Application of Fuzzy Decision Making with Multiple Criteria in Ranking Natural Radioactivity Levels of Beach Sediments

Abstract

Objectives: Fuzzy set theory is a marvelous tool to handle uncertainty associated with vagueness, imprecision and lack of information. The objective of this paper is to solve a Multiple Criteria Decision Making problem (MCDM) in fuzzy environment using LR Fuzzy number with a numerical example. Methods/Statistical Analysis: Decision making is a process of selecting a possible course of action from all available alternatives. The scope of the problem is to rank the natural radioactivity levels of various sites of Kerala beaches from the pre-investigated radioactivity supporting parameters of the beach sites. This can be achieved by using vertex method. The parameters are categorized in to cost and benefit criteria and the basic ranking is based on the performance index which is close to 1. Findings: The data for the current study is collected from a researcher, in which the radioactivity levels are calculated using experimental studies. In this paper, just by considering radioactivity supporting parameters of the beach sites, the sites are ranked. As the samples are collected from first three feet of the sites, the data are taken as LR fuzzy numbers. Using vertex method, performance index is calculated and the sites are ranked. The sites which are mentioned as most hazardous and least hazardous in the pre- investigated study is found to take first and last few ranks in the present study. Finally, the result is analyzed for various risk attitudes and several levels of confidence. Application/Improvements: Any real life problem with multiple criteria can be modeled as fuzzy multi criteria decision making problem using any type of fuzzy number and can be solved by vertex method. The type of fuzzy number is decided depending upon the data.