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Some results on state ideals in state residuated lattices

  • Fuzzy systems and their mathematics
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Abstract

In a large number of multivalued logic and fuzzy logic of algebraic systems, residuated lattices play a prominent role and have considerable applications. States operators have been introduced on residuated lattices, and their properties are useful for the development of an algebraic theory of probabilistic models of those algebras. In this paper, we introduce the notion of state ideal in the framework of state residuated lattices, investigate some related properties, and provide several examples. Also, we present two types of state residuated lattices: state i-simple residuated lattices and state i-local residuated lattices, and characterize them. Moreover, the relationship between state ideals and state filters is analyzed using the set of complement elements. Furthermore, we prove that the lattice of all state ideals of a given state residuated lattice is a complete lattice. The notion of obstinate state ideals in state residuated lattices is also introduced, and several characterizations are presented.

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Acknowledgements

Authors would like to thank the anonymous referees for many valuable comments that have substantially improved this paper.

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The authors did not receive support from any organization for the submitted work.

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Authors and Affiliations

  1. Department of Mathematics and Computer Science, Faculty of Science, University of Dschang, Dschang, Cameroon

    Francis Woumfo & Blaise Bleriot Koguep Njionou

  2. Department of Mathematics, École Normale Supérieure de Yaoundé, University of Yaoundé 1, P.O. Box 47, Yaoundé, Cameroon

    Etienne Romuald Temgoua

  3. Tokyo Denki University, Tokyo, Japan

    Michiro Kondo

Authors
  1. Francis Woumfo
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  2. Blaise Bleriot Koguep Njionou
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  3. Etienne Romuald Temgoua
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  4. Michiro Kondo
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Contributions

All authors contributed to the study conception and design. Material preparation and data collection were performed by Etienne Romuald Temgoua Alomo. The first draft of the manuscript was written by Francis Woumfo, and Blaise Bleriot Koguep Njionou checked the results and commented on previous versions of the manuscript. Michiro Kondo verified the relevance of the results and the quality of the writing. All authors read and approved the final manuscript.

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Correspondence to Blaise Bleriot Koguep Njionou.

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Woumfo, F., Koguep Njionou, B.B., Temgoua, E.R. et al. Some results on state ideals in state residuated lattices. Soft Comput 28, 163–176 (2024). https://doi.org/10.1007/s00500-023-09300-8

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  • DOI: https://doi.org/10.1007/s00500-023-09300-8

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