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Covering problem on fuzzy graphs and its application in disaster management system

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Abstract

Nowadays the fuzzy graphs gained popularity due to their wide applications in different areas of science, engineering, social sciences, etc.In this paper, we consider covering problem in fuzzy graph. Different types of covering problems have been defined in this paper. Almost all problems are new. For each of these problems separate study is required. Also, the covering set, strong covering set, minimal covering set, etc., are defined and explained with examples. In a graph, each vertex can cover only those vertices that lie within its covering radius along shortest path and no vertex can cover itself. Here, an algorithm is designed to find the different types of covering sets on a fuzzy graph. An imprecise number, instead of a real number, namely interval number and triangular fuzzy number are considered as arc length of a fuzzy graph. To the best of our knowledge no works are available for covering problem on fuzzy graphs/networks. An application of covering set in natural disaster management is discussed to highlight the importance of the covering problem. In this application, an algorithm is designed to find all the facility vertices (or supply vertices) for given vertex and covering radius.

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References

  • Abu Nayeem SkMd, Pal M (2005) Shortest path problem on a network with imprecise edge weight. Fuzzy Optim Decis Mak 4:293–312

    Article  MathSciNet  Google Scholar 

  • Agarwal PK, Ezra E, Sharir M (2012) Near-linear approximation algorithms for geometric hitting sets. Algorithmica 63:1–25

    Article  MathSciNet  Google Scholar 

  • Bhutani KR, Battou A (2003) On \(M\)-strong fuzzy graphs. Inf Sci 155(1–2):103–109

    Article  MathSciNet  Google Scholar 

  • Chaudhry SS (1993) New heuristics for the conditional covering problem. Opsearch 30:42–47

    MATH  Google Scholar 

  • Chaudhry SS, Moon ID, McCormick ST (1987) Conditional covering: greedy heuristics and computational results. Comput Oper Res 14:11–18

    Article  MathSciNet  Google Scholar 

  • Clarkson KL, Varadarajan KR (2007) Improved approximation algorithms for geometric set cover. Discrete Comput Geom 37:43–58

    Article  MathSciNet  Google Scholar 

  • Dinur I, Safra S (2005) On the hardness of approximating minimum vertex cover. Ann Math 162(1):1–32

    Article  MathSciNet  Google Scholar 

  • Dubois D, Prade H (1983) Ranking fuzzy numbers in the setting of possibility theory. Inf Sci 30:183–224

    Article  MathSciNet  Google Scholar 

  • Hastad J (2001) Some optimal inapproximality results. J ACM 48(4):798–859

    Article  MathSciNet  Google Scholar 

  • Khot S, Regev O (2008) Vertex cover might be hard to approximate to within \(2-\epsilon \). J Comput Syst Sci 74:335–349

    Article  MathSciNet  Google Scholar 

  • Koczy LT (1992) Fuzzy graphs in the evaluation and optimization of networks. Fuzzy Sets Syst 46:307–319

    Article  MathSciNet  Google Scholar 

  • Li K, Chen M (1994) The fuzzy shortest path problem and its most vital arcs. Fuzzy Sets Syst 58:343–353

    MathSciNet  Google Scholar 

  • Lotfi V, Moon ID (1997) Hybrid heuristics for conditional covering problem. Int J Model Simul 17:185–190

    Article  Google Scholar 

  • Lunday BJ, Smith JC, Goldberg JB (2005) Algorithms for solving the conditional covering problem on paths. Naval Res Logist 52:293–301

    Article  MathSciNet  Google Scholar 

  • Moon ID, Chaudhry SS (1984) An analysis of network location problems with distance constraints. Manag Sci 30:290–307

    Article  Google Scholar 

  • Moon ID, Papayanopoulos L (1995) Facility location on a tree with maximum distance constraints. Comput Oper Res 22:905–914

    Article  Google Scholar 

  • Ni Y (2005) Models and algorithm for stochastic minimum weight edge covering problem In: Proceedings of the fourth international conference on information and management sciences, Yunnan, China, pp 445–451

