Fuzzy minimum spanning tree with interval type 2 fuzzy arc length: formulation and a new genetic algorithm

Fuzzy minimum spanning tree (FMST) has emerged from various real-life applications in different areas by considering uncertainty that exists in arc lengths of a fuzzy graph. In most relevant studies regarding FMST, type 1 fuzzy set was used to represent edge weights. Nonetheless, its membership values are totally crisp which is hard to determine its exact value by human perception. Interval type 2 fuzzy set (IT2FS) increases the number of degrees of freedom to express uncertainty of the edge weight and has more capacity to describe fuzzy information in a logically correct manner. In this paper, we propose the minimum spanning tree problem with undirected connected weighted interval type 2 fuzzy graph (FMST-IT2FS). Herein, the interval type 2 fuzzy set is used to represent the arc lengths of a fuzzy graph. Then, a new genetic algorithm is proposed to solve the FMST-IT2FS problem with the addition, ranking and defuzzification of IT2FSs being used. Illustrative examples are included to demonstrate the effectiveness of the proposed algorithm.

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