|Table of Contents|

Operations and decompositions of m-polar fuzzy graphs(PDF)

《纺织高校基础科学学报》[ISSN:1006-6977/CN:61-1281/TN]

Issue:
2017年02期
Page:
149-162
Research Field:
Publishing date:

Info

Title:
Operations and decompositions of m-polar fuzzy graphs
Author(s):
LI Shenggang1YANG Xiaofei2LI Hongxia3MA Miao4
 1.College of Mathematics and Information Science, Shaanxi Normal University, Xi’an 710119, China;
2.School of Science, Xi’an Polytechnic University,Xi’an 710048, China;
3.School of Mathematics and Statistics, Longdong University, Qingyang 745000,Gansu, China;
4.College of Computer Science, Shaanxi Normal University, Xi’an 710119, China
Keywords:
m-polar fuzzy graph operation on m-polar fuzzy graphs decomposition of m-polar fuzzy graphs
PACS:
O 157.5
DOI:
10.13338/j.issn.1006-8341.2017.02.001
Abstract:
The operations union, join, composition, cartesian product, direct product, strong product, semi strong product, and dictionary product on m-polar fuzzy graphs are defined, and some necessary or sufficient conditions under which an m-polar fuzzy graph can be decomposed into the union(resp., join, composition, cartesian product, direct product, strong product, semi strong product,dictionary product)of two m-polar fuzzy graphs are given. Based on these results, equivalent definitions of m-polar fuzzy graph and union(resp., join, composition, cartesian product,direct product, strong product, semi strong product, dictionary product)of two finite m-polar fuzzy graphs are obtain. This not only exhibits the rationality of these operations defined on m-polar fuzzy graphs but also provides a way to fuzzify some crisp mathematical operations(e.g. union of two matroids, intersection of two matroids, etc.).

References:

[1] LI S G,LU J,ZHONG X J.Survey of local connectedness axioms and their properties in L-topological spaces[J].Fuzzy Sets and Systems,2008,159(5):588-604. [2] ZADEH L A.Fuzzy sets[J].Information and Control,1965,8(3):338-353. [3] CHEN J J,LI S G,WA S,et al.m-polar fuzzy sets:An extension of bipolar fuzzy sets[J].The Scientific World Journal,2014,DOI:10.1155/2014/415530. [4] KOCZY L T.Vectorial I-fuzzy sets[M].Approximate Reasoning in Decision Analysis,1982:151-156. [5] WANG G J,ZHOU H J.Quantitative logic[J].Information Sciences,2009,179(3):226-247. [6] LIANG J Y,LI R,QIAN Y H.Distance:A more comprehensible perspective for measures in rough set theory[J].Knowledge-Based Systems,2012,27:126-136. [7] AKRAM M.Bipolar fuzzy graphs[J].Information Sciences,2011,181(24):5548-5564. [8] YANG H L,LI S G,YANG W H,et al.Notes on bipolar fuzzy graphs[J].Information Sciences,2013,242(1):113-121. [9] MORDESON J N,NAIR P S.Fuzzy graphs and fuzzy hypergraphs[M].Berlin: Physica Verlag,2000. [10] HARARY F.Graph theory[M].3rd ed.Reading,Massachusetts:Addison Wesley,1972. [11] SABIDUSSI G.Graph multiplication[J].Mathematische Zeitschrift,1960,72:446-457. [12] WHITEHEAD A N, RUSSELL B.Principia mathematica[M].London: Cambridge University Press,1912. [13] IMRICH W, KLAVZAR S.Products graphs:Structure and recognition[M].New York: Wiley,2000. [14] ROBERTSON N,SEYMOUR P D.Graph minors,II,algorithmic aspects of tree-width[J].Journal of Algorithms,1986,7(3):309-322. [15] KOSTER A M C A,Van HOESEL S P M,KOLEN A W J.Solving frequency assignment problems via tree-decompositionp[J].Electronic Notes in Discrete Mathematics,1993,3(5):102-105. [16] BACH F R,JORDAN M I.Thin junction trees[J].Advances in Neural Information Processing Systems,2002,14(2):569-576.

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Last Update: 2017-07-22