Development of environmental quality indexes based on fuzzy logic. A case study

Fuzzy logic is a suitable mathematical tool to treat information of very different nature, which is partially affected by uncertainty and subjectivity. Its successful application in the environmental field in recent years shows its great potential for the design of environmental quality indexes. ork deals with a rigorous and versatile methodology based on fuzzy logic for the design and the subsequent assessment of environmental quality indexes (EQI). It enables the design of specific indexes to evaluate the quality from different perspectives in any environmental compartment. formation required to design the EQI should be supplied by a panel of experts in all the different aspects related to the quality under assessment. An environmentalist team should coordinate the panel and the acquisition, management and treatment of the information supplied at each step of the procedure. Conventional convergence methods should be used to obtain a joint assessment at each step in order to rigorously integrate the panelʹs contributions. e design of the EQI, firstly, a set of attributes A = {ai} is defined, which should include all the significant properties influencing the quality under consideration. Next, a conventionally accepted indicator Ii is selected to quantify each attribute ai, together with the range of values [minIi, maxIi]. Next, a normalized indicator Si is calculated for each Ii and a linguistic variable LSi is assigned to each Si. Then, a fuzzy set B i ¯ is defined to each LSi, which describes in fuzzy terms the “Beneficial” contribution of ai to the environmental quality assessed by the EQI. Next, a pair-wise comparison matrix X ¯ = [ x ¯ i j ] of the relative importances of the attributes ai is calculated and subsequently, a standardized priority vector W′ = {wi′} is determined from matrix X ¯ , so that each component wi′ provides the relative significance of the attribute ai in the EQI – represented as a fraction of unity. The final value of the index is obtained as result of a fuzzy inference procedure based on the zero-order Method of Takagi and Sugeno. The value of the EQI is a non-dimensional magnitude ranging from 0 to 1, the quality being greater the closer the index is to 1. This methodology is applied to a simplified case study in order to illustrate its practical application, which is the design and assessment of a physical–chemical soil quality index at a particular site.