Hexagonal fuzzy number inadvertences and its applications to MCDM and HFFLS based on complete ranking by score functions
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Hexagonal fuzzy number inadvertences and its applications to MCDM and HFFLS based on complete ranking by score functions V. Lakshmana Gomathi Nayagam1 · Jagadeeswari Murugan1
· K. Suriyapriya1
Received: 5 September 2019 / Revised: 8 April 2020 / Accepted: 6 August 2020 © SBMAC - Sociedade Brasileira de Matemática Aplicada e Computacional 2020
Abstract Zadeh introduced fuzzy set theory in the year 1965 to overcome the enigma and obscurity in the real world problems. The underlying power of fuzzy sets is that linguistic / qualitative variables can be used along with quantitative variables to represent continuous imprecise concepts. The continuous anagram concepts need to be modeled by continuous fuzzy numbers instead of intervals and real numbers. So, many researchers developed various fuzzy numbers such as triangular fuzzy numbers, trapezoidal fuzzy numbers, hexagonal fuzzy numbers, octagonal fuzzy numbers and decagonal fuzzy numbers based on shapes in literature. While offering these fuzzy numbers, there are some inadvertences in the existing definition of hexagonal, octagonal and decagonal fuzzy numbers. In this study, some flaws in the concept of hexagonal fuzzy numbers in literature are rectified and a new definition of hexagonal fuzzy numbers in the general form is proposed. Moreover, a complete ranking of hexagonal fuzzy numbers using score functions has also been proposed and is validated through fuzzy Multi Attribute Decision Making (MADM) problem and fuzzy linear system. Further, an algorithm for solving fully fuzzy generalized hexagonal fuzzy linear system of equations as an application of proposed ranking principle is given and is numerically illustrated. Keywords Hexagonal fuzzy number · Midpoint score · Compass or span · Left dissimilitude and aggregation of the slope score · Right dissimilitude and aggregation of the slope score Mathematics Subject Classification 03E72 · 90C70 · 68U35 · 65K05 · 68T35 · 90B50 · 91B06
Communicated by Marcos Eduardo Valle.
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Jagadeeswari Murugan [email protected] V. Lakshmana Gomathi Nayagam [email protected] K. Suriyapriya [email protected]
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Department of Mathematics, National Institute of Technology, Tiruchirappalli, India 0123456789().: V,-vol
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V. L. G. Nayagam et al.
1 Introduction Zadeh (1965) introduced fuzzy sets which has various generalizations such as Type 1 Fuzzy Sets (T1FSs), Type 2 Fuzzy Sets (T2FSs), Type 3 Fuzzy Sets (T3FSs), Level 1 Fuzzy Sets (L1FSs), Level 2 Fuzzy Sets (L2FSs), Intuitionistic fuzzy sets (IFSs), Hesitant Fuzzy sets (HFSs), Dual hesitant fuzzy sets, Bi-polar fuzzy sets and Neutrosophic sets to deal with qualitative and quantitative information. Some researchers proposed various types of membership functions for fuzzy numbers (FNs) such as triangular, trapezoidal, hexagonal, octagonal, decagonal to represent uncertain information. But, some of fuzzy numbers such as hexagonal, octagonal and decagonal are not properly defined in the literature. Hexagonal Fuzzy Number (HXFN) was first defin
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