China
Africa
Explore chapters and articles related to this topic
Introduction
Published in John N. Mordeson, Davender S. Malik, Fuzzy Automata and Languages, 2002
John N. Mordeson, Davender S. Malik
The real unit interval equipped with an averaging operator M=*, [141], gives an example of a commutative cl-semigroup as does a complete Heyting algebra with ∧=*.
Axiomatic characterizations of (𝔾, 𝕆)-fuzzy rough approximation operators via overlap and grouping functions on a complete lattice
Published in International Journal of General Systems, 2023
Yan Sun, Bin Pang, Ju-Sheng Mi
Rough set theory has been proposed by Pawlak (1982) for 40 years. Combining with fuzzy set theory, fuzzy rough set theory has deserved more and more attention. In the framework of (fuzzy) rough set theory, axiomatic and constructive approaches to the pair of upper and lower (fuzzy) rough approximation operators, which are based on coverings (Zhu and Wang 2003, 2007; Zhang, Li, and Wu 2010; Zhang and Luo 2011), generalized neighborhood systems (Li et al. 2021; Yao 1998b; Zhao, Pang, and Mi 2022; Zhao et al. 2019; Zhao and Shi 2021) and binary relations (Mi and Zhang 2004; Shao, Wu, and Wang 2019; Wu, Shao, and Wang 2019; Wei, Pang, and Mi 2021; Yao 1998a), are developed rapidly. In order to define fuzzy rough approximation operators, a suitable truth value lattice should be chosen to describe the degree of membership. From the side of lattice theory, the underlying truth value lattice has been generalized from the unit interval (Wu and Zhang 2004; Yao and Lin 1996; Yao 1997) to a residuated lattice (She and Wang 2009), an integral and commutative quantale (Zhao et al. 2019), a completely distributive De Morgan algebra (Pang, Mi, and Xiu 2019; Li et al. 2021), a complete Heyting algebra (Pang and Mi 2020) and a GL-quantale (Wei, Pang, and Mi 2021). In this paper, we also continue to explore axiomatic characterizations of upper and lower fuzzy rough approximation operators on a complete lattice with an involution negation.
On the representations of L-equivalence relations on L-fuzzy sets with applications to locally vague environments
Published in International Journal of General Systems, 2020
It is worth of notice that if is particularly chosen as a complete Heyting algebra (i.e. ), then since for all with (Pu and Zhang 2012), an -relation E on a is μ-transitive iff E satisfies (P2). This shows that an -equivalence relation on μ coincides with an -valued equivalence on μ in Krapež, Šešelja, and Tepavčević (2019) if is a complete Heyting algebra.
Fragments of quasi-Nelson: residuation
Published in Journal of Applied Non-Classical Logics, 2023
Let a bounded implicative semilattice with a nucleus and let be a complete Heyting algebra. Suppose . Letting, for all , we have that is nuclear Heyting algebra and agrees with on S.