As an emerging area considering behavioral aspects of decision making, target-oriented decision model lies in the philosophical root of bounded rationality as well as represents the S-shaped value function. This paper deals with multi-attribute decision analysis from target-oriented viewpoint. First, the basic (random) target-oriented decision model is extended to involve three types of target ...

The inherent fault tolerance of artificial neural networks (ANNs) is usually assumed, but several authors have claimed that ANNs are not always fault tolerant and have demonstrated the need to evaluate their robustness by quantitative measures. For this purpose, various alternatives have been proposed. In this paper we show the direct relation between the mean square error (MSE) and the statist...

Fuzzy measures generalize additive and probabilities. Their advantage with respect to ones is that they permit model interactions between objects. Mesiar introduced in 1999 k-order Pan-additive fuzzy k-maxitive ones. They are related the Möbius transform generalizations. In this paper we introduce some other transforms call ( M a x , + ) ? represent convenient way when use genetic algorithms me...

Effect algebras are the main object of study in quantum mechanics. Module measures those defined on an effect algebra with values a topological module. Let R be ring and M R-module. L algebra. The range module measure ?:L?M is studied. Among other results, we prove that if sRDP ?-effect natural basis ?:L?R countably additive measure, then ? has bounded variation.

If (X,X ) is a measure space and F◦ ⊂ X is a field generated either by a countable class of sets or by a Vapnik-Červonenkis class, then if μ is purely finitely additive, there exist uncountably many μ′ agreeing with μ on F◦ and having |μ(A) − μ′(A)| = 1 for uncountably many A. If μ is also non-atomic, then for any r ∈ (0, 1], |μ(Ar)− μ(Ar)| = r for uncountably many Ar. Al-Najjar’s [1] unlearnab...

The notion of a signed measure arises if a measure is allowed to take on both positive and negative values. A set that is both positive and negative with respect to a signed measure is termed as a null set. Some concepts in measure theory can be generalized by means of classes of null sets. An abstract formulation and proof of the Lebesgue decomposition theorem using the concept of null sets is...

In decision under uncertainty, the Choquet integral yields the expectation of a random variable with respect to a fuzzy measure (or non-additive probability or capacity). In general, for the discrete setting, this technique allows to integrate functions taking values on a finite n-set with respect to a (fuzzy) measure taking values on subsets of such a set. Yet, the integrand may well be treate...

A general methodology for modeling loss data depending on covariates is developed. The parameters of the frequency and severity distributions of the losses may depend on covariates. The loss frequency over time is modeled via a non-homogeneous Poisson process with integrated rate function depending on the covariates. This corresponds to a generalized additive model which can be estimated with s...

It is shown that any nonnegative bounded supermartingale admits a Doob-Meyer decomposition as a difference of a martingale and an adapted increasing process upon appropriate choice of a reference probability measure which may be only finitely additive. Introduction. In [Armstrong, 1983] it is shown that every bounded finitely additive supermartingale is a decreasing process with respect to some...

Let h(a1 , •.. , an) denote the harmonic mean n(a1 1 + ... +a; 1) -1 of positive num­ bers a1 , ••. , all' and extend this definition (by continuity) to the non-negative case by setting h(a l' ... , an) = 0 if ai = 0 for some i ~ n. Recall that a measure J1. is non-atomic if every measurable set A of strictly positive measure has a measur­ able subset B ~ A satisfying J1.(A) > J1.(B) > O. A mea...