311 research outputs found
Weighted lattice polynomials
We define the concept of weighted lattice polynomial functions as lattice
polynomial functions constructed from both variables and parameters. We provide
equivalent forms of these functions in an arbitrary bounded distributive
lattice. We also show that these functions include the class of discrete Sugeno
integrals and that they are characterized by a median based decomposition
formula.Comment: Revised version (minor changes
On indefinite sums weighted by periodic sequences
For any integer we provide a formula to express indefinite sums of
a sequence weighted by -periodic sequences in terms of
indefinite sums of sequences , where
. When explicit expressions for the latter sums are
available, this formula immediately provides explicit expressions for the
former sums. We also illustrate this formula through some examples
Weighted lattice polynomials of independent random variables
We give the cumulative distribution functions, the expected values, and the
moments of weighted lattice polynomials when regarded as real functions of
independent random variables. Since weighted lattice polynomial functions
include ordinary lattice polynomial functions and, particularly, order
statistics, our results encompass the corresponding formulas for these
particular functions. We also provide an application to the reliability
analysis of coherent systems.Comment: 14 page
Computing subsignatures of systems with exchangeable component lifetimes
The subsignatures of a system with continuous and exchangeable component
lifetimes form a class of indexes ranging from the Samaniego signature to the
Barlow-Proschan importance index. These indexes can be computed through
explicit linear expressions involving the values of the structure function of
the system. We show how the subsignatures can be computed more efficiently from
the reliability function of the system via identifications of variables,
differentiations, and integrations
Algorithms and formulas for conversion between system signatures and reliability functions
The concept of signature is a useful tool in the analysis of semicoherent
systems with continuous and i.i.d. component lifetimes, especially for the
comparison of different system designs and the computation of the system
reliability. For such systems, we provide conversion formulas between the
signature and the reliability function through the corresponding vector of
dominations and we derive efficient algorithms for the computation of any of
these concepts from the other. We also show how the signature can be easily
computed from the reliability function via basic manipulations such as
differentiation, coefficient extraction, and integration
Structure functions and minimal path sets
In this short note we give and discuss a general multilinear expression of
the structure function of an arbitrary semicoherent system in terms of its
minimal path and cut sets. We also examine the link between the number of
minimal path and cut sets consisting of 1 or 2 components and the concept of
structure signature of the system
Meaningful aggregation functions mapping ordinal scales into an ordinal scale: a state of the art
We present an overview of the meaningful aggregation functions mapping
ordinal scales into an ordinal scale. Three main classes are discussed, namely
order invariant functions, comparison meaningful functions on a single ordinal
scale, and comparison meaningful functions on independent ordinal scales. It
appears that the most prominent meaningful aggregation functions are lattice
polynomial functions, that is, functions built only on projections and minimum
and maximum operations
Derivative relationships between volume and surface area of compact regions in R^d
We explore the idea that the derivative of the volume, V, of a region in R^d
with respect to r equals its surface area, A, where r = d V/A. We show that the
families of regions for which this formula for r is valid, which we call
homogeneous families, include all the families of similar regions. We determine
equivalent conditions for a family to be homogeneous, provide examples of
homogeneous families made up of non-similar regions, and offer a geometric
interpretation of r in a few cases.Comment: 15 page
Axiomatizations of quasi-polynomial functions on bounded chains
Two emergent properties in aggregation theory are investigated, namely
horizontal maxitivity and comonotonic maxitivity (as well as their dual
counterparts) which are commonly defined by means of certain functional
equations. We completely describe the function classes axiomatized by each of
these properties, up to weak versions of monotonicity in the cases of
horizontal maxitivity and minitivity. While studying the classes axiomatized by
combinations of these properties, we introduce the concept of quasi-polynomial
function which appears as a natural extension of the well-established notion of
polynomial function. We give further axiomatizations for this class both in
terms of functional equations and natural relaxations of homogeneity and median
decomposability. As noteworthy particular cases, we investigate those
subclasses of quasi-term functions and quasi-weighted maximum and minimum
functions, and provide characterizations accordingly
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