Using Fuzzy Value Tree Analysis to Support The Verification, Validation, and Accreditation of Models and Simulations

Abstract

The process of accrediting a model can roughly be divided into first gathering and evaluating results of conducted verification and validation (V& V) activities, and then aggregating these (raw) results into a total value: the accreditation decision. Especially the second part is not trivial, because results of V& V activities are quite manifold and at first sight not comparable with each other. Consider for example the evaluation of subject matter expert statements in contrast to real numbers as an outcome of statistical tests.

Classical decision analysis is one possibility to support the accreditation decision by using a structured, scientifically justified approach. For that purpose, mainly the concept of value tree analysis is used. In previous papers, the current state-of-the-art concerning decision analytic methodologies supporting VV&A was reviewed. Also a critical examination, describing gaps and deficiencies was conducted. A concept was drafted, how fuzzy value tree analysis, a branch of decision analysis incorporating fuzzy set theory, can be used to overcome some of these deficiencies, as there are: First, modeling subject matter experts statements, second, quantifying not only the value, but also the knowledge resp. ignorance about the model under study, and finally, being able to distinguish between compensational and non-compensational attributes in the value tree.

Fuzzy value tree analysis consists of the steps

• establishing the value tree,

• assigning values to attributes,

• aggregating the attribute values, and

• interpreting the result.

A raw draft of the concept, as well as a definition of attribute values in a fuzzy value tree analysis was dealt with in previous publications. The paper at hand takes these publications as a starting point and presents a concept how attribute values in a fuzzy value tree analysis can be aggregated, i. e. the aggregator is defined.

Starting from establishing requirements and constraints, these postulations are transformed into mathematical properties the aggregator must adhere to. After scanning the literature for possible fuzzy set theoretic operators, it is proven that the defined aggregator fulfills the mathematical properties established and therefore all requirements and constraints. The paper closes with illustrative examples.