Fuzzy risk analysis using similarity measure of interval-valued fuzzy numbers and its application in poultry farming

Similarity measure plays an important role in the decision-making process under an uncertain environment where parameters involved are linguistics terms. Mostly, similarity measure is discussed on generalized fuzzy numbers. However, a few efforts have been made to study this measure on interval-valued fuzzy numbers. Sometimes, methods involving interval-valued fuzzy numbers depict limitations and drawbacks. Moreover, some of the methods are just confined to interval-valued fuzzy numbers. Hence, these methods fail when similarity has to be determined between crisp-valued fuzzy numbers and interval-valued fuzzy numbers. Hence, a new method of similarity measure has been developed based on the concepts of geometric distance, heights and the radius of gyration of the interval-valued fuzzy numbers. Although the method is being discussed on interval-valued fuzzy numbers, yet it is not just confined to such numbers. This method can be applied efficiently to generalized fuzzy numbers too. The method seems to out-perform in many situations and overcome the drawbacks and limitations of existing methods. A few sets of fuzzy numbers are considered for a comparative study and draw out the out-performance of the proposed method. A real-life problem of risk analysis in poultry farming has been discussed using the proposed similarity measure.