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2020 | 30 | 4 | 29-38

Article title

Intuitionistic fuzzy sets in assessing the marginal value of the elements of a multigraph

Content

Title variants

Languages of publication

EN

Abstracts

EN
The paper presents a method of assessing the value of individual elements of the multigraph, i.e., the value of its vertices and arcs, considering the fuzziness of its parameters. The need to take into account the specificity of the existing types of vertices (including logical functions specified on them) and the possibility of multiple relationships between two neighbouring vertices make it necessary to use a multigraph. The assumed basis for the evaluation of the individual elements of the multigraph was their marginal value, which is the so-called contribution of a given element to the entire multigraph, assuming that the given element affects not only the adjacent elements directly related to it but in a way, perhaps indirect, every other element of the multigraph.

Year

Volume

30

Issue

4

Pages

29-38

Physical description

Contributors

  • Wrocław University of Science and Technology, Łukasiewicza 5, 50-371 Wrocław, Poland
author
  • WSB University in Wroclaw, Fabryczna 29–31, 53-609 Wrocław, Poland

References

  • ATTANASSOV K.T., Intuitionistic Fuzzy Sets: Theory and Applications, Physica-Verlag, Springer, Heidelberg 1999.
  • FORLICZ S., MERCIK J., STACH I., RAMSEY D., The Shapley value for multigraphs [In:] N.T. Nguyen, E. Pimenidis, Z. Khan, B. Trawiński (Eds.), Computational Collective Intelligence, ICCCI, 2018, Lecture Notes in Computer Science, Vol. 11056, Springer, Cham, 213–221.
  • GŁADYSZ B., MERCIK J., RAMSEY D., A Fuzzy Approach to Some Shapley Value Problems in Group Decision Making, [In:] E. Algaba, V. Fragnelli, J. Sanchez-Soriano (Eds.), Handbook of the Shapley Value, CRC Press, Taylor and Francis Group, 2020, 483–514.
  • GŁADYSZ B., MERCIK J., The Shapley value in fuzzy simple cooperative games, [In:] N.T. Nguyen, D. Hoang, T.P. Hong, H. Pham, B. Trawiński (Eds.), Intelligent Information and Database Systems, ACIIDS 2018, Lecture Notes in Computer Science, Vol. 10751, Springer, Cham, 410–418.
  • GŁADYSZ B., MERCIK J., STACH I., Fuzzy Shapley value-based solution for communication network, [In:] N. Nguyen, R. Chbeir, E. Exposito, P. Aniorté, B. Trawiński (Eds.), Computational Collective Intelligence, ICCCI, 2019, Lecture Notes in Computer Science, Vol. 11683, Springer, Cham, 535–544.
  • MERCIK J., A power-graph analysis of non-fast information transmission, [In:] N.T. Nguyen, S. Toyo, L.M. Nguyen, B. Trawiński (Eds.), Intelligent Information and Database Systems, Part I, ACIIDS, 2017, Lecture Notes in Computer Science, Vol. 10191, 89–99, DOI: 10.1007/978-3-319-54472-4_9.
  • MERCIK J., ŁOBOS K., Index of implicit power as a measure of reciprocal ownership, Trans. Comp. Coll. Int., 2016, 23, 128–140.
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  • MYERSON R., Graphs and cooperation in games, Math. Oper. Res., 1997, 2, 225–229.
  • OWEN G., Values of games with a priori unions, [In:] R. Henn, O. Moeschlin (Eds.), Mathematical Economics and Game Theory, Springer-Verlag, Berlin 1977, 76–88.
  • SHAPLEY L.S., A value for n-person games, [In:] H. Kuhn, A.W. Tucker (Eds.), Contributions to the Theory of Games II, Princeton University Press, Ann. Math. Studies, 1953, 28, 307–317.
  • STACH I., Sub-coalitional approach to values, Springer Trans. Comp. Coll. Int., 2017, 10480, 75–87.
  • WANG F., ZENG S.L., ZHANG C.H., A method based on intuitionistic fuzzy dependent aggregation operators for suppliers selection, Math. Probl. Eng., 2013, Article ID 481202.
  • XU Z.S., Intuitionistic fuzzy aggregation operator, IEEE Trans. Fuzzy Syst., 2007, 15 (6), 1179–1187.
  • ZADEH L.A., Fuzzy sets, Inf. Control, 1965, 8, 338–353.

Document Type

Publication order reference

Identifiers

YADDA identifier

bwmeta1.element.desklight-4c130cdb-9760-4ff2-b0b5-2a2b7f5fb69b
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