Associativity, preassociativity, and string functions

Scientific Conference (2014, June 20)

On structure signatures and probability signatures of general decomposable systems (invited talk)

Scientific Conference (2014, June 16)

Analyse de fiabilité des systèmes et description par des polynômes latticiels

Presentation (2014, March 07)

Subsignatures of systems

in Journal of Multivariate Analysis (2014), 124

We introduce the concept of subsignature for semicoherent systems as a class of indexes that range from the system signature to the Barlow-Proschan importance index. Specifically, given a nonempty subset ... [more ▼]

We introduce the concept of subsignature for semicoherent systems as a class of indexes that range from the system signature to the Barlow-Proschan importance index. Specifically, given a nonempty subset M of the set of components of a system, we define the M-signature of the system as the |M|-tuple whose k-th coordinate is the probability that the k-th failure among the components in M causes the system to fail. We give various explicit linear expressions for this probability in terms of the structure function and the distribution of the component lifetimes. We also examine the case of exchangeable lifetimes and the special case when the lifetime are i.i.d. and M is a modular set. [less ▲]

Actes des 22èmes rencontres francophones sur la Logique Floue et ses Applications, 10-11 octobre 2013, Reims, France

Book published by Université de Reims Champagne-Ardenne (2013)

Discrete integrals based on comonotonic modularity

in Axioms (2013), 2(3), 390-403

It is known that several discrete integrals, including the Choquet and Sugeno integrals as well as some of their generalizations, are comonotonically modular functions. Based on a recent description of ... [more ▼]

It is known that several discrete integrals, including the Choquet and Sugeno integrals as well as some of their generalizations, are comonotonically modular functions. Based on a recent description of the class of comonotonically modular functions, we axiomatically identify more general families of discrete integrals that are comonotonically modular, including signed Choquet integrals and symmetric signed Choquet integrals as well as natural extensions of Sugeno integrals. [less ▲]

Computing system signatures through reliability functions

in Statistics & Probability Letters (2013), 83(3), 710-717

It is known that the Barlow-Proschan index of a system with i.i.d. component lifetimes coincides with the Shapley value, a concept introduced earlier in cooperative game theory. Due to a result by Owen ... [more ▼]

It is known that the Barlow-Proschan index of a system with i.i.d. component lifetimes coincides with the Shapley value, a concept introduced earlier in cooperative game theory. Due to a result by Owen, this index can be computed efficiently by integrating the first derivatives of the reliability function of the system along the main diagonal of the unit hypercube. The Samaniego signature of such a system is another important index that can be computed for instance by Boland's formula, which requires the knowledge of every value of the associated structure function. We show how the signature can be computed more efficiently from the diagonal section of the reliability function via derivatives. We then apply our method to the computation of signatures for systems partitioned into disjoint modules with known signatures. [less ▲]

On the cardinality index of fuzzy measures and the signatures of coherent systems

in Mesiar, Radko; Pap, Endre; Klement, Erich Peter (Eds.) 34th Linz Seminar on Fuzzy Set Theory (LINZ 2013) - Non-Classical Measures and Integrals (2013)

Quasi-extensions de Lovász et leur version symétrique

in Rencontres francophones sur la logique floue et ses applications 2012 (2012, November 15)

We present a study of the class of quasi-Lovász extensions (i.e. functions which are a composition of a Lovász extension with a nondecreasing function vanishing at the origin) as well as that of their ... [more ▼]

We present a study of the class of quasi-Lovász extensions (i.e. functions which are a composition of a Lovász extension with a nondecreasing function vanishing at the origin) as well as that of their symmetric variants. These functions appear naturally within the scope of decision making under uncertainty since they subsume overall preference functionals associated with discrete Choquet integrals and symmetric discrete Choquet integrals, respectively, whose variables are transformed by a given utility function. [less ▲]

Locally monotone Boolean and pseudo-Boolean functions

in Discrete Applied Mathematics (2012), 160(12), 1651-1660

We propose local versions of monotonicity for Boolean and pseudo-Boolean functions: say that a pseudo-Boolean (Boolean) function is p-locally monotone if none of its partial derivatives changes in sign on ... [more ▼]

We propose local versions of monotonicity for Boolean and pseudo-Boolean functions: say that a pseudo-Boolean (Boolean) function is p-locally monotone if none of its partial derivatives changes in sign on tuples which differ in less than p positions. As it turns out, this parameterized notion provides a hierarchy of monotonicities for pseudo-Boolean (Boolean) functions. Local monotonicities are shown to be tightly related to lattice counterparts of classical partial derivatives via the notion of permutable derivatives. More precisely, p-locally monotone functions are shown to have p-permutable lattice derivatives and, in the case of symmetric functions, these two notions coincide. We provide further results relating these two notions, and present a classification of p-locally monotone functions, as well as of functions having p-permutable derivatives, in terms of certain forbidden "sections", i.e., functions which can be obtained by substituting constants for variables. This description is made explicit in the special case when p=2. [less ▲]