Cooperation Game on Communication Multigraph with Fuzzy Parameters

• Published in: Computational Collective Intelligence Vol. 13501; pp. 16 - 28
• Main Authors: Gładysz, Barbara, Mercik, Jacek
• Format: Book Chapter
• Language: English
• Published: Switzerland Springer International Publishing AG 2022; Springer International Publishing
• Series: Lecture Notes in Computer Science
• Subjects: Fuzzy communication structure; Fuzzy cooperative game; Maximal flow; Sub-additive characteristic function
• ISBN: 9783031160134; 3031160134
• ISSN: 0302-9743; 1611-3349
• DOI: 10.1007/978-3-031-16014-1_2

In this paper, we derive the Mean Value for nodes in Fuzzy Communication Structure (FCS). The novel solution is proposed for a class of cooperative games over FCS with a sub-additive characteristic function. We propose two cooperative game concepts over communication multigraph with fuzzy parameters. We also introduce how the fuzzy characteristic function is calculated via maximal flow. In the first model, parameters (arc capacities) of FCS are given by fuzzy numbers. In the second model, parameters (arc capacities) of FCS are given by fuzzy numbers, too, and there is also given fuzzy goal determining the degree of satisfaction with the flow value that can be transmitted in the network between each pair of network vertices. In order to compare nodes’ Mean Values, we use the possibility measure and expected fuzzy number value. Obtained results may be useful for managing of development of a network of communication nature. Illustrating examples are presented.