Oligopolistic competition among the wireless internet service providers of Malaysia using fuzzy soft graphs

The competitive relationship among the objects of a system often show variation when it is examined relative to different aspects or attributes. Fuzzy soft theory allows parametrization in the problems with vague data, as it inherits the properties of a fuzzy set and soft set simultaneously. This feature of fuzzy soft theory influenced us to represent the variation in competition that appears among the constituents of a system. This article presents the competition graph and economic competition graph in fuzzy soft theory; the fuzzy soft competition graph and fuzzy soft economic competition graph. Various extensions of the proposed graphs like fuzzy soft k-competition graphs, p-competition fuzzy soft graph and m-step fuzzy soft competition graphs have also been defined together with examples and some important results. An application to fuzzy soft economic competition graphs is provided that shows diverse competition among the wireless internet service providers of Malaysia. As there exist only a few mobile operators which facilitate the whole country with the wireless internet service, this competitive market structure is an oligopoly. The strength of oligopolistic (economic) competition is also manipulated. An algorithm is also established that evaluates the strength of any fuzzy soft economic competition among the sellers.

Automated summary

This article introduces competition graph and economic competition graph in fuzzy soft theory, as well as various extensions such as fuzzy soft k-competition graphs and p-competition fuzzy soft graph. An algorithm is presented to evaluate the strength of fuzzy soft economic competition among sellers, with an application demonstrating diverse competition among wireless internet service providers in Malaysia.