Fuzzy risk analysis in poultry farming based on a novel similarity measure of fuzzy numbers

Abstract

Similarity measure between fuzzy numbers is a very important tool in fuzzy risk analysis problems where the parameters involved are linguistic terms. Such types of measure already exist in the literature. The emergence of different types of fuzzy numbers has led to generalization and modification of existing similarity measures. Moreover, newer measures are being proposed owing to the limitations and drawbacks in existing methods. It is seen that most existing similarity measures have numerous drawbacks and limitations. Namely, most of the method is based on geometric distance, hence the concept of the height is missing, which depicts a limitation on the existing method. Further, crisp-valued fuzzy numbers are not at all considered in some of the existing methods. Hence, in this paper, a new method to measure the degree of similarity between fuzzy numbers has been proposed. This measure has been discussed on generalized fuzzy numbers with different left heights and right heights. This measure is not just confined to generalized fuzzy numbers with different left heights and right heights, but also can deal with arbitrary fuzzy numbers. The proposed similarity measure is based on geometric distance, height and radius of gyration point of fuzzy number. In fact, a much generalized method has been proposed which removes all the drawbacks and limitations of the existing similarity measures. The out-performance of the proposed method is illustrated by comparing with existing methods of similarity measure. Further, the proposed method is effectively applied in risk analysis of poultry farming.