We investigate essential relationships between generalization capabilities and fuzziness of fuzzy classifiers (viz., the classifiers whose outputs are vectors of membership grades of a pattern to the individual classes). The study makes a claim and offers sound evidence behind