If an application has to make decisions based on inexact concepts, it may not be a priori clear which semantic interpretation to choose for these concepts, and which (if any) consequences the choice of an alternative might have on the outcome of the decision process. This paper addresses this problem of fuzzy semantics by exploring which properties are preserved in a fuzzy logic formula under different transformations of the structure in which the formula is evaluated.

To make the paper self-contained, the authors first provide an exhaustive introduction to the fundamental concepts of fuzzy model theory, to provide a basis on which the presented results can be understood. Then, they show under which constraints the essential properties of a formula remain unchanged, if the valuation of the basic predicates is modified by applying a homomorphism to another suitable valuation structure. Next, they generalize this result to a modification of the operations of the valuation structure, which shows that, in a sense, the scale of the structure can be modified in an almost arbitrary way. Finally, they describe how the results also apply to a “cutting” process by which all the properties are forced to be precise.

The authors state, “All [of] the results are either easy to prove or well known.” Nevertheless, the paper presents a comprehensive picture of the topic. By choosing a slight modification to the generally used “approach to fuzzy semantics in which the valuation structures can vary freely,” it also puts forward a question and indicates possible paths.