Vague multigraphs
A vague graph is a generalized structure of a fuzzy graph that gives more precision, flexibility and compatibility to a system when compared with systems that are designed using fuzzy graphs. In this paper, we applied the notion of vague sets to multigraphs and we introduce the concepts of vague mul...
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| Published in | Soft computing (Berlin, Germany) Vol. 23; no. 23; pp. 12607 - 12619 |
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| Main Authors | , |
| Format | Journal Article |
| Language | English |
| Published |
Berlin/Heidelberg
Springer Berlin Heidelberg
01.12.2019
Springer Nature B.V |
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| Abstract | A vague graph is a generalized structure of a fuzzy graph that gives more precision, flexibility and compatibility to a system when compared with systems that are designed using fuzzy graphs. In this paper, we applied the notion of vague sets to multigraphs and we introduce the concepts of vague multiset and Vague multigraph, which are two subclass of vague sets and vague graphs, respectively. Then we define the fundamental concepts of Vague multigraphs and get some related results. Moreover, by considering the notions of strength of edge, effective edge and effective vague multigraph, we investigate the planarity of a vague multigraph. Finally, we give an application for designing and modeling of streets in a city, by vague multigraphs. |
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| AbstractList | A vague graph is a generalized structure of a fuzzy graph that gives more precision, flexibility and compatibility to a system when compared with systems that are designed using fuzzy graphs. In this paper, we applied the notion of vague sets to multigraphs and we introduce the concepts of vague multiset and Vague multigraph, which are two subclass of vague sets and vague graphs, respectively. Then we define the fundamental concepts of Vague multigraphs and get some related results. Moreover, by considering the notions of strength of edge, effective edge and effective vague multigraph, we investigate the planarity of a vague multigraph. Finally, we give an application for designing and modeling of streets in a city, by vague multigraphs. |
| Author | Borzooei, R. A. Baghernejad, M. |
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| Keywords | Vague multigraph Vague graph Planarity of vague multigraph Vague multiset |
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| References | Akram, Sarwar, Borzooei (CR4) 2018; 35 Borzooei, Rashmanlou (CR9) 2015; 29 Ramakrishna (CR16) 2009; 7 Rashmanlou, Borzooei (CR17) 2015; 30 Yager (CR19) 1986; 13 Gani, Latha (CR12) 2012; 6 CR14 Maheswari, Sekar (CR15) 2015; 5 Borzooei, Rashmanlou (CR8) 2015; 33 Akram, Chen, Shum (CR1) 2013; 37 Zadeh (CR20) 1965; 8 Baowen, Peizhuang, Xihui, Yong (CR5) 1988; 15 Pramanik, Samanta, Pal (CR13) 2016; 7 Gau, Buherer (CR11) 1993; 23 Akram, Gani, Saeid (CR3) 2014; 26 Blizard (CR7) 1988; 30 Diestel (CR10) 2017 Bhattacharya (CR6) 1987; 6 Rosenfeld (CR18) 1975 Akram, Feng, Sarwar, Jun (CR2) 2014; 67 WL Gau (3814_CR11) 1993; 23 R Diestel (3814_CR10) 2017 3814_CR14 RR Yager (3814_CR19) 1986; 13 N Ramakrishna (3814_CR16) 2009; 7 T Pramanik (3814_CR13) 2016; 7 LA Zadeh (3814_CR20) 1965; 8 M Akram (3814_CR2) 2014; 67 H Rashmanlou (3814_CR17) 2015; 30 A Rosenfeld (3814_CR18) 1975 L Baowen (3814_CR5) 1988; 15 AN Gani (3814_CR12) 2012; 6 M Akram (3814_CR3) 2014; 26 P Bhattacharya (3814_CR6) 1987; 6 RA Borzooei (3814_CR9) 2015; 29 M Akram (3814_CR1) 2013; 37 RA Borzooei (3814_CR8) 2015; 33 M Akram (3814_CR4) 2018; 35 WD Blizard (3814_CR7) 1988; 30 NRS Maheswari (3814_CR15) 2015; 5 |
| References_xml | – volume: 15 start-page: 811 issue: 10 year: 1988 end-page: 818 ident: CR5 article-title: Fuzzy bags and relations with set-valued statistics publication-title: Comput Math Appl doi: 10.1016/0898-1221(88)90118-6 contributor: fullname: Yong – year: 2017 ident: CR10 publication-title: Graph theory doi: 10.1007/978-3-662-53622-3 contributor: fullname: Diestel – volume: 8 start-page: 338 year: 1965 end-page: 353 ident: CR20 article-title: Fuzzy sets publication-title: Inf Control doi: 10.1016/S0019-9958(65)90241-X contributor: fullname: Zadeh – volume: 6 start-page: 517 year: 2012 end-page: 523 ident: CR12 article-title: On irregular fuzzy graphs publication-title: Appl Math Sci contributor: fullname: Latha – volume: 7 start-page: 653 issue: 4 year: 2016 end-page: 664 ident: CR13 article-title: Interval-valued fuzzy planar graphs publication-title: Int J Mach Learn Cybern doi: 10.1007/s13042-014-0284-7 contributor: fullname: Pal – volume: 7 start-page: 51 year: 2009 end-page: 58 ident: CR16 article-title: Vague graphs publication-title: Int J Comput Cognit contributor: fullname: Ramakrishna – start-page: 77 year: 1975 end-page: 95 ident: CR18 publication-title: Fuzzy graphs, fuzzy sets and their applications contributor: fullname: Rosenfeld – ident: CR14 – volume: 5 start-page: 135 issue: 2 year: 2015 end-page: 144 ident: CR15 article-title: Semi neighbourly irregular graphs publication-title: Int J Comb Graph Theory Appl contributor: fullname: Sekar – volume: 30 start-page: 371 issue: 1 year: 2015 end-page: 382 ident: CR17 article-title: Product vague graphs and its applications publication-title: J Intell Fuzzy Syst doi: 10.3233/IFS-151762 contributor: fullname: Borzooei – volume: 26 start-page: 647 year: 2014 end-page: 653 ident: CR3 article-title: Vague hypergraphs publication-title: J Intell Fuzzy Syst contributor: fullname: Saeid – volume: 30 start-page: 36 issue: 1 year: 1988 end-page: 66 ident: CR7 article-title: Multiset theory publication-title: Notre Dame J Form Log doi: 10.1305/ndjfl/1093634995 contributor: fullname: Blizard – volume: 13 start-page: 23 year: 1986 end-page: 37 ident: CR19 article-title: On the theory of bags publication-title: Int. 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