We show that Maskin monotone social choice correspondences on sufficiently rich domains satisfy a generalized strategy-proofness property, thus generalizing Muller and Satterthwaite's (1977) theorem to correspondences. From the point of view of Nash implementation theory, the result yields a partial characterization of the restrictions entailed by Nash implementability. Alternatively, the resul...

The concept of comonotonicity is a useful tool for solving various problems in insurance and financial economics. The credibilistic comonotonicity of fuzzy vector is defined via its comonotonic support. In general case, the properties of comonotonic fuzzy vector are discussed based on the relation between the joint monotone distribution of a fuzzy vector and its marginal monotone distributions....

| The simplest nontrivial monotone functions are \staircases." The problem arises: what is the best approximation of some monotone function f(x) by a staircase with M jumps? In particular: what if f(x) is itself a staircase with N, N > M, steps? This paper considers algorithms for solving, and theorems relating to, this problem. All of the algorithms we propose are space-optimal up to a constan...

Radó has noted that (II) implies (r) and that the sphere and 2-cell each have (II). In this paper it will be shown that (1) for locally connected continua in general, property (II) is equivalent to unicoherence, (2) for plane locally connected continua, property (ir) is equivalent to unicoherence, and (3) every closed 2-dimensional connected manifold has property (x). To clarify our meaning, we...

We study definability in terms of monotone generalized quantifiers satisfying Isomorphism closure, Conservativity and Extension. Among the quantifiers with the latter three properties — here called CE quantifiers — one finds the interpretations of determiner phrases in natural languages. The property of monotonicity is also linguistically ubiquitous, though some determiners like an even number ...

In this paper, some properties of the monotone set-valued function defined by the set-valued Choquet integral are discussed. It is shown that several important structural characteristics of the original set function, such as null-additivity, strong order continuity, property(S) and pseudometric generating property, etc., are preserved by the new set-valued function. It is also shown that integr...

Estimation of monotone functions has broad applications in statistics, engineering, and science. This paper addresses asymptotic behaviors of monotone penalized spline estimators using constrained dynamical optimization techniques. The underlying regression function is approximated by a B-spline of an arbitrary degree subject to the first-order difference penalty. The optimality conditions for ...