Intuitionistic Fuzzy Sets in Assessing the Marginal Value of the Elements of a Multigraph

• Autorzy: Barbara Gładysz , Jacek Mercik
• Języki publikacji: EN

Abstrakty

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. (original abstract)

Słowa kluczowe

EN

Graphs; Communication system; Fuzzy sets

PL

Grafy; System komunikacyjny; Zbiory rozmyte

• Czasopismo: Operations Research and Decisions
• Rocznik: 2020
• Tom: 30
• Numer: nr 4
• Strony: 29--38

Twórcy

autor

Barbara Gładysz

• Wrocław University of Science and Technology, Wrocław, Poland

autor

Jacek Mercik

• WSB University in Wroclaw, Wrocław, Poland

Bibliografia

• [1] ATTANASSOV K.T., Intuitionistic Fuzzy Sets: Theory and Applications, Physica-Verlag, Springer, Heidelberg 1999.
• [2] 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.
• [3] 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.
• [4] 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.
• [5] 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.
• [6] 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.
• [7] MERCIK J., ŁOBOS K., Index of implicit power as a measure of reciprocal ownership, Trans. Comp. Coll. Int., 2016, 23, 128-140.
• [8] MERCIK J., STACH I., On measurement of control in corporate structures, [In:] N. Nguyen, R. Kowalczyk, J. Mercik, A. Motylska-Kuźma (Eds.), Transactions on Computational Collective Intelligence, TCCI, 2018, Lecture Notes in Computer Science, Vol. 11290, Springer, Berlin, 64-79.
• [9] MYERSON R., Graphs and cooperation in games, Math. Oper. Res., 1997, 2, 225-229.
• [10] 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.
• [11] 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.
• [12] STACH I., Sub-coalitional approach to values, Springer Trans. Comp. Coll. Int., 2017, 10480, 75-87.
• [13] 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.
• [14] XU Z.S., Intuitionistic fuzzy aggregation operator, IEEE Trans. Fuzzy Syst., 2007, 15 (6), 1179-1187.
• [15] ZADEH L.A., Fuzzy sets, Inf. Control, 1965, 8, 338-353.

Identyfikatory

DOI

10.37190/ord200402