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Lattice-valued soft algebras

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Abstract

Motivated by the rapidly developing theory of lattice-valued (or, more generally, variety-based) topological systems, which takes its origin in the crisp concept of S. Vickers (introduced as a common framework for both topological spaces and their underlying algebraic structures—frames or locales), the paper initiates a deeper study of one of its incorporated mathematical machineries, i.e., the realm of soft sets of D. Molodtsov. More precisely, we start the theory of lattice-valued soft universal algebra, which is based in soft sets and lattice-valued algebras of A. Di Nola and G. Gerla. In particular, we provide a procedure for obtaining soft versions of algebraic structures and their homomorphisms, as well as basic tools for their investigation. The proposed machinery underlies many concepts of (lattice-valued) soft algebra, which are currently available in the literature, thereby enabling the respective researchers to avoid its reinvention in future.

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Authors and Affiliations

  1. Department of Mathematics and Statistics, Faculty of Science, Masaryk University, Kotlarska 2, 611 37, Brno, Czech Republic

    Sergey A. Solovyov

  2. Institute of Mathematics and Computer Science, University of Latvia, Raina bulvaris 29, 1459, Riga, Latvia

    Sergey A. Solovyov

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  1. Sergey A. Solovyov
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Correspondence to Sergey A. Solovyov.

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Communicated by A. Jung.

This research was supported by the ESF Project No. CZ.1.07/2.3.00/20.0051 “Algebraic methods in Quantum Logic” of the Masaryk University in Brno, Czech Republic.

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Solovyov, S.A. Lattice-valued soft algebras. Soft Comput 17, 1751–1766 (2013). https://doi.org/10.1007/s00500-013-1020-z

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