Research of fuzzy implications via fuzzy linear regression in data analysis for a fuzzy model

Abstract

The effect of eutrophication is characterized by dense algal and plant growth due to the enrichment of nutrients for photosynthesis. As a result, it often plays an important role to the formation of plants that float in the surface of a water body. When nutrients are increasing in aquatic ecosystems, the photosynthetic plants grow rapidly. As a result, the algae limit the amount of dissolved oxygen required for respiration by other species in the water. Multi-criteria analysis has helped us towards the understanding and estimation of all physical, chemical and biological functions. In this paper, the examined water body, as a rich and variable system, is an ideal case for our study. Our purpose is to investigate some of the factors responsible for eutrophication (water temperature, nitrates, total phosphorus, Secchi depth, chlorophyll-a) using fuzzy logic. In this method, there are infinite numbers of fuzzy implications which can be used, since the proposition can take any value in the close interval [0,1]; hence, the investigation of the most appropriate implication is required. In this paper, we propose a method of evaluating fuzzy implications constructing triangular fuzzy numbers for all of the studied factors coming from statistical data. The deviation of the true value is the key for the selection of the most appropriate fuzzy implication describing the functions and the mechanisms in this ecosystem.