Optimization and solution approximation of design problems formulated by axiomatic design and paracomplete logic

Of primary importance in Axiomatic Design (AD) theory is Suh‘s first axiom, stating that the independence of functional requirements should be maintained throughout the design process. Para-complete logics, such as fuzzy logic, can be used to express the relationship between functional requirements (FRs) and design parameters (DPs) in AD. This is especially true in cases where this relationship can only be codified using linguistic variables. In fact, para-complete logics violate the principle of the excluded third party, allowing for the effects of changes in DP within the same FR to be considered partially independent of each other. Recently, a paper was published investigating changes in the concept of decoupled design when para-complete logics are applied to FRs-DPs link definition. Using an example case, this paper evaluated the impact of a designer‘s decoupling capability using composition rules for FRs, in order to make the design matrix diagonal or lower triangular by decoupling the effects of several DPs on different FRs using fuzzy formulation. -cut is a powerful instrument used to modify membership functions in order to approximate a non- optimized solution to an optimized one, by simply modifying the membership values. In this paper, we attempt to elaborate a simple optimization method based on a controlled approximation given by several values applied to different membership functions. We then introduce a new method to control and evaluate the amount of that approximation.