In this paper, for a complete lattice L, we introduce interval-valued L-fuzzy ideal (prime ideal) of a near-ring which is an extended notion of fuzzy ideal (prime ideal) of a near-ring. Some characterization and properties are discussed.

The expressive truth functions of two-valued logic have all been characterized, as have the expressive unary truth functions of finitely-many-valued logic. This paper introduces some techniques for identifying expressive functions in three-valued logics. 1  We are going to explore a property of truth functions known as “expressiveness.” Before subjecting readers to the long-winded exp...

Lattice-valued entropy functions defined by a lattice-valued possibilistic distribution π on a space Ω are defined as the expected value (in the sense of Sugeno integral) of the complement of the value π(ω) with ω ranging over Ω. The analysis is done in parallel for two alternative interpretations of the notion of complement in the complete lattice in question. Supposing that this complete latt...

We provide a comprehensive analysis of matrix-valued Herglotz functions and illustrate their applications in the spectral theory of self-adjoint Hamiltonian systems including matrix-valued Schrödinger and Dirac-type operators. Special emphasis is devoted to appropriate matrix-valued extensions of the well-known Aronszajn-Donoghue theory concerning support properties of measures in their Nevanli...

We develop the flow analog of the classical Yosida adjunction between spaces and archimedean lattice-ordered groups with strong unit. A product of this development is the flow counterpart of the classical compactification of a space. We characterize those flows which are compactifiable, i.e., dense subflows of a compact flow. Finally, we exhibit a duality between the compactifications of a give...

In this letter, we provide a study of learning in a Hilbert space of vectorvalued functions. We motivate the need for extending learning theory of scalar-valued functions by practical considerations and establish some basic results for learning vector-valued functions that should prove useful in applications. Specifically, we allow an output space Y to be a Hilbert space, and we consider a repr...

We define a class, denoted APP, of real-valued functions f : {0, 1}n → [0, 1] such that f can be approximated to within any > 0 by a probabilistic Turing machine running in time poly(n, 1/ ). The class APP can be viewed as a generalization of BPP. We argue that APP is more natural and more important than BPP, and that most results about BPP are better stated as results about APP. We show that A...

The main objective of the paper is to state newly fixed point theorems for set-valued mappings in the framework of 0-complete partial metric spaces which speak about a location of a fixed point with respect to an initial value of the set-valued mapping by using some $C$-class functions. The results proved herein generalize, modify and unify some recent results of the existing literature. As an ...

At first, we consider nonnegative monotone interval-valued set functions and nonnegative measurable interval-valued functions. In this paper we investigate some properties and structural characteristics of the monotone interval-valued set function defined by an interval-valued Choquet integral.