fuzzy-nominal-sets-–-springer

Fuzzy nominal sets – Springer

Abstract

In this paper, we use two approaches to define the concept of fuzzy nominal sets: classic and universal algebraic. We see that the fuzzy nominal sets obtained using the universal algebraic approach (so-called fuzzy nominal sets) are within finitely supported mathematics, whereas the fuzzy nominal sets derived using the classical approach (so-called fuzzy nominal (nu _{_{textrm{supp}}})-sets) are within ordinary mathematics and each fuzzy nominal set can be considered as a fuzzy nominal (nu _{textrm{supp}})-set. We also go over the presheaf representation of fuzzy nominal sets and some other properties of these various types of fuzzy nominal sets.

Access this article

Log in via an institution

Subscribe and save

  • Get 10 units per month
  • Download Article/Chapter or Ebook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime

Subscribe now

Buy Now

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Data Availability

Our research does not involve any original data collection, and the study is based on existing literature and theoretical analysis.

References

  • Adamek J, Herrlich H, Strecker GE (2004) Abstract and concrete categories. The joy of cats

  • Ajmal N (1994) Fuzzy lattices. Inf Sci 79:271–291

    Article  MathSciNet  Google Scholar 

  • Alexandru A, Ciobanu G (2018) Fuzzy sets within finitely supported mathematics. Fuzzy Sets Syst 339:119–133

    Article  MathSciNet  Google Scholar 

  • Alexandru A, Ciobanu G (2020) Foundations of finitely supported structures: a set theoretical viewpoint. Springer

    Book  Google Scholar 

  • Boixader D, Recasens J (2018) Fuzzy actions. Fuzzy Sets Syst 339:17–30

    Article  MathSciNet  Google Scholar 

  • Demirci M, Recasens J (2004) Fuzzy groups, fuzzy functions and fuzzy equivalence relations. Fuzzy Sets Syst 144:441–458

    Article  MathSciNet  Google Scholar 

  • Dixit VN, Rujesh K, Ajmal N (1992) On fuzzy rings. Fuzzy Sets Syst 49:205–213

    Article  Google Scholar 

  • Ebrahimi MM, Mahmoudi M (2001) The category of M-sets. Ital J Pure Appl Math 9:123–132

    Google Scholar 

  • Fraenkel JA (1922) Der begriff definit und die unabhangigkeit des auswahlsaxioms. Sitzungsberichte der Preussischen Akademie der Wissenschaften, Physikalisch-mathematische Klasse, pp 253–257

  • Fernandez M, Gabbay M (2007) Nominal rewriting. Inf Comput 205:917–965

    Article  MathSciNet  Google Scholar 

  • Gabbay M, Hofmann M (2008) Nomianl renaming sets. In: International conference on logic for programming, artificial intelligence, and reasoning, pp 158–173

  • Gabbay M, Pitts A (2002) A new approach to abstract syntax with variable binding. Form Asp Comput 13(3–5):341–363

    Article  Google Scholar 

  • Goguen JA (1967) L-fuzzy sets. J Math Anal Appl 18(1):145–174

    Article  MathSciNet  Google Scholar 

  • Haddadi M (2014) Fuzzy acts over fuzzy semigroups and sheaves. Iran J Fuzzy Syst 11(4):61–73

    MathSciNet  Google Scholar 

  • Kilp M, Knauer U, Mikhalev A (2000) Monoids, acts and categories. Walter de Gruyter, Berlin

  • Kurz A, Petrişan D (2010) On universal algebra over nominal sets. Math Struct Comput Sci 20(2):285–318

    Article  MathSciNet  Google Scholar 

  • Kurz A, Petrişan D, Velebil J (2014) Algebraic theories over nominal sets. In: International conference on relational and algebraic methods in computer science, pp 429–445

  • Mordeson JN, Bhutani R, Rosenfeld A (2005) Fuzzy group theory. Springer

    Book  Google Scholar 

  • Pasbani H, Haddadi M (2022) The fresh-graph of a nominal set. DMAA 15:2250161

    MathSciNet  Google Scholar 

  • Pitts A (2013) Nominal sets, names and symmetry in computer science. Cambridge University Press, Cambridge

    Book  Google Scholar 

  • Pitts A (2015) Nominal presentation of cubical sets models of type theory. Leibniz Int Proc Inform 39:202–220

    MathSciNet  Google Scholar 

  • Rajaretnam T, Ayyaswamy SK (2011) Fuzzy monoids in a fuzzy finite state automaton with unique membership transition on an input symbol. Int J Math Sci Comput I I:48–51

    Google Scholar 

  • Tennison BR (1975) Sheaf theory, vol 21. Cambridge University Press, Cambridge

    Book  Google Scholar 

  • Zadeh LA (1965) Fuzzy sets. Inf Control 8:338–353

    Article  Google Scholar 

Download references

Funding

The authors received no financial support for the research, authorship, and/or publication of this article.

Author information

Authors and Affiliations

  1. Faculty of Mathematics, Statistics and Computer Science, Semnan University, Semnan, Iran

    N. S. Razmara & M. Haddadi

  2. Department of Mathematics, Velayat University, Iranshahr, Sistan and Balouchestan, Iran

    Kh. Keshvardoost

Contributions

N.S. R.: conceptualization, and writing original draft. M. H.: supervision, review, and editing. Kh. K.: review and editing.

Corresponding author

Correspondence to M. Haddadi.

Ethics declarations

Conflict of interest

The authors declare that they have no conflict of interest.

Ethical approval

Not applicable.

Informed consent

Not applicable.

Additional information

Publisher’s Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Razmara, N.S., Haddadi, M. & Keshvardoost, K. Fuzzy nominal sets. Soft Comput (2024). https://doi.org/10.1007/s00500-024-09709-9

Download citation

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/s00500-024-09709-9

Keywords

Mathematics Subject Classification