Fuzzy Sets vereinen Ratings und Rankings bei LV-Produkten

TL;DR

Robert Holz shows ratings, rankings, and scorings as special fuzzy sets to unify their comparison.
Applies this to LV-Produktratings (life insurance product ratings) using fuzzy logic for real informational value.
Offers critique of current methods and outlook for fuzzy set advances in actuarial ratings.[[1]](https://doi.org/10.1007/BF02808296)[[2]](https://link.springer.com/article/10.1007/BF02808296)

The story at a glance

Robert Holz's paper in Blätter der DGVFM argues for treating ratings, rankings, and scorings as fuzzy sets to enable theoretical comparison, with fuzzy logic capturing their true information content. It uses life insurance product ratings (LV-Produktratings) as the main example and reviews existing procedures. This appeared in 1998 amid growing interest in fuzzy methods for handling uncertainty in insurance and actuarial work.[[1]](https://doi.org/10.1007/BF02808296)[[2]](https://link.springer.com/article/10.1007/BF02808296)

Key points

Ratings, rankings, and scorings are special cases of fuzzy sets, allowing analysis under one theory.[[1]](https://doi.org/10.1007/BF02808296)
Fuzzy logic describes the actual statement value or informational content of ratings better than crisp methods.
Example focuses on LV-Produktratings, merging rating styles for life insurance products.
Reviews current procedures like those from Capital, Finanztest, and actuarial reports (e.g., Ackermann 1996, Finsinger 1997).
Provides outlook on further fuzzy set theory applications in ratings.[[2]](https://link.springer.com/article/10.1007/BF02808296)

Details and context

The paper builds on foundational fuzzy set work by Zadeh (1965) and texts like Klir & Yuan (1995), applying it to actuarial science where uncertainty is common, as in Holz's prior book Fuzzy Sets in der Tarifierung (1996).[[2]](https://link.springer.com/article/10.1007/BF02808296)

Blätter der DGVFM (now Blätter DGVFM) is the journal of the German Association for Insurance Mathematics, targeting actuaries on risk modeling and insurance evaluation.

Life insurance ratings in 1990s Germany involved comparing products on criteria like costs and performance, but methods varied; fuzzy sets address vagueness in such assessments, differing from probabilistic stochastic approaches.

References cite German insurance critiques (e.g., Heimes & Will 1995 on company ratings) and fuzzy applications (e.g., Ostaszewski 1993).[[2]](https://link.springer.com/article/10.1007/BF02808296)

Key quotes

None available from full text; abstract states: "Die Fuzzy-Logik erweist sich außerdem als adäquates Mittel zur Beschreibung des realen Aussagewertes von Ratings." (Robert Holz, abstract).[[1]](https://doi.org/10.1007/BF02808296)

Why it matters

Unifying rating methods via fuzzy sets improves handling of imprecise data in insurance evaluation, key for actuaries modeling real-world uncertainty.

It means better tools for comparing life insurance products, aiding consumers and firms in decisions beyond binary scores.

Watch for later fuzzy applications in finance, though adoption depends on empirical validation against traditional statistics.[[2]](https://link.springer.com/article/10.1007/BF02808296)