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An investigation on m-polar fuzzy threshold graph and its application on resource power controlling system

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Abstract

The threshold graph is a well studied topic. But, the fuzzy threshold graph is defined recently and investigated many properties. In a fuzzy threshold graph, only one threshold is considered for every vertex and edge. In a m-polar fuzzy graph, each vertex and each edge has a m number of membership values. So, defining a threshold graph for m-polar fuzzy graph is not easy and needs some new ideas. By considering m thresholds each for each component out of m components of membership values of a vertex or edge, we defined m-polar fuzzy threshold graph (mPFTG). Many interesting properties are also presented on mPFTG. The mPFTG is also decomposed in a very unique way and this decomposition generates m different fuzzy threshold graphs and the properties of decomposed graphs are explained. The important parameters viz. m-polar fuzzy threshold dimension and mPF threshold partition number are also defined and investigated thoroughly. Finally, a real-life application using mPFTG on a resource power controlling system is presented.

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Acknowledgements

The authors are grateful to the learned reviewers for their valuable comments and suggestions to improve the quality of the article. Financial support of the first author offered by University Grants commission, New Delhi, India (UGC Ref.No:1215/CSIR-UGC NET DEC.2016) is thankfully acknowledged.

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  1. Department of Applied Mathematics with Oceanology and Computer Programming, Vidyasagar University, Midnapore, 721102, India

    Tanmoy Mahapatra & Madhumangal Pal

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  1. Tanmoy Mahapatra
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  2. Madhumangal Pal
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Correspondence to Madhumangal Pal.

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Mahapatra, T., Pal, M. An investigation on m-polar fuzzy threshold graph and its application on resource power controlling system . J Ambient Intell Human Comput 13, 501–514 (2022). https://doi.org/10.1007/s12652-021-02914-6

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