Abstract
Identification of a suitable form for the membership function and assigning values for certain parameters in them while dealing with fuzzy environments is a challenging task in Credibility theory. Recently, Sampath and Ramya [15] considered a criterion called “membership ratio criterion” for testing the validity of a given hypothesis regarding the credibility distribution of a fuzzy variable against a rival hypothesis. A study on the application of the proposed criterion has been made with reference to the parameters involved in triangular credibility distributions. In this paper, a detailed study is made with reference to the fuzzy normal distribution. Test resulting from the application of membership ratio criterion for testing hypothesis about the expected value of the fuzzy normal distribution is considered assuming the variance of the distribution is known. Optimal properties of the derived tests are also studied.