Mathematics and Statistics Vol. 10(1), pp. 176 - 186
DOI: 10.13189/ms.2022.100116
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Fuzzy Number – A New Hypothesis and Solution of Fuzzy Equations

Vijay C. Makwana ¹, Vijay. P. Soni ¹, Nayan I. Patel ², Manoj Sahni ^3,*
1 Department of Mathematics, Government Engineering College, Patan, Gujarat, India
² Department of Mathematics, Adani Institute of Infrastructure Engineering, Ahmedabad, Gujarat, India
³ Department of Mathematics, Pandit Deendayal Energy University, Gandhinagar, Gujarat, India

ABSTRACT

In this paper, a new hypothesis of fuzzy number has been proposed which is more precise and direct. This new proposed approach is considered as an equivalence class on set of real numbers R with its algebraic structure and its properties along with theoretical study and computational results. Newly defined hypothesis provides a well-structured summary that offers both a deeper knowledge about the theory of fuzzy numbers and an extensive view on its algebra. We defined field of newly defined fuzzy numbers which opens new era in future for fuzzy mathematics. It is shown that, by using newly defined fuzzy number and its membership function, we are able to solve fuzzy equations in an uncertain environment. We have illustrated solution of fuzzy linear and quadratic equations using the defined new fuzzy number. This can be extended to higher order polynomial equations in future. The linear fuzzy equations have numerous applications in science and engineering. We may develop some iterative methods for system of fuzzy linear equations in a very simple and ordinary way by using this new methodology. This is an innovative and purposefulness study of fuzzy numbers along with replacement of this newly defined fuzzy number with ordinary fuzzy number.

KEYWORDS
Fuzzy Number, Arithmetic of Fuzzy Numbers, Fuzzy Algebraic Structure, Solution of Fuzzy Equation

Cite This Paper in IEEE or APA Citation Styles
(a). IEEE Format:
[1] Vijay C. Makwana , Vijay. P. Soni , Nayan I. Patel , Manoj Sahni , "Fuzzy Number – A New Hypothesis and Solution of Fuzzy Equations," Mathematics and Statistics, Vol. 10, No. 1, pp. 176 - 186, 2022. DOI: 10.13189/ms.2022.100116.

(b). APA Format:
Vijay C. Makwana , Vijay. P. Soni , Nayan I. Patel , Manoj Sahni (2022). Fuzzy Number – A New Hypothesis and Solution of Fuzzy Equations. Mathematics and Statistics, 10(1), 176 - 186. DOI: 10.13189/ms.2022.100116.