T authors propose two variants of lexicographic preference rules. They obtain the necessary and sufficient conditions under which a linear utility function represents a standard lexicographic rule, and each of the proposed variants, over a set of discrete attributes. They then: (i) characterize the measurement properties of the parameters in the representations; (ii) propose a nonmetric procedu...

Numerous problems arising in engineering applications can have several objectives to be satisfied. An important class of problems of this kind is lexicographic multi-objective problems where the first objective is incomparably more important than the second one which, in its turn, is incomparably more important than the third one, etc. In this paper, Lexicographic Multi-Objective Linear Program...

Helly’s theorem says that, if every d+1 elements of a given finite set of convex objects in Rd have a common point, there is a point common to all of the objects in the set. In discrete Helly theorems the common point should belong to an a priori given set. In lexicographic Helly theorems the common point should not be lexicographically greater than a given point. Using discrete and lexicograph...

This paper focuses on the difficulty of standard life-cycle models to predict the behavior observed in the reality, most noticeably the excess sensitivity of consumption to income, the under-provision for old-age consumption, the limited participation in the financial market, and the lack of asset decumulation after retirement. It shows that allowing for preference reversals, as it is the case ...

An appropriately designed sensor network is crucial for the success of any fault diagnostic strategy. In previous works (Bhushan and Rengaswamy, 2002a,b) strategies for optimally locating sensors based on criteria of reliability maximization and cost minimization have been devised. These opposing objectives were treated in a lexicographic (a special type of multiobjective optimization) manner. ...

A short new proof of the fact that all shifted complexes are fixed by reverse lexicographic shifting is given. A notion of lexicographic shifting, ∆lex — an operation that transforms a monomial ideal of S = k[xi : i ∈ N] that is finitely generated in each degree into a squarefree strongly stable ideal — is defined and studied. It is proved that (in contrast to the reverse lexicographic case) a ...

This overview focuses on lexicographic choice under conditions of uncertainty. First, lexicographic versions of traditional (von Neumann-Morgenstern) expected utility theory are described where the usual Archimedean axiom is weakened. The role of these lexicographic variants in explaining some well-known “paradoxes” of choice theory is reviewed. Next, the significance of lexicographic choice fo...