Fractional transportation problem under interval-valued Fermatean fuzzy sets

Muhammad Akram; Syed Muhammad Umer Shah; Mohammed M. Ali Al-Shamiri; S. A. Edalatpanah; Muhammad Akram; Syed Muhammad Umer Shah; Mohammed M. Ali Al-Shamiri; S. A. Edalatpanah

doi:10.3934/math.2022954

AIMS Mathematics

2022, Volume 7, Issue 9: 17327-17348. doi: 10.3934/math.2022954

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Research article

Fractional transportation problem under interval-valued Fermatean fuzzy sets

1.
Department of Mathematics, University of the Punjab, New Campus, Lahore- 54590, Pakistan
2.
Department of Mathematics, Faculty of science and arts, Mahayl Assir, King Khalid University, Saudi Arabia
3.
Department of Mathematics and Computer, Faculty of Science, Ibb University, Ibb, Yemen
4.
Department of Applied Mathematics, Ayandegan Institute of Higher Education, Tonekabon, Iran

Received: 15 June 2022 Revised: 09 July 2022 Accepted: 13 July 2022 Published: 25 July 2022
MSC : 90C32, 90C70

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.
- interval-valued Fermatean fuzzy sets,
- fractional linear programming,
- fractional transportation problem
Citation: Muhammad Akram, Syed Muhammad Umer Shah, Mohammed M. Ali Al-Shamiri, S. A. Edalatpanah. Fractional transportation problem under interval-valued Fermatean fuzzy sets[J]. AIMS Mathematics, 2022, 7(9): 17327-17348. doi: 10.3934/math.2022954

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Abstract

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.

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