Consensus via penalty functions for decision making in ensembles in fuzzy rule-based classification systems

On the generalized law of O-conditionality for interval fuzzy implications

Interval fuzzy implications play an important role in both theoretical and applied communities of interval-valued fuzzy sets and have been widely studied. Recently, Dimuro et al. analyzed the law of O-conditionality for fuzzy implications in general. However, there is no corresponding researches about the interval extension. To fill the gap, in this paper, we introduce the generalized law of O-conditionality 𝕆 ( X ,   𝕀 ( X ,   Y ) ) ≤ Y (GOC), where 𝕀 is an interval fuzzy implication and 𝕆 is an interval overlap function. Meanwhile, we discuss the advantages one may get using it. Moreover, we consider the conditional antecedent boundary condition (CABC) for interval fuzzy implications derived from interval overlap and grouping functions, including, interval R 𝕆 - ,   ( 𝔾 ,   ℕ ) - ,   ( 𝕆 ,   𝔾 ,   ℕ ) - and ( 𝔾 ,   𝕆 ,   ℕ ) - implications. Finally, we further analyze the generalized law of O-conditionality for these four classes of interval fuzzy implications.

On (GO, O)-fuzzy rough sets derived from overlap and grouping functions

Rough sets, as a powerful tool to deal with uncertainties and inaccuracies in data analysis, have been continuously concerned and studied by many scholars since it was put forward, especially the research on various rough set models. On the other hand, overlap and grouping functions, as two newly aggregation operators and mathematical model to handle the problems involving in information fusion, have been successfully applied in many real-life problems. In this paper, based on overlap and grouping functions, we propose a new fuzzy rough set model named (GO, O)-fuzzy rough sets and consider its characterizations along with topological properties. Properly speaking, firstly, we utilize QL-operators (and also QL-implications) constructed from overlap and grouping functions and fuzzy negations to define the lower approximation operator in (GO, O)-fuzzy rough set model named GO-lower fuzzy rough approximation operator and the upper approximation operator in (GO, O)-fuzzy rough set model is considered as the O-upper fuzzy rough approximation operator in (IO, O)-fuzzy rough set model proposed by Qiao recently. Secondly, we discuss lots of basic properties of (GO, O)-fuzzy rough sets, especially for the properties of GO-lower fuzzy rough approximation operator. Thirdly, we focus on the relationship between (GO, O)-fuzzy rough sets and concrete fuzzy relations. Finally, we give the topological properties of the upper and lower approximation operators in (GO, O)-fuzzy rough set model.

On the Composition of Overlap and Grouping Functions

Obtaining overlap/grouping functions from a given pair of overlap/grouping functions is an important method of generating overlap/grouping functions, which can be viewed as a binary operation on the set of overlap/grouping functions. In this paper, firstly, we studied closures of overlap/grouping functions w.r.t. ⊛-composition. In addition, then, we show that these compositions are order preserving. Finally, we investigate the preservation of properties like idempotency, migrativity, homogeneity, k-Lipschitz, and power stable.