B. R. Ebanks

Application of measures of fuzziness to risk classification in insurance

The authors show how measures of fuzziness can be used to classify risks considered for insurance purposes, using the example of life insurance. A risk given is described as a fuzzy preferred risk, and then its fuzziness is measured to indicate its classification. They compare various measures of fuzziness, including the classical entropy measure of De Luca and Termini (1992), the distance measure of Yager (1979), and the axiomatic product measure (see e.g., Ebanks (1983)), and discuss their applicability to risk classification.<<ETX>>

Generalized fundamental equation of information of multiplicative type

The general solution of the generalized multidimensional fundamental equation of information of multiplicative type on the open domain is obtained.

On generalized cocycle equations

SummaryMotivated by results on the classical cocycle equation, we solved the more general equationF1(x + y, z) + F2(y + z, x) + F3(z + x, y) + F4(x, y) + F5(y, z) + F6(z, x) = 0 for six unknown functions mapping ordered pairs from an abelian group into a vector space over the rationals.

Factoring multiadditive mappings

There are two main results. One is a necessary and sufficient condition for a biadditive mapping to be the product of two additive maps. The other is a necessary and sufficient condition for a symmetric multiadditive map F to be of the form for some constant c and additive map A. In addition, an application to quadratic functionals is given.

On A Functional Equation of Abel

We determine the general solution of the functional equation % MathType!MTEF!2!1!+-% feaaeaart1ev0aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXanrfitLxBI9gBaerbd9wDYLwzYbItLDharqqt% ubsr4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq% -Jc9vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0x% fr-xfr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamyuam% aaBaaaleaacaaIXaGaaGimaaqabaGccqGH9aqpciGGSbGaaiOBaiaa% ysW7caWGRbWaaSbaaSqaaiaadsfacaaIXaaabeaakiaac+cacaWGRb% WaaSbaaSqaaiaadsfacaaIYaaabeaakiabg2da9iabgkHiTmaabmaa% baGaamyramaaBaaaleaacaWGHbaabeaakiaac+cacaWGsbaacaGLOa% GaayzkaaGaey41aq7aaiWaaeaadaqadaqaaiaadsfadaWgaaWcbaGa% aGOmaaqabaGccqGHsislcaWGubWaaSbaaSqaaiaaigdaaeqaaaGcca% GLOaGaayzkaaGaai4laiaacIcacaWGubWaaSbaaSqaaiaaikdaaeqa% aOGaaGjbVlaadsfadaWgaaWcbaGaamysaaqabaGccaGGPaaacaGL7b% GaayzFaaaaaa!5C4A!

Branching inset entropies on open domains

\psi(x+y)=g(xy)+h(x-y),\ \ \ x,y\in\ {\rm \bf K}

Generalized characteristic equation of branching information measures

for ψ,g,h: K → G, where K is a field belonging to a certain class, and G is an abelian group. This functional equation was one of the several treated by Abel in his 1823 manuscript. Recently, this equation was solved by Aczél and also independently by Lajko without any regularity assumption when K = G = ℜ (reals). We consider also the conditional Cauchy equation % MathType!MTEF!2!1!+-% feaaeaart1ev0aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXanrfitLxBI9gBaerbd9wDYLwzYbItLDharqqt% ubsr4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq% -Jc9vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0x% fr-xfr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamyuam% aaBaaaleaacaaIXaGaaGimaaqabaGccqGH9aqpciGGSbGaaiOBaiaa% ysW7caWGRbWaaSbaaSqaaiaadsfacaaIXaaabeaakiaac+cacaWGRb% WaaSbaaSqaaiaadsfacaaIYaaabeaakiabg2da9iabgkHiTmaabmaa% baGaamyramaaBaaaleaacaWGHbaabeaakiaac+cacaWGsbaacaGLOa% GaayzkaaGaey41aq7aaiWaaeaadaqadaqaaiaadsfadaWgaaWcbaGa% aGOmaaqabaGccqGHsislcaWGubWaaSbaaSqaaiaaigdaaeqaaaGcca% GLOaGaayzkaaGaai4laiaacIcacaWGubWaaSbaaSqaaiaaikdaaeqa% aOGaaGjbVlaadsfadaWgaaWcbaGaamysaaqabaGccaGGPaaacaGL7b% GaayzFaaaaaa!5C4A!