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

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Abstract

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.

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Acknowledgements

The author was supported by the Education for Competitiveness Operational Programme project “Encourage the creation of excellent research teams and intersectoral mobility at Palacky University in Olomouc” Reg. No. CZ.1.07/2.3.00/30.0004, which is co-financed by the European Social Fund and the state budget of the Czech Republic.

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Authors and Affiliations

  1. Department of Mathematics, Mata Gujri College, Fatehgarh Sahib, 140407, India

    Pushpinder Singh

  2. Department of Mathematics, Lovely Professional University, Phagwara, Punjab, 144 411, India

    Nitin Kumar Mishra, Manoj Kumar & Seema Saxena

  3. Department of Mathematics, IKGPTU Campus, Batala, Punjab, 143506, India

    Vikramjeet Singh

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  1. Pushpinder Singh
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  2. Nitin Kumar Mishra
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  3. Manoj Kumar
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  4. Seema Saxena
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  5. Vikramjeet Singh
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Correspondence to Pushpinder Singh.

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Singh, P., Mishra, N.K., Kumar, M. et al. Risk analysis of flood disaster based on similarity measures in picture fuzzy environment. Afr. Mat. 29, 1019–1038 (2018). https://doi.org/10.1007/s13370-018-0597-x

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