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Multi attribute decision-making and interval-valued picture (S, T)-fuzzy graphs

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Abstract

In this manuscript, we introduce the notion of interval-valued picture (S, T)-fuzzy graphs (IVP-(S, T)-fuzzy graphs) which is the interplay between (S, T)-norms and picture fuzzy graphs. Interval-valued picture (S, T)-fuzzy graphs (IVP-(S, T)-fuzzy graphs) is also the extension of the picture fuzzy graphs. Since interval-valued picture fuzzy sets (IVPFSs) is the most extended form of the fuzzy sets to deal uncertainties, interval-valued picture (S, T)-fuzzy graphs (IVP-(S, T)-fuzzy graphs) would be more efficient to deal with the problems containing vagueness. For the sake of investigation, firstly we introduce and apply various operations like union, join, cartesian product, direct product, lexicographic product, ring sum, complement etc to interval-valued picture (S, T)-fuzzy graphs. Then, we study the structural properties of interval-valued picture (S, T)-fuzzy graphs (IVP-(S, T)-fuzzy graphs) through homomorphism, co-weak homomorphism, isomorphism etc. Afterwards, we initiate different types of interval-valued picture (S, T)-fuzzy graphs such as regular, total regular, constant etc. Moreover, we also explore some relationships among different types of interval-valued picture (S, T)-fuzzy graphs. Finally, we provide an application of interval-valued picture (S, T)-fuzzy graphs (IVP-(S, T)-fuzzy graphs) towards multiple attribute decision-making (MADM).

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Author notes

  1. Waheed Ahmad Khan, Hossein Rashmanlou, Asghar Khan and Adnan Muhammad have contributed equally to this work.

Authors and Affiliations

  1. Department of Mathematics, Abdul Wali Khan University, Mardan, Khyber Pakhtunkhwa, Pakistan

    Waqar Arif & Asghar Khan

  2. Division of Science and Technology, Department of Mathematics, University of Education Lahore, Attock Campus, Punjab, Pakistan

    Waheed Ahmad Khan

  3. Department of Mathematics, University of Mazandaran, Babolsar, Iran

    Hossein Rashmanlou

  4. School of Mathematics, Damghan University, Damghan, 3671641167, Iran

    Hossein Rashmanlou

  5. Department of Mathematics, University of Wah, Wah Cantt, Punjab, Pakistan

    Adnan Muhammad

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  1. Waqar Arif
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Correspondence to Waheed Ahmad Khan.

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Arif, W., Khan, W.A., Rashmanlou, H. et al. Multi attribute decision-making and interval-valued picture (S, T)-fuzzy graphs. J. Appl. Math. Comput. 69, 2831–2856 (2023). https://doi.org/10.1007/s12190-023-01862-y

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