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Imposing restrictions on density functions utilised in computing with words

Marcus Gemeinder (2002)

International Journal of Applied Mathematics and Computer Science

Applying the generalised extension principle within the area of Computing with Words typically leads to complex maximisation problems. If distributed quantities-such as, e.g., size distributions within human populations-are considered, density functions representing these distributions become involved. Very often the optimising density functions do not resemble those found in nature; for instance, an optimising density function could consist of two single Dirac pulses positioned near the opposite...

Improving the generalization ability of neuro-fuzzy systems by ε-insensitive learning

Jacek Łęski (2002)

International Journal of Applied Mathematics and Computer Science

A new learning method tolerant of imprecision is introduced and used in neuro-fuzzy modelling. The proposed method makes it possible to dispose of an intrinsic inconsistency of neuro-fuzzy modelling, where zero-tolerance learning is used to obtain a fuzzy model tolerant of imprecision. This new method can be called ε-insensitive learning, where, in order to fit the fuzzy model to real data, the ε-insensitive loss function is used. ε-insensitive learning leads to a model with minimal Vapnik-Chervonenkis...

Inference in conditional probability logic

Niki Pfeifer, Gernot D. Kleiter (2006)

Kybernetika

An important field of probability logic is the investigation of inference rules that propagate point probabilities or, more generally, interval probabilities from premises to conclusions. Conditional probability logic (CPL) interprets the common sense expressions of the form “if ..., then ...” by conditional probabilities and not by the probability of the material implication. An inference rule is probabilistically informative if the coherent probability interval of its conclusion is not necessarily...

Influence of modeling structure in probabilistic sequential decision problems

Florent Teichteil-Königsbuch, Patrick Fabiani (2006)

RAIRO - Operations Research

Markov Decision Processes (MDPs) are a classical framework for stochastic sequential decision problems, based on an enumerated state space representation. More compact and structured representations have been proposed: factorization techniques use state variables representations, while decomposition techniques are based on a partition of the state space into sub-regions and take advantage of the resulting structure of the state transition graph. We use a family of probabilistic exploration-like...

Information boundedness principle in fuzzy inference process

Peter Sarkoci, Michal Šabo (2002)

Kybernetika

The information boundedness principle requires that the knowledge obtained as a result of an inference process should not have more information than that contained in the consequent of the rule. From this point of view relevancy transformation operators as a generalization of implications are investigated.

Interpretability of linguistic variables: a formal account

Ulrich Bodenhofer, Peter Bauer (2005)

Kybernetika

This contribution is concerned with the interpretability of fuzzy rule-based systems. While this property is widely considered to be a crucial one in fuzzy rule-based modeling, a more detailed formal investigation of what “interpretability” actually means is not available. So far, interpretability has most often been associated with rather heuristic assumptions about shape and mutual overlapping of fuzzy membership functions. In this paper, we attempt to approach this problem from a more general...

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