One of the key operations in fuzzy logic and approximate reasoning is the fuzzy implication, which is usually performed by a binary operator, called an implication function or, simply, an implication. Many fuzzy rule based systems do their inference processes through these operators that also take charge of the propagation of uncertainty in fuzzy reasonings. Moreover, they have proved to be useful also in other fields like composition of fuzzy relations, fuzzy relational equations, fuzzy mathematical morphology, and image processing. This paper aims to present an overview on fuzzy implication functions that usually are constructed from t-norms and t-conorms but also from other kinds of aggregation operators. The four most usual ways to define these implications are recalled and their characteristic properties stated, not only in the case of [0,1] but also in the discrete case.

A Survey on Fuzzy Implication Functions

NMGRS: Neighborhood-based multigranulation rough sets

Rough set theory was developed by Pawlak as a formal tool for approximate reasoning about data Various fuzzy generalizations of rough approximations have been proposed in the literature As a further generalization of the notion of rough sets, L-fuzzy rough sets were proposed by Radzikowska and Kerre In this paper, we present an operator-oriented characterization of L-fuzzy rough sets, that is, L-fuzzy approximation operators are defined by axioms The methods of axiomatization of L-fuzzy upper and L-fuzzy lower set-theoretic operators guarantee the existence of corresponding L-fuzzy relations which produce the operators Moreover, the relationship between L-fuzzy rough sets and L-topological spaces is obtained The sufficient and necessary condition for the conjecture that an L-fuzzy interior (closure) operator derived from an L-fuzzy topological space can associate with an L-fuzzy reflexive and transitive relation such that the corresponding L-fuzzy lower (upper) approximation operator is the L-fuzzy interior (closure) operator is examined

Daowu Pei

Papers

Topology vs generalized rough sets

On equivalent forms of fuzzy logic systems NM and IMTL

R 0 implication: characteristics and applications

Formalization of implication based fuzzy reasoning method

Robustness analysis of full implication inference method