Encoding fuzzy possibilistic diagnostics as a constrained optimization problem

Fuzzy-stochastic-based violation analysis method for planning water resources management systems with uncertain information

“…where l D ; l G and l C denote membership functions of fuzzy decision D, fuzzy goal G, and fuzzy constraint C, respectively [37]. Letting l C i ðXÞ be membership functions of constraints C i ði ¼ 1; 2; .…”

“…FMP is effective in dealing with decision problems under fuzzy goal and constraints and in handling ambiguous coefficients of objective function and constraints caused by imprecision and vagueness [2,10,15,26,28,37,42,46,47]. SMP is an extension of mathematical programming to decision problems whose coefficients (input data) are not certainly known but could be represented as chances or probabilities [3,6,16,17].…”

Dynamic estimations of metabolic fluxes with constraint-based models and possibility theory

“…The framework exploits the notion of "possibilistic constraint satisfaction problems", which was introduced in (Dubois, 1996). Similar optimization approaches to logic reasoning were previously explored in (Sala, 2001;Sala, 2008). The framework is based on two ideas: (1) represent knowledge with constraints satisfied to a certain degree, thus transforming the feasibility of a potential solution into a gradual notion of "possibility" that accounts for uncertainty, and (2) use computationally efficient optimisation-based methods to query for the "most possible" solutions.…”

Fault detection and isolation based on fuzzy automata

“…To some level, physical systems can be described by continuous-time variables and for such models efficient FDI methodologies have been established [1,11]. On the other hand there are systems which can be better described using a discrete state space and event driven dynamics, and for this type of systems fault diagnosis based on automata has to be performed [28,29].…”