An application of testing fuzzy hypotheses: Soil study on the bioavailability of cadmium

Abstract

Fuzzy set theory models situations in which the uncertainty is due to the non-precise (fuzzy) environment. One such case is testing the hypotheses problem where hypotheses are fuzzy rather than crisp and the data are crisp. Pais and Benton (1997) [1] present a suitable amount of cadmium absorption which is more appropriate for modeling by a fuzzy subset. In this paper, on real-world agricultural data generated by Ivani (2007) [2], the suitableness of the mean absorption cadmium in the plant from the polluted soil is tested at the given significance level. Due to uncertainty in the suitable amount of cadmium absorption, in order to test this amount, we use fuzzy hypotheses testing instead of classical hypotheses testing. The fuzzy p-value approach is used for this test to conclude whether or not the mean absorption of cadmium coincides with the proposed amounts by Pais and Benton [1]. As expected, in fuzzy hypotheses testing, the degree of acceptance or rejection of the null fuzzy hypothesis is computed for each treatment of pollution. The data are from two plants: radish and cress, which are experimented on in soil polluted with CdNO3 salt. The results showed that using classical hypotheses testing may lead to contradictory decisions, and the proposed fuzzy hypotheses testing is a rational substitute for classical hypotheses testing when the environment is in a vague status.