We study the space of all continuous fuzzy-valued functions  from a space $X$ into the space of fuzzy numbers $(mathbb{E}sp{1},dsb{infty})$  endowed with the pointwise convergence topology.   Our results generalize the classical ones for  continuous real-valued functions.   The field of applications of this approach seems to be large, since the classical case  allows many known devices to be fi...

1. General remarks Boolean valued analysis is a branch of functional analysis which uses a special model-theoretic technique that is embodied in the Boolean valued models of set theory. The term was coined by G. Takeuti. The invention of Boolean valued models was not connected with the theory of Boolean algebras but rather has revealed a gemstone among the diverse applications of the latter. It...

‎The notion of (Boolean) uni-soft filters‎ ‎in MTL-algebras is introduced‎, ‎and several properties of them are‎ ‎investigated‎. ‎Characterizations of (Boolean) uni-soft filters are discussed‎, ‎and some (necessary and sufficient) conditions‎ ‎for a uni-soft filter to be Boolean are provided‎. ‎The condensational property for a Boolean uni-soft filter is established.

Covering-based rough sets provide an efficient theory to deal with covering data which widely exist in practical applications. Boolean matrix decomposition has been widely applied to data mining and machine learning. In this paper, three types of existing covering approximation operators are represented by boolean matrices, and then they are used to decompose into boolean matrices. First, we de...

Properties valid on the classical theory (Boolean laws) have been extended to fuzzy set theory and so-called Boolean-like laws. The fact that they are not always valid in any standard fuzzy set theory induced a wide investigation. In this paper we show the sufficient and necessary conditions that the Boolean-like law y ≤ I(x, y) holds in fuzzy logic. We focus the investigation on the following ...