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A Network Shortest Path Algorithm via Hesitancy Fuzzy Digraph

Year 2019, Issue: 27, 52 - 62, 01.03.2019

Parimala Mani Said Broumi Karthika Muthusamy

Abstract

Many extension and generalization of fuzzy sets have been studied and introduced in the literature. Hesitancy fuzzy digraph is a generalization of intuitionistic fuzzy set and fuzzy graph.  In this paper, we redefine some basic operations of hesitancy fuzzy graph and it is referred as hesitancy fuzzy digraph (in short HFDG). We discuss some arithmetic operations and relations among HFDG. We further proposed a method to solve a shortest path problem through score function.

Keywords

Digraphs Hesitancy fuzzy sets Hesitancy fuzzy digraphs

References

  • [1] K. Atanassov, Intuitionistic fuzzy sets, Fuzzy Sets and Systems vol. 20 (1986) 87-96.
  • [2] N. X. Thao, F. Smarandache, N. V. Dinh. Support-Neutrosophic Set: A New Concept in Soft Computing, Neutrosophic Sets and Systems 16 (2017) 93-98.
  • [3] L. Zadeh, Fuzzy sets, Inform and Control 8 (1965) 338-353
  • [4] F. Smarandache, A Unifying Field in Logics. Neutrosophic Logic: Neutrosophy, Neutrosophic Set, Neutrosophic Probability, Rehoboth: American Research Press (1999).
  • [5] M. Parimala, M. Karthika, S. Jafari, F. Smarandache, and R. Udhayakumar, Decision-Making via Neutrosophic Support Soft Topological Spaces, Symmetry 10(6) (2017) 1-10.
  • [6] A. Kau®man, Introduction a la Theorie des Sous-emsembles Flous, Masson et Cie 1 1973.
  • [7] S. Broumi, M. Talea, A. Bakali, and F. Smarandache, Single-valued neutrosophic graphs ,Journal of New Theory 10 (2016) 86-101.
  • [8] M. Akram and S. Shahzadi, Neutrosophic soft graphs with application, Journal of Intelligent and Fuzzy Systems 32 (2017) 841-858.
  • [9] M. Akram, S. Shahzadi, and S. Broumi, Single-valued neutrosophic hypergraphs, TWMS Journal of Applied and Engineering Mathematics 2016.

Year 2019, Issue: 27, 52 - 62, 01.03.2019

Parimala Mani Said Broumi Karthika Muthusamy

Abstract

References

  • [1] K. Atanassov, Intuitionistic fuzzy sets, Fuzzy Sets and Systems vol. 20 (1986) 87-96.
  • [2] N. X. Thao, F. Smarandache, N. V. Dinh. Support-Neutrosophic Set: A New Concept in Soft Computing, Neutrosophic Sets and Systems 16 (2017) 93-98.
  • [3] L. Zadeh, Fuzzy sets, Inform and Control 8 (1965) 338-353
  • [4] F. Smarandache, A Unifying Field in Logics. Neutrosophic Logic: Neutrosophy, Neutrosophic Set, Neutrosophic Probability, Rehoboth: American Research Press (1999).
  • [5] M. Parimala, M. Karthika, S. Jafari, F. Smarandache, and R. Udhayakumar, Decision-Making via Neutrosophic Support Soft Topological Spaces, Symmetry 10(6) (2017) 1-10.
  • [6] A. Kau®man, Introduction a la Theorie des Sous-emsembles Flous, Masson et Cie 1 1973.
  • [7] S. Broumi, M. Talea, A. Bakali, and F. Smarandache, Single-valued neutrosophic graphs ,Journal of New Theory 10 (2016) 86-101.
  • [8] M. Akram and S. Shahzadi, Neutrosophic soft graphs with application, Journal of Intelligent and Fuzzy Systems 32 (2017) 841-858.
  • [9] M. Akram, S. Shahzadi, and S. Broumi, Single-valued neutrosophic hypergraphs, TWMS Journal of Applied and Engineering Mathematics 2016.
There are 9 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Research Article
Authors

Parimala Mani This is me

Said Broumi

Karthika Muthusamy This is me

Publication Date March 1, 2019
Submission Date September 3, 2018
Published in Issue Year 2019 Issue: 27

Cite

APA Mani, P., Broumi, S., & Muthusamy, K. (2019). A Network Shortest Path Algorithm via Hesitancy Fuzzy Digraph. Journal of New Theory(27), 52-62.
AMA Mani P, Broumi S, Muthusamy K. A Network Shortest Path Algorithm via Hesitancy Fuzzy Digraph. JNT. March 2019;(27):52-62.
Chicago Mani, Parimala, Said Broumi, and Karthika Muthusamy. “A Network Shortest Path Algorithm via Hesitancy Fuzzy Digraph”. Journal of New Theory, no. 27 (March 2019): 52-62.
EndNote Mani P, Broumi S, Muthusamy K (March 1, 2019) A Network Shortest Path Algorithm via Hesitancy Fuzzy Digraph. Journal of New Theory 27 52–62.
IEEE P. Mani, S. Broumi, and K. Muthusamy, “A Network Shortest Path Algorithm via Hesitancy Fuzzy Digraph”, JNT, no. 27, pp. 52–62, March 2019.
ISNAD Mani, Parimala et al. “A Network Shortest Path Algorithm via Hesitancy Fuzzy Digraph”. Journal of New Theory 27 (March 2019), 52-62.
JAMA Mani P, Broumi S, Muthusamy K. A Network Shortest Path Algorithm via Hesitancy Fuzzy Digraph. JNT. 2019;:52–62.
MLA Mani, Parimala et al. “A Network Shortest Path Algorithm via Hesitancy Fuzzy Digraph”. Journal of New Theory, no. 27, 2019, pp. 52-62.
Vancouver Mani P, Broumi S, Muthusamy K. A Network Shortest Path Algorithm via Hesitancy Fuzzy Digraph. JNT. 2019(27):52-6.
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