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

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Abstract

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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Authors and Affiliations

  1. Department of Computer Science and Engineering, Saroj Mohan Institute of Technology, Hooghly, India

    Arindam Dey

  2. VNU Information Technology Institute, Vietnam National University, Hanoi, Vietnam

    Le Hoang Son

  3. Department of Mathematics, National Institute of Technology, Durgapur, India

    Anita Pal

  4. Division of Computational Mathematics and Engineering, Institute for Computational Science, Ton Duc Thang University, Ho Chi Minh City, Vietnam

    Hoang Viet Long

  5. Faculty of Mathematics and Statistics, Ton Duc Thang University, Ho Chi Minh City, Vietnam

    Hoang Viet Long

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  1. Arindam Dey
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  2. Le Hoang Son
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  3. Anita Pal
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  4. Hoang Viet Long
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Correspondence to Hoang Viet Long.

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Dey, A., Son, L.H., Pal, A. et al. Fuzzy minimum spanning tree with interval type 2 fuzzy arc length: formulation and a new genetic algorithm. Soft Comput 24, 3963–3974 (2020). https://doi.org/10.1007/s00500-019-04166-1

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  • DOI: https://doi.org/10.1007/s00500-019-04166-1

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