JID:FSS AID:8320 /FLA [m3SC+; v1.354] P.1(1-21) Available online at www.sciencedirect.com ScienceDirect Fuzzy Sets and Systems ••• (••••) •••–••• www.elsevier.com/locate/fss An implementation of coloring of non-disjoint union of fuzzy graphs and fuzzy inference systems to coordinate traffic flows in paired intersections Isnaini Rosyida a,d , Dian Tri Wiyanti a , M. Fajar Safaatullah a , Alfa Narendra b , Nurhaida c,∗ a Department of Mathematics, Faculty of Mathematics and Natural Sciences, Universitas Negeri Semarang, Indonesia b Department of Civil Engineering, Faculty of Engineering, Universitas Negeri Semarang, Indonesia c Department of Mathematics and Statistics, Faculty of Mathematics and Natural Sciences, Universitas Papua, Indonesia d Postgraduate School, Department of Doctor of Information System, Universitas Diponegoro, Semarang, Indonesia Received 14 October 2021; received in revised form 16 March 2022; accepted 20 May 2022 Abstract In this paper, we have extended the formula of fuzzy chromatic number (FCN) for the non-disjoint union of two fuzzy graphs. Further, we constructed an algorithm based on the FCN for determining a fuzzy phase system in order to coordinate traffic flow of two paired intersections. By combining the fuzzy phase system and the fuzzy inference system, we were able to construct another algorithm to determine all possible phase timings for coordinating the intersections. Performance of the algorithms was evaluated through a case study at two intersections in Semarang City, Indonesia. The results showed that the proposed phase and timing systems for the two paired intersections could reduce the red and cycle times compared with the control of two intersections separately. The present findings might serve as a feasible proposal for congestion problems in any paired intersections.  2022 Elsevier B.V. All rights reserved. Keywords: Intersection; Traffic flows; Coloring; Non-disjoint; Union; Fuzzy graph; Mamdani; Fuzzy inference system 1. Introduction The economy of a country relies on several factors, including implementation of an effective and efficient trans- portation system. In fact, there are still many phenomena of traffic congestions at intersections during rush hours. Traffic congestions cause longer traffic time which in turn creates big losses in several sectors, such as the increase of the degree of air pollution, the rise of fuel consumption, and etc. * Corresponding author. E-mail addresses: isnaini@mail.unnes.ac.id, iisisnaini@gmail.com (I. Rosyida), dian.t.wiyanti@gmail.com (D.T. Wiyanti), mfajarsafaatullah@mail.unnes.ac.id (M.F. Safaatullah), alfa.narendra@mail.unnes.ac.id (A. Narendra), n.nurhaida@unipa.ac.id ( Nurhaida). https://doi.org/10.1016/j.fss.2022.05.017 0165-0114/ 2022 Elsevier B.V. All rights reserved.