  • Ni Y (2008) Fuzzy minimum weight edge covering problem. Appl Math Model 32:1327–1337

    Article  MathSciNet  Google Scholar 

  • Okada S, Gen M (1993) Order relation between intervals and its application to shortest path problem. Comput Ind Eng 25:147–150

    Article  Google Scholar 

  • Okada S, Soper T (1997) A method for solving shortest path problem on the network with fuzzy arc lengths. Fuzzy Syst Assoc World Congress 3:189–194

    Google Scholar 

  • Pramanik T, Samanta S, Pal M (2014) Interval-valued fuzzy planar graphs. Int J Mach Learn Cybern 7(4):653–664

    Article  Google Scholar 

  • Pramanik T, Samanta S, Sarkar B, Pal M (2016) Fuzzy \(\phi \)-tolerance competition graphs. Soft Comput 2016:1–12. https://doi.org/10.1007/s00500-015-2026-5

    Article  Google Scholar 

  • Rosenfield A (1975) Fuzzy graphs fuzzy sets and their application (Zadeh LA, Fu KS, Shimura M, eds). Academic Press, New York, pp 77–95

  • Sahoo S, Pal M (2015a) Different types of products on intuitionistic fuzzy graphs. Pac Sci Rev A Nat Sci Eng 17(3):87–96

    Google Scholar 

  • Sahoo S, Pal M (2015b) Intuitionistic fuzzy competition graph. J Appl Math Comput 52(1):37–57

    MathSciNet  MATH  Google Scholar 

  • Sahoo S, Pal M (2016a) Product of intuitionistic fuzzy graphs and degree. J Intell Fuzzy Syst 32(1):1059–1067

    Article  Google Scholar 

  • Sahoo S, Pal M (2016b) Intuitionistic fuzzy tolerance graphs with application. J Appl Math Comput. https://doi.org/10.1007/s12190-016-1047-2

  • Samanta S, Pal M (2011a) Fuzzy tolerance graphs. Int J Latest Trends Math 1(2):57–67

    Google Scholar 

  • Samanta S, Pal M (2011b) Fuzzy threshold graphs. CIIT Int J Fuzzy Syst 3(12):360–364

    Google Scholar 

  • Samanta S, Pal M (2012a) Bipolar fuzzy hypergraphs. Int J Fuzzy Log Syst 2(1):17–28

    Article  Google Scholar 

  • Samanta S, Pal M (2012b) Irregular bipolar fuzzy graphs. Int J Appl Fuzzy Sets 2:91–102

    Google Scholar 

  • Samanta S, Pal M (2014) Some more results on bipolar fuzzy sets and bipolar fuzzy intersection graphs. J Fuzzy Math 22(2):253–262

    MATH  Google Scholar 

  • Samanta S, Pal M (2015) Fuzzy planar graphs. IEEE Trans Fuzzy Syst 23(6):1936–1942

    Article  Google Scholar 

  • Samanta S, Pramanik T, Pal M (2016) Fuzzy colouring of fuzzy graphs. Afr Mat 27(1):37–50

    Article  MathSciNet  Google Scholar 

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Acknowledgements

Financial support of first author by University Grants Commission, New Delhi, India (Fl-17.112014-15/RGNF-2014-15-SC-WES-63919(SA-Ill/Website)) is thankfully acknowledged. The authors are highly grateful to the reviewers for their critical comments and suggestions for the improvement of the paper.

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Authors and Affiliations

  1. Department of Applied Mathematics with Oceanology and Computer Programming, Vidyasagar University, Midnapore, 721 102, India

    Sonia Mandal & Madhumangal Pal

  2. Department of Mathematics, Raja N. L. Khan Women’s College, Gope Palace, Midnapore, 721102, India

    Nupur Patra

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  1. Sonia Mandal
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  2. Nupur Patra
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  3. Madhumangal Pal
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Correspondence to Sonia Mandal.

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Mandal, S., Patra, N. & Pal, M. Covering problem on fuzzy graphs and its application in disaster management system. Soft Comput 25, 2545–2557 (2021). https://doi.org/10.1007/s00500-020-05263-2

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