25,296 research outputs found
Data granulation by the principles of uncertainty
Researches in granular modeling produced a variety of mathematical models,
such as intervals, (higher-order) fuzzy sets, rough sets, and shadowed sets,
which are all suitable to characterize the so-called information granules.
Modeling of the input data uncertainty is recognized as a crucial aspect in
information granulation. Moreover, the uncertainty is a well-studied concept in
many mathematical settings, such as those of probability theory, fuzzy set
theory, and possibility theory. This fact suggests that an appropriate
quantification of the uncertainty expressed by the information granule model
could be used to define an invariant property, to be exploited in practical
situations of information granulation. In this perspective, a procedure of
information granulation is effective if the uncertainty conveyed by the
synthesized information granule is in a monotonically increasing relation with
the uncertainty of the input data. In this paper, we present a data granulation
framework that elaborates over the principles of uncertainty introduced by
Klir. Being the uncertainty a mesoscopic descriptor of systems and data, it is
possible to apply such principles regardless of the input data type and the
specific mathematical setting adopted for the information granules. The
proposed framework is conceived (i) to offer a guideline for the synthesis of
information granules and (ii) to build a groundwork to compare and
quantitatively judge over different data granulation procedures. To provide a
suitable case study, we introduce a new data granulation technique based on the
minimum sum of distances, which is designed to generate type-2 fuzzy sets. We
analyze the procedure by performing different experiments on two distinct data
types: feature vectors and labeled graphs. Results show that the uncertainty of
the input data is suitably conveyed by the generated type-2 fuzzy set models.Comment: 16 pages, 9 figures, 52 reference
The application of ANFIS prediction models for thermal error compensation on CNC machine tools
Thermal errors can have significant effects on CNC machine tool accuracy. The errors come from thermal deformations of the machine elements caused by heat sources within the machine structure or from ambient temperature change. The effect of temperature can be reduced by error avoidance or numerical compensation. The performance of a thermal error compensation system essentially depends upon the accuracy and robustness of the thermal error model and its input measurements. This paper first reviews different methods of designing thermal error models, before concentrating on employing an adaptive neuro fuzzy inference system (ANFIS) to design two thermal prediction models: ANFIS by dividing the data space into rectangular sub-spaces (ANFIS-Grid model) and ANFIS by using the fuzzy c-means clustering method (ANFIS-FCM model). Grey system theory is used to obtain the influence ranking of all possible temperature sensors on the thermal response of the machine structure. All the influence weightings of the thermal sensors are clustered into groups using the fuzzy c-means (FCM) clustering method, the groups then being further reduced by correlation analysis.
A study of a small CNC milling machine is used to provide training data for the proposed models and then to provide independent testing data sets. The results of the study show that the ANFIS-FCM model is superior in terms of the accuracy of its predictive ability with the benefit of fewer rules. The residual value of the proposed model is smaller than ±4 μm. This combined methodology can provide improved accuracy and robustness of a thermal error compensation system
A fuzzy approach for the network congestion problem
In the recent years, the unpredictable growth of the Internet has moreover pointed out the congestion problem, one of the problems that historicallyha ve affected the network. This paper deals with the design and the evaluation of a congestion control algorithm which adopts
a FuzzyCon troller. The analogyb etween Proportional Integral (PI) regulators and Fuzzycon trollers is discussed and a method to determine the scaling factors of the Fuzzycon troller is presented. It is shown that
the Fuzzycon troller outperforms the PI under traffic conditions which are different from those related to the operating point considered in the design
MODELLING EXPECTATIONS WITH GENEFER- AN ARTIFICIAL INTELLIGENCE APPROACH
Economic modelling of financial markets means to model highly complex systems in which expectations can be the dominant driving forces. Therefore it is necessary to focus on how agents form their expectations. We believe that they look for patterns, hypothesize, try, make mistakes, learn and adapt. AgentsÆ bounded rationality leads us to a rule-based approach which we model using Fuzzy Rule-Bases. E. g. if a single agent believes the exchange rate is determined by a set of possible inputs and is asked to put their relationship in words his answer will probably reveal a fuzzy nature like: "IF the inflation rate in the EURO-Zone is low and the GDP growth rate is larger than in the US THEN the EURO will rise against the USD". æLowÆ and ælargerÆ are fuzzy terms which give a gradual linguistic meaning to crisp intervalls in the respective universes of discourse. In order to learn a Fuzzy Fuzzy Rule base from examples we introduce Genetic Algorithms and Artificial Neural Networks as learning operators. These examples can either be empirical data or originate from an economic simulation model. The software GENEFER (GEnetic NEural Fuzzy ExplorER) has been developed for designing such a Fuzzy Rule Base. The design process is modular and comprises Input Identification, Fuzzification, Rule-Base Generating and Rule-Base Tuning. The two latter steps make use of genetic and neural learning algorithms for optimizing the Fuzzy Rule-Base.
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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