For L being a GL-quantale and based on the concept of L-valued relations, we propose generalized L-fuzzy rough sets as a further generalization of L-fuzzy rough sets, and then characterized the L-fuzzy rough sets are from both constructive and axiomatic approaches.Li, FeiYue, YueliYao, ...
The purpose of this note is to point out a mistake in [W. Yao, On many-valued L-fuzzy convergence spaces, Fuzzy Sets and Systems 159 (2008) 2503–2519] and to give a solution.关键词: Topology Stratified) L-filter Stratified) L-fuzzy convergence space Enriched) L-fuzzy topological space...
L-valued rough setFuzzy unionFuzzy intersectionL-valued relationTopologyIn this paper, considering L being a GL-quantale, we further develop the theory of L-valued rough sets with an L-set as the basic universe of defining L-valued rough approximation operators. Choosing an L-set as the ...
In this paper, we will develop the axiomatization of a comprehensive fuzzy rough set theory, that is, the so-called L-valued rough sets with an L-set serving as the foundational universe (referred to as the L-universe) for defining L-valued rough approximation operators, where L typically ...
Adopting the idea of single axiomatic characterizations of fuzzy rough sets , we will present the axiomatic characterizations of L -valued upper and lower rough approximation operators on an L -set with respect to reflexive, symmetric, transitive L -valued relations on an L -set as well as ...
(A. ostak, Towards the theory of approximate systems: variable-range categories. Proceedings of ICTA2011, Cambridge Univ. Publ. (2012) 265–284.) Such variable-range (quasi-)approximate systems can be realized as special families of L -fuzzy rough sets indexed by elements of a complete ...
L-fuzzy setM-relationL-fuzzy rough setCl-monoidM-valued measure of inclusionL, $$ L , M)-fuzzy topologyL, $$ L , M)-fuzzy co-topologyWe develop a scheme allowing to measure the "quality" of rough approximation of fuzzy sets. This scheme is based on what we call "an approximation ...
L-fuzzy rough setCl-monoidM-valued measure of inclusion(LM)-fuzzy topology(LM)-fuzzy co-topologyWe develop a scheme allowing to measure the "quality" of rough approximation of fuzzy sets. This scheme is based on what we call "an approximation quadruple" (L, M, Φ, ψ) where L and ...