Fuzzy set applications in engineering optimization: Multilevel fuzzy optimization

A formulation for multilevel optimization with fuzzy objective functions is presented. With few exceptions, formulations for fuzzy optimization have dealt with a one-level problem in which the objective is the membership function of a fuzzy set formed by the fuzzy intersection of other sets. In the problem examined here, the goal set G is defined in a more general way, using an aggregation operator H that allows arbitrary combinations of set operations (union, intersection, addition) on the individual sets Gi. This is a straightforward extension of the standard form, but one that makes possible the modeling of interesting evaluation strategies. A second, more important departure from the standard form will be the construction of a multilevel problem analogous to the design decomposition problem in optimization. This arrangement facilitates the simulation of a system design process in which different components of the system are designed by different teams, and different levels of design detail become relevant at different time stages in the process: global design features early, local features later in the process

Dynamical compensation and structural identifiability: analysis, implications, and reconciliation

The concept of dynamical compensation has been recently introduced to describe the ability of a biological system to keep its output dynamics unchanged in the face of varying parameters. Here we show that, according to its original definition, dynamical compensation is equivalent to lack of structural identifiability. This is relevant if model parameters need to be estimated, which is often the case in biological modelling. This realization prompts us to warn that care should we taken when using an unidentifiable model to extract biological insight: the estimated values of structurally unidentifiable parameters are meaningless, and model predictions about unmeasured state variables can be wrong. Taking this into account, we explore alternative definitions of dynamical compensation that do not necessarily imply structural unidentifiability. Accordingly, we show different ways in which a model can be made identifiable while exhibiting dynamical compensation. Our analyses enable the use of the new concept of dynamical compensation in the context of parameter identification, and reconcile it with the desirable property of structural identifiability

Fixing the shadows while moving the gnomon

It is a common practice to fix a vertical gnomon and study the moving shadow cast by it. This shows our local solar time and gives us a hint regarding the season in which we perform the observation. The moving shadow can also tell us our latitude with high precision. In this paper we propose to exchange the roles and while keeping the shadows fixed on the ground we will move the gnomon. This lets us understand in a simple way the relevance of the tropical lines of latitude and the behavior of shadows in different locations. We then put these ideas into practice using sticks and threads during a solstice on two sites located on opposite sides of the Tropic of Capricorn.Comment: Published version available at http://cms.iafe.uba.ar/gangui/didaastro/#Publication