A new approach for testing fuzzy hypotheses based on likelihood ratio statistic

In this paper, a new approach for testing fuzzy hypotheses based on likelihood ratio test statistic is presented. In this approach, we first formulate the hypotheses of interest by fuzzy sets, and then, a likelihood ratio statistic is defined based on the δ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\delta $$\end{document}-cut of null fuzzy hypothesis. Also, in order to establish critical region, we give new definitions for the probabilities of type I and type II errors.