391 research outputs found
Analysis and guidelines to obtain a good uniform fuzzy partition granularity for fuzzy rule-based systems using simulated annealing
In this contribution, we will analyse the importance of the fuzzy partition granularity for the linguistic variables in the design of fuzzy rule-based systems (FRBSs). In order to put this into effect, we will study the FRBS behaviour considering uniform fuzzy partitions with the same number of labels for all the linguistic variables, and considering uniform fuzzy partitions with any number of labels for each linguistic variable. We will present a method based on Simulated Annealing (SA) in order to obtain a good uniform fuzzy partition granularity that improves the FRBS behaviour. It is an efficient granularity search method for finding a good number of labels per variable.CICYT projects TIC96-0778 and PB98-131
Learning concurrently partition granularities and rule bases of Mamdani fuzzy systems in a multi-objective evolutionary framework
AbstractIn this paper we propose a multi-objective evolutionary algorithm to generate Mamdani fuzzy rule-based systems with different good trade-offs between complexity and accuracy. The main novelty of the algorithm is that both rule base and granularity of the uniform partitions defined on the input and output variables are learned concurrently. To this aim, we introduce the concepts of virtual and concrete rule bases: the former is defined on linguistic variables, all partitioned with a fixed maximum number of fuzzy sets, while the latter takes into account, for each variable, a number of fuzzy sets as determined by the specific partition granularity of that variable. We exploit a chromosome composed of two parts, which codify the variables partition granularities, and the virtual rule base, respectively. Genetic operators manage virtual rule bases, whereas fitness evaluation relies on an appropriate mapping strategy between virtual and concrete rule bases. The algorithm has been tested on two real-world regression problems showing very promising results
Learning of interval and general type-2 fuzzy logic systems using simulated annealing: theory and practice
This paper reports the use of simulated annealing to design more efficient fuzzy logic systems to model problems with associated uncertainties. Simulated annealing is used within this work as a method for learning the best configurations of interval and gen- eral type-2 fuzzy logic systems to maximize their modeling ability. The combination of simulated annealing with these models is presented in the modeling of four bench- mark problems including real-world problems. The type-2 fuzzy logic system models are compared in their ability to model uncertainties associated with these problems. Issues related to this combination between simulated annealing and fuzzy logic sys- tems, including type-2 fuzzy logic systems, are discussed. The results demonstrate that learning the third dimension in type-2 fuzzy sets with a deterministic defuzzifier can add more capability to modeling than interval type-2 fuzzy logic systems. This finding can be seen as an important advance in type-2 fuzzy logic systems research and should increase the level of interest in the modeling applications of general type-2 fuzzy logic systems, despite their greater computational load
Sum Normal Optimization of Fuzzy Membership Functions
Given a fuzzy logic system, how can we determine the membership functions that will result in the best performance? If we constrain the membership functions to a certain shape (e.g., triangles or trapezoids) then each membership function can be parameterized by a small number of variables and the membership optimization problem can be reduced to a parameter optimization problem. This is the approach that is typically taken, but it results in membership functions that are not (in general) sum normal. That is, the resulting membership function values do not add up to one at each point in the domain. This optimization approach is modified in this paper so that the resulting membership functions are sum normal. Sum normality is desirable not only for its intuitive appeal but also for computational reasons in the real time implementation of fuzzy logic systems. The sum normal constraint is applied in this paper to both gradient descent optimization and Kalman filter optimization of fuzzy membership functions. The methods are illustrated on a fuzzy automotive cruise controller
Learning of Type-2 Fuzzy Logic Systems using Simulated Annealing.
This thesis reports the work of using simulated annealing to design more efficient fuzzy logic systems to model problems with associated uncertainties. Simulated annealing is
used within this work as a method for learning the best configurations of type-1 and
type-2 fuzzy logic systems to maximise their modelling ability. Therefore, it presents
the combination of simulated annealing with three models, type-1 fuzzy logic systems,
interval type-2 fuzzy logic systems and general type-2 fuzzy logic systems to model
four bench-mark problems including real-world problems. These problems are: noise-free
Mackey-Glass time series forecasting, noisy Mackey-Glass time series forecasting
and two real world problems which are: the estimation of the low voltage electrical
line length in rural towns and the estimation of the medium voltage electrical line
maintenance cost. The type-1 and type-2 fuzzy logic systems models are compared in
their abilities to model uncertainties associated with these problems. Also, issues related
to this combination between simulated annealing and fuzzy logic systems including
type-2 fuzzy logic systems are discussed.
The thesis contributes to knowledge by presenting novel contributions. The first is
a novel approach to design interval type-2 fuzzy logic systems using the simulated
annealing algorithm. Another novelty is related to the first automatic design of general
type-2 fuzzy logic system using the vertical slice representation and a novel method
to overcome some parametrisation difficulties when learning general type-2 fuzzy logic
systems. The work shows that interval type-2 fuzzy logic systems added more abilities
to modelling information and handling uncertainties than type-1 fuzzy logic systems but
with a cost of more computations and time. For general type-2 fuzzy logic systems, the
clear conclusion that learning the third dimension can add more abilities to modelling
is an important advance in type-2 fuzzy logic systems research and should open the
doors for more promising research and practical works on using general type-2 fuzzy
logic systems to modelling applications despite the more computations associated with
it
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