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Filter theory of extended implicative groupoids

Abstract

We investigate the filter theory of weak extended implicative groupoids. First, we introduce the well-known families of filters on weak extended implicative groupoids, and we study their basic properties. The family of weak extended implicative groupoids is very large and not well behaved; for providing a good characterization of the specific filters, such as positive implicative filters, we ought to separate this family into smaller parts. For this, we distinguish some types of weak extended implicative groupoids. Then we characterize the essential properties of these filters and the relation between these filters on different types of weak extended implicative groupoids.

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All authors contributed to the study conception and design. Material preparation, data collection and analysis were performed by all. The first draft of the manuscript was co-written and all authors commented on previous versions of the manuscript. All authors read and approved the final manuscript.

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Correspondence to R. A. Borzooei.

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Sameri, E., Borzooei, R.A. & Bagha, D.E. Filter theory of extended implicative groupoids. Soft Comput 25, 14499–14508 (2021). https://doi.org/10.1007/s00500-021-06383-z

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Keywords

  • Weak extended implicative groupoid
  • Filter
  • Positive implicative filter
  • Residuated structure