Affiliations: [a] Department of Mathematics, University of the Punjab, New Campus, Lahore, Pakistan
| [b] Faculty of Pure and Applied Mathematics, Wroclaw University of Science and Technology, Wyb. Wyspianskiego 27, Poland
| [c] Department of Mathematics, Faculty of Science, King Abdulaziz University, Saudi Arabia
Correspondence:
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Corresponding author. Wieslaw A. Dudek, Faculty of Pure and Applied Mathematics, Wroclaw University of Science and Technology, Wyb. Wyspianskiego 27, 50-370 Wroclaw, Poland. E-mail: [email protected].
Abstract: The imperfect competition models are equipped by fuzzy set theory with direct assessments of uncertainty. An appropriate point of departure for origination of a system with potentially broader coverage can be provided in view of fuzzy sets. In this way, several extensions of fuzzy set have been introduced to deal with uncertain and ambiguous information including relationships between objects. The q-rung picture fuzzy (q-RPF) model, which inherits the virtues of q-rung orthopair fuzzy set and picture fuzzy set, is one of the convenient way to represent such information. In order to exhibit interactions in various economic structures the conception of q-RPF economic competition graphs can be employed. Thus the intention of present study is to deal with q-rung picture fuzzy competition graphs (q-RPFCGs) and in particular, q-rung picture fuzzy economic competition graphs (q-RPFECGs) with its generalizations: q-RPF k-economic competition graphs; p-economic competition q-RPFGs; and m-step q-RPFECGs through several important results. Furthermore, this paper offers a brief review for perfect and imperfect competition in competitive market structures and sketch q-RPFECGs to represent duopoly, oligopoly, and monopolistic competitions in graph theoretic approach. Also, it designs an algorithm to calculate the strength of economic competition among buyers and sellers in imperfect competitive markets with q-RPF information.
