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Bipolar fuzzy matrices

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Abstract

In this article, bipolar fuzzy algebra and bipolar fuzzy relation are defined, and then, the bipolar fuzzy matrix is introduced. Also, an order relation (\(\le \)) is defined and it is proved that the bipolar fuzzy set is a poset and a lattice. Some results on transitive closure and power-convergent of bipolar fuzzy matrices are investigated. Some applications of bipolar fuzzy sets and bipolar fuzzy matrix are included in this study.

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Authors have no funding support to study and introduce the article.

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Authors and Affiliations

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

    Madhumangal Pal & Sanjib Mondal

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  1. Madhumangal Pal
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  2. Sanjib Mondal
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Correspondence to Sanjib Mondal.

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Communicated by A. Di Nola.

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Pal, M., Mondal, S. Bipolar fuzzy matrices. Soft Comput 23, 9885–9897 (2019). https://doi.org/10.1007/s00500-019-03912-9

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