International Research Journal of Engineering and Technology (IRJET)
e-ISSN: 2395-0056
Volume: 10 Issue: 05 | May 2023
p-ISSN: 2395-0072
www.irjet.net
ULTRA NOVEL FOURIER INNOVATIVE OPTIMIZATION TECHNIQUE FOR ANALYSIS OF FERMATEAN FUZZY OPERATORS WITH SOLID TRANSPORTATION PROBLEM P. Rajarajeswari1, M. Sangeetha2, T. Thirunamakkani3, P. Pooranadevi4 1,3Department of Mathematics, Chikkanna Government Arts College, Tirupur, Tamil Nadu- 641602, India. 2Department of Mathematics, Dr. N. G. P. Arts and Science College, Coimbatore-641 048, India.
4Department of Science and Humanities, Info Institute of Engineering, Coimbatore-641 107, India.
---------------------------------------------------------------------***--------------------------------------------------------------------Abstract - Fermatean fuzzy set is an effective and immense of exploration. The Fermatean fuzzy set acquire more fortunate optimal solution than Intuitionistic fuzzy set and Pythagorean fuzzy set. It is manipulated extensively in numerous area of expertise. They are contemplated as efficacious apparatus for assess the specified information. Hamacher Operator is one of the trenchant operators. It is prominent to shrink the influence of refusal particulars. It contribute more authentic outcome. We solicit FFIWG, FFEIWG operators on Fermatean fuzzy sets to acquire satisfactory choice. The scope of research solid transportation problem is an extensiveness of conventional transportation problem. In this paper, Fermatean fuzzy solid transportation problem is build on the basis of Fermatean fuzzy number. The two prominent operators in particular Fermatean Fuzzy Iterative Weighted Geometric [FFIWG] operator and Fermatean Fuzzy Einstein Iterative Weighted Geometric [FFEIWG] operator are implemented to acquire the rebuild Fermatean fuzzy conventional transportation problem. A novel defuzzification function for Fermatean fuzzy number is elucidated and utilized to acquire crisp transportation problem. A new ultra-novel Fourier Elimination method harnessing FFIWG, FFEIWG operators is proposed. The proposed technique is described with numerical values. Key Words: Fermatean fuzzy set, Fermatean fuzzy solid transportation problem, Fourier Elimination method, FFIWG, FFEIWG operators.
1. INTRODUCTION In 1986, Atanassov [1] introduced the approach of Intuitionistic fuzzy sets in which the acceptance grade and nonacceptance grade is described and gratifying the limitation that the sum of acceptance grade and non- acceptance grade is confine to unity. In 2019 Zhuang [12] ; 2021 Rani [9]; 2021 Hao [7]; based on this solitary utility IFS has performed as particular beneficial technique for indicating unreliability and ambiguity of actual issue. In 2014, Yagar [11] determined the modernized form of IFS, characterized by the acceptance grade and non- acceptance grade and non- acceptance grade and satisfied the restriction that the square sum of acceptance grade and non- acceptance grade limited to unity, is known as the approach of Pythagorean Fuzzy. In 2020, Guleria and Bajaj [6] newly suggested a contemporary (R,S) norm report established mixture decision-making framework for PFS and further used it for unravelling an MCDM issue. In 2019, Senapati and Yagar [11] presented the concept of Fermatean fuzzy set, to characterize this consequence. They conferred fundamental functioning regulations for Fermatean fuzzy sets and extended score and accuracy procedures for Fermatean fuzzy numbers. They also offered a fiction decision-making framework underneath Fermatean fuzzy sets circumstances and also generated some weighted averaging and weighted geometric operators for Fermatean fuzzy sets, for their application in MCDM situations. In 2020, Aydemir and Gunduz [3] expanded the Dombi Aggregation operators for Fermatean fuzzy sets. In a current investigation in 2020, Akram [2] proposed a new Aggregation operators established Fermatean fuzzy based decision making framework for assessing the numerous appropriate sanitizer to diminish COVID19 condition. Later, In 2020, Garg [4] suggested a series of Fermatean fuzzy aggregation operators and further utilized them to solve the COVID-19 establishment evaluation issue. In 2020, Ghorabaee [5] suggested a Fermatean fuzzy established judgment approval technique for assessing and determining the most acceptable feasible structure supplier.
2. PRELIMINARIES Definition 2.1: Let be a set of universe. Let be the Fermatean fuzzy set contained in i.e, . Then the nonempty Fermatean fuzzy set is characterized by
y, y , y
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