A study of triangular membership function and multiple regressions to calculate MSW compost index

Abstract

The triangular membership function evaluates each element of a fuzzy set to both discrete and continuous values, and regressions analysis estimates the relationship between values.  The municipal solid waste compost consists of elements with varied composition including light and heavy metal elements. For MSW compost to acts as a soil conditioner, validation of elements is obligatory. In this paper, a triangular membership function (µf) is studied and used to characterize the effect of individual elements available in the compost sample. The characterization determines the variation in the composition of critical and sensitive elements available in the compost sample and accordingly calculates its score_i.  Further, a reinvestigation is done by applying multiple regression analysis, especially on heavy metals to compare its composition with light mineral nutrients and other supplementary elements in the sample. Based on one or more attribute values of elements in the MSW compost sample, the classes are defined and the outcome is predicted. A relationship R and R² is derived to determine the predicted value and defines the composition of heavy metals as attributed by another mineral nutrient. Furthermore, a correlation (Co) is derived to find the performance of the compost sample so as to decide whether both light and supplementary mineral nutrients are capable of minimizing the overall effect of heavy metals in the compost sample. A gratuity score (G_si) is added to each heavy metal respectively depending on correlation value Co(x,y) to form compost_i . The summation of score_i and compost_i forms compost usability and sustainability index (C_i), a discrete value to declare compost sample is mature to use it for agriculture and enhance crops productivity. Hence, ensures agricultural stakeholders to believe in use of MSW compost.