Risk analysis of flood disaster based on similarity measures in picture fuzzy environment

Flood is a common natural disaster in the world. Flood often takes place around the river and plains, which indicates a higher risk of flooding in these areas. In order to represent the consequences (affected area, the number of deaths, housing collapse, direct economic losses) of flood disaster picture fuzzy sets have been used. Picture fuzzy sets are the extensions of intuitionistic fuzzy sets. Picture fuzzy sets based models may be adequate in situations when we face human opinions involving more answers of the type: yes, abstain, no, refusal. In this paper, we propose several distance and similarity measures for picture fuzzy sets which considers the degree of positive membership, degree of neutral membership, the degree of negative membership and degree of refusal membership. Geometrical interpretation of the picture fuzzy sets has been investigated. On the basis of proposed similarity measures a clustering algorithm is adopts to assess flood disaster risk in South region of India. A case study of 2009 Indian flood is captured to investigate the risk analysis of flood disaster considering some important criterion such as affected area, the number of deaths, housing collapse and direct economic losses.