International Journal of Electrical and Computer Engineering (IJECE) Vol. 11, No. 6, December 2021, pp. 5286~5291 ISSN: 2088-8708, DOI: 10.11591/ijece.v11i6.pp5286-5291  5286 Journal homepage: http://ijece.iaescore.com An approximation of balanced score in neutrosophic graphs with weak edge weights V. Srisarkun 1 , C. Jittawiriyanukoon 2 1 Martin de Tours School of Management and Economics, Assumption University, Thailand 2 Graduate School of Business and Advanced Technology Management, Assumption University, Thailand Article Info ABSTRACT Article history: Received Aug 22, 2020 Revised Apr 21, 2021 Accepted May 19, 2021 Neutrosophic concept is known undirected graph theory to involve with complex logistic networks, not clearly given and unpredictable real life situations, where fuzzy logic malfunctions to model. The transportation objective is to ship all logistic nodes in the network. The logistic network mostly experiences in stable condition, but for some edges found to be volatile. The weight of these erratic edges may vary at random (bridge- lifting/bascule, ad hoc accident on road, traffic condition) In this article, we propose an approximation algorithm for solving minimum spanning tree (MST) of an undirected neutrosophic graphs (UNG), in which the edge weights represent neutrosophic values. The approximation upon the balanced score calculation is introduced for all known configurations in alternative MST. As the result, we further compute decisive threshold value for the weak weights amid minimum cost pre-computation. If the threshold triggers then the proper MST can direct the decision and avoid post-computation. The proposed algorithm is also related to other existing approaches and a numerical analysis is presented. Keywords: Approximation method Balanced score Logistic networks Minimum spanning tree Undirected neutrosophic graph This is an open access article under the CC BY-SA license. Corresponding Author: Chanintorn Jittawiriyanukoon Graduate School of Business and Advanced Technology Management Assumption University Bangkok, 10240, Thailand Email: pct2526@yahoo.com 1. INTRODUCTION Neutrosophy [1] is a new chapter of science that focuses on the scope of neutralities such as the origin, philosophy and nature. It differs from fuzzy logic [2] which studies the theory of truth degree. Some scholars have announced intuitionistic fuzzy set [3] by introducing the notion of false degree to the set. Later on neutrosophic concept has been firstly brought up by tallying the idea of indeterminate degree to the intuitionistic fuzzy set. Somehow a neutrosophic graph reflects generalities of intuitionistic fuzzy graph but also includes some faults in the definition as explained in [4]. They use some examples to prove that the complement of a neutrosophic graph does not always result a neutrosophic graph, but a graph developed from binary operations such as union, composition, join, is guaranteed to be a new neutrosophic graph. The neutrosophic graph extends the concept of conventional fuzzy set and intuitionistic fuzzy set by adding three independent functions, namely a truth membership (T), an indeterminate membership (I) and a false membership (F). The weights of individual t, i and f are falling within the interval range zero to one for the sake of associating them in real-world complications effectively [5]. The model is helpful as it represents uncertain real-life information such as inconsistency, incompletion or indetermination. It is applicable in multiple fields of engineering and computer science. In general, there are various algorithms [6] for solving