Let (S, d) be a metric space, G a σ-field on S and (μn : n ≥ 0) a sequence of probabilities on G. Suppose G countably generated, the map (x, y) 7→ d(x, y) measurable with respect to G ⊗ G, and μn perfect for n > 0. Say that (μn) has a Skorohod representation if, on some probability space, there are random variables Xn such that Xn ∼ μn for all n ≥ 0 and d(Xn, X0) P −→ 0. It is shown that (μn) h...

(2) Let L, S, T be complete non empty posets, f be a CLHomomorphism of L, S, and g be a CLHomomorphism of S, T . Then g · f is a CLHomomorphism of L, T . (3) For every non empty relational structure L holds idL is infs-preserving. (4) For every non empty relational structure L holds idL is directed-sups-preserving. (5) For every complete non empty poset L holds idL is a CLHomomorphism of L, L. ...

In this contribution, we will extend results relating to representability of a fuzzy function using a crisp function. And additionally, we show for which functions there exist fuzzy function of a specific form. Our notion of fuzzy function has a graded character. More precisely, any fuzzy relation has a property of being a fuzzy function that is expressed by a truth degree. And it consists of t...

This article discusses relations between several notions of continuity in rank-dependent utility, and in the generalized version of rank-dependent utility as initiated by Segal. Primarily, examples are given to show logical independencies between these notions of continuity. This also leads to counterexamples to Segal's (1989) characterizing theorem 1.

We consider complete lattices equipped with preorderings indexed by the ordinals less than a given (limit) ordinal subject to certain axioms. These structures, called stratified complete lattices, and weakly monotone functions over them, provide a framework for solving fixed point equations involving non-monotone operations such as negation or complement, and have been used to give semantics to...

Effect algebras have important applications in the foundations of quantum mechanics and in fuzzy probability theory. An effect algebra that possesses a convex structure is called a convex effect algebra. Our main result shows that any convex effect algebra admits a representation as a generating initial interval of an ordered linear space. This result is analogous to a classical representation ...

Following Richter (1966), we provide criteria under which a preference relation implied by a finite set of choice observations has a complete extension that can in turn be represented by a utility function. These criteria rely on a mapping over preference relations, the rational closure, which is a generalization of the transitive closure and is employed to construct the complete extension. We ...

An MV-pair is a pair (B, G) where B is a Boolean algebra and G is a subgroup of the automorphism group of B satisfying certain conditions. Let ∼G be the equivalence relation on B naturally associated with G. We prove that for every MV-pair (B, G), the effect algebra B/ ∼G is an MV-effect algebra. Moreover, for every MV-effect algebra M there is an MV-pair (B, G) such that M is isomorphic to B/ ∼G.

1. INDUCTION IN A FINITE LATTICE Let L be a 1-sorted structure and let A, B be subsets of L. Let us observe that A⊆ B if and only if: (Def. 1) For every element x of L such that x ∈ A holds x ∈ B. Let L be a lattice. Observe that there exists a chain of L which is non empty. Let L be a lattice and let x, y be elements of L. Let us assume that x ≤ y. A non empty chain of L is called a x-chain of...

The virtual reflector method simulates new seismic signals by processing traces recorded by a plurality of sources and receivers. The approach is based on the crossconvolution of the recorded signals and makes it possible to obtain the Green's function of virtual reflected signals as if in the position of the receivers (or sources) there were a reflector, even if said reflector is not present. ...