRAS method and the WASPAS method can all identify the optimal stock portfolio and the best stock portfolio for the highest return.