Similarity measure of the interval-valued fuzzy numbers and its application in risk analysis in paddy cultivation

Abstract

Generally, in a risk analysis problems, data are collected from experts in terms of linguistic variables, which are then observed as fuzzy numbers. Eventually, the total risk is calculated, and obtained as fuzzy numbers, using the arithmetic operations of fuzzy numbers. Finally, the risk so obtained has to be expressed in terms of linguistic variables, so that it becomes communicable to the general audience. One such tool in fuzzy mathematics is the similarity measure. In this paper, a new method of determining the similarity between two interval-valued fuzzy numbers has been developed. Generally, various parameters were used in deriving a similarity measure. However, the parameters that describe the shape of an interval-valued fuzzy numbers was never a concern in the earlier studies. Hence, in this study, these parameters are incorporated in the similarity measure. Further, a few reasonable properties are being developed, which will be considered as standard in developing a similarity measure. Finally, a risk analysis problem in paddy cultivation is discussed. Using the proposed similarity measure, the final risk is expressed in terms of a linguistic variable. The final risk so obtained for paddy cultivation, under the assumed scenario, is low.