Abstract
An m-polar fuzzy model is useful for multipolar information, multi-agent, multi-attribute and multi-object network models. In this research paper, the concept of m-polar fuzzy competition graphs is introduced and some related properties of m-polar open neighbourhood graphs, m-polar fuzzy closed neighbourhood graphs, m-polar fuzzy k-competition graphs and underlying m-polar fuzzy graphs are investigated. Some interesting applications of m-polar fuzzy competition graphs in different fields including business marketing, politics, network communication and social networks are described. Certain algorithms for computing strength of competition in each application are presented.












Similar content being viewed by others
Explore related subjects
Discover the latest articles, news and stories from top researchers in related subjects.References
Al-Hawary T (2011) Complete fuzzy graphs. Int J Math Comb 4:26–34
Al-Shehri NO, Akram M (2015) Bipolar fuzzy competition graphs. Ars Comb 121:385–402
Akram M (2011) Bipolar fuzzy graphs. Inf Sci 181(24):5548–5564
Akram M, Waseem N (2016) Certain metrices in \(m\)-polar fuzzy graphs. N Math Nat Comput 12(2):135–155
Akram M, Sarwar M (2016) Novel applications of \(m\)-polar fuzzy hypergraphs. J Intell Fuzzy Syst. doi:10.3233/JIFS-16859
Akram M, Adeel A (2016) \(m\)-polar fuzzy labeling graphs with application. Math Comput Sci 10:387–402
Akram M, Younas HR (2016) Certain types of irregular m-polar fuzzy graphs. J Appl Math Comput. doi:10.1007/s12190-015-0972-9
Bhattacharya P (1987) Some remarks on fuzzy graphs. Pattern Recogn Lett 6(5):297–302
Bhutani KR, Rosenfeld A (2003) Strong arcs in fuzzy graphs. Inf Sci 152:319–322
Butt A, Akram M (2016) A novel fuzzy decision-making system for CPU scheduling algorithm. Neural Comput Appl 27:1927–1939
Chen J, Li S, Ma S, Wang X (2014) \(m\)-polar fuzzy sets: an extension of bipolar fuzzy sets. The Scientific World Journal 2014 Article ID 416530
Cohen JE (1968) Interval graphs and food webs: a finding and a problem, Document 17696-PR. RAND Coporation, Santa Monica
Deli I, Eraslan S, Cagman N (2016) ivnpiv-Neutrosophic soft sets and their decision making based on similarity measure. Neural Comput Appl. doi:10.1007/s00521-016-2428-z
Djouadi Y, Prade H (2009) Interval-valued fuzzy formal concept analysis. In: International symposium on methodologies for intelligent systems. Springer, Berlin Heidelberg, pp 592-601
Harary F (1972) Graph theory. Addison-Wesley, Boston
Hsu W (2015) A fuzzy multiple criteria decision making system for analyzin gaps of service quality. Int J Fuzzy Syst 17(2):256–267
Kaufmann A (1975) Introduction la thorie des sous-ensembles flous lusage des ingnieurs (fuzzy sets theory). Masson, Paris
Kumar ChA (2012) Fuzzy clustering-based formal concept analysis for association rules mining. Appl Artif Intell 26(3):274–301
Kumar ChA, Srinivas S (2010) Concept lattice reduction using fuzzy K-means clustering. Exp Syst Appl 37(3):2696–2704
Mordeson JN, Chang-Shyh P (1994) Operations on fuzzy graphs. Inf Sci 79(3):159–170
Mordeson JN, Nair PS (1998) Fuzzy graphs and fuzzy hypergraphs. Physica, Heidelberg Second Edition 2001
Mathew S, Sunitha M (2009) Types of arcs in a fuzzy graph. Inf Sci 179(11):1760–1768
Pramanik T, Samanta S, Sarkar B, Pal M (2016) Fuzzy \(\phi \)-tolerance competition graphs. Soft Comput. doi:10.1007/s00500-015-2026-5
Pramanik T, Samanta S, Pal M, Mondal S, Sarkar B (2016) Interval-valued fuzzy phi-tolerance competition graphs. SpringerPlus 5(1):1981
Rosenfeld A (1975) Fuzzy Sets and their Applications. In: Zadeh LA, Fu KS, Shimura M (eds), Academic, New York, pp 77–95
Samanta S, Pal M (2013) Fuzzy \(k-\)competition and \(p-\)competition graphs. Fuzzy Inf Eng 2:191–204
Samanta S, Sarkar B, Shin D, Pal M (2016) Completeness and regularity of generalized fuzzy graphs. SpringerPlus 5(1):1979
Singh PK, Kumar ChA (2014) Bipolar fuzzy graph representation of concept lattice. Inf Sci 288:437–448
Sarwar M, Akram M (2016) Novel concepts bipolar fuzzy competition graphs. J Appl Math Comput. doi:10.1007/s12190-016-1021-z
Wang J, Wanf J-Q, Zhang HY, Chen X-H (2016) Multi-criteria group decision-making approach based on 2-tuple linguistic aggregation operators with multi-hesitant fuzzy linguistic information. Int J Fuzzy Syst 18:81–97
Yang HL, Li SG, Yang WH, Lu Y (2013) Notes on bipolar fuzzy graphs. Inf Sci 242:113–121
Zadeh LA (1965) Fuzzy sets. Inf Control 8(3):338–353
Zadeh LA (1971) Similarity relations and fuzzy orderings. Inf Sci 3(2):177–200
Zhang W -R (1994) Bipolar fuzzy sets and relations: a computational framework for cognitive modeling and multiagent decision analysis. In Proceeding of IEEE conference on fuzzy information processing society biannual conference, pp 305–309
Acknowledgements
The authors are thankful to Editor-in-Chief, Professor John MacIntyre, and the referees for their invaluable comments and suggestions.
Author information
Authors and Affiliations
Corresponding author
Ethics declarations
Conflicts of interest
The authors declare that there is no conflict of interest regarding the publication of this research paper.
Rights and permissions
About this article
Cite this article
Akram, M., Sarwar, M. Novel applications of m-polar fuzzy competition graphs in decision support system. Neural Comput & Applic 30, 3145–3165 (2018). https://doi.org/10.1007/s00521-017-2894-y
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00521-017-2894-y