Credibility models are actuarial tools to distribute premiums fairly among a heterogeneous group of policyholders (henceforth called entities). More generally, they can be seen as prediction methods applicable in any setting where repeated measures are made for subjects with different risk levels. The credibility theory features of actuar consist of matrix hachemeister containing the famous dat...

fuzzy control systems have had various applications in a wide range of science and engineering in recent years. since an unstable control system is typically useless and potentially dangerous, stability is the most important requirement for any control system (including fuzzy control system). conceptually, there are two types of stability for control systems: lyapunov stability (a special case ...

The literature on portfolio analysis assumes that the securities returns are random variables with fixed expected returns and variances values (see Bachelier [1], Briec et al. [4] and Markowitz [10]). However, since investors receive efficient or inefficient information from the real world, ambiguous factors usually exist in it. Consequently, we need to consider not only random conditions but a...

In this paper, the minimum spanning tree problem is investigated on the graph with fuzzy edge weights. The notion of fuzzy α-minimum spanning tree is presented based on the credibility measure, and then the solutions of the fuzzy α-minimum spanning tree problem are discussed under different assumptions. First, we respectively assume that all the edge weights are triangular fuzzy numbers and tra...

This paper owes a great deal to Doug Laxton. We also thank Phil Lowe, Glenn Stevens and participants in a seminar at the Reserve Bank of Australia for helpful comments. The views expressed in this paper are those of the authors and not necessarily those of the Reserve Bank of Australia. Use of any results from this paper should clearly attribute the work to the authors and not to the Reserve Ba...

Fuzzy Cognitive Maps (FCM) are a promising approach for socio-ecological systems modelling. FCMs represent problem knowledge extracted from different stakeholders in the form of connected factors/variables with imprecise cause-effect relationships and many feedback loops. These typically large maps are condensed and aggregated to obtain a summary view of the system. However, representation, con...

This article addresses exact controllability for Caputo fuzzy fractional evolution equations in the credibility space from perspective of Liu process. The class or problems considered here are differential with derivatives order β∈(1,2), 0CDtβu(t,ζ)=Au(t,ζ)+f(t,u(t,ζ))dCt+Bx(t)Cx(t)dt initial conditions u(0)=u0,u′(0)=u1, where u(t,ζ) takes values U(⊂EN),V(⊂EN) is other bounded space, and EN rep...

In order to improve online learning speed and accuracy of CMAC, a fuzzy CMAC neural network model based on credit assignment concept is designed. In the conventional CMAC and fuzzy CMAC learning scheme, the corrected amounts of errors are equally distributed into all addressed hypercubes, regardless of the credibility of those hypercubes values. The proposed improved learning approach is to use...

In order to measure fuzzy event, credibility measure is proposed as a non-additive set function. In this paper, this concept is extended to fuzzy sets. First, a mean measure is defined by Lebesgue integral and some properties are investigated such as the monotonicity theorem, self-duality theorem and subadditivity theorem. Furthermore, by using Sugeno integral, an equilibrium measure is propose...