Arithmetic Operations on Generalized Parabolic Fuzzy Numbers and Its Application

In this paper, we have studied the basic arithmetic operations for two generalized positive parabolic fuzzy numbers by using the concept of the distribution and complementary distribution functions. The major advantage of these operations is that they do not need the computation of α\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\alpha $$\end{document}-cut of the fuzzy number and hence it becomes more powerful where the standard method i.e., α\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\alpha $$\end{document}-cuts method fails. Based on these operations, some elementary applications on mensuration have been illustrated and compared their results with generalized triangular fuzzy numbers.