Tamás Waldhauser

On signature-based expressions of system reliability

The concept of signature was introduced by Samaniego for systems whose components have i.i.d. lifetimes. This concept proved to be useful in the analysis of theoretical behaviors of systems. In particular, it provides an interesting signature-based representation of the system reliability in terms of reliabilities of k-out-of-n systems. In the non-i.i.d. case, we show that, at any time, this representation still holds true for every coherent system if and only if the component states are exchangeable. We also discuss conditions for obtaining an alternative representation of the system reliability in which the signature is replaced by its non-i.i.d. extension. Finally, we discuss conditions for the system reliability to have both representations.

Decompositions of functions based on arity gap

We study the arity gap of functions of several variables defined on an arbitrary set A and valued in another set B. The arity gap of such a function is the minimum decrease in the number of essential variables when variables are identified. We establish a complete classification of functions according to their arity gap, extending existing results for finite functions. This classification is refined when the codomain B has a group structure, by providing unique decompositions into sums of functions of a prescribed form. As an application of the unique decompositions, in the case of finite sets we count, for each n and p, the number of n-ary functions that depend on all of their variables and have arity gap p.

AXIOMATIZATIONS AND FACTORIZATIONS OF SUGENO UTILITY FUNCTIONS

In this paper we consider a multicriteria aggregation model where local utility functions of different sorts are aggregated using Sugeno integrals, and which we refer to as Sugeno utility functions. We propose a general approach to study such functions via the notion of pseudo-Sugeno integral (or, equivalently, pseudo-polynomial function), which naturally generalizes that of Sugeno integral, and provide several axiomatizations for this class of functions. Moreover, we address and solve the problem of factorizing a Sugeno utility function as a composition q(φ1(x1),…,φn(xn)) of a Sugeno integral q with local utility functions φi, if such a factorization exists.

Sugeno utility functions I: axiomatizations

In this paper we consider a multicriteria aggregation model where local utility functions of different sorts are aggregated using Sugeno integrals, and which we refer to as Sugeno utility functions. We propose a general approach to study such functions via the notion of pseudo-Sugeno integral (or, equivalently, pseudo-polynomial function), which naturally generalizes that of Sugeno integral, and provide several axiomatizations for this class of functions.

Sugeno utility functions II: factorizations

In this paper we address and solve the problem posed in the companion paper [3] of factorizing an overall utility function as a composition q(ϕ1(x1),..., ϕn(xn)) of a Sugeno integral q with local utility functions ϕi, if such a factorization exists.

Minimal clones generated by majority operations

Abstract. The minimal majority functions of the four-element set are determined.

The arity gap of order-preserving functions and extensions of pseudo-Boolean functions

The aim of this paper is to classify order-preserving functions according to their arity gap. Noteworthy examples of order-preserving functions are the so-called aggregation functions. We first explicitly classify the Lovasz extensions of pseudo-Boolean functions according to their arity gap. Then we consider the class of order-preserving functions between partially ordered sets, and establish a similar explicit classification for this function class. Highlights? We investigate the notion of arity gap of functions of several variables. ? We explicitly classify Lovasz extensions according to their arity gap. ? Similarly, we classify order-preserving functions between partially ordered sets.

Parametrized Arity Gap

We propose a parametrized version of arity gap. The parametrized arity gap gap (f, ℓ) of a function

Relation Graphs and Partial Clones on a 2-Element Set

f \colon A^n \to B

Decision-Making with Sugeno Integrals

measures the minimum decrease in the number of essential variables of f when ℓ consecutive identifications of pairs of essential variables are performed. We determine gap (f, ℓ) for an arbitrary function f and a nonnegative integer ℓ. We also propose other variants of arity gap and discuss further problems pertaining to the effect of identification of variables on the number of essential variables of functions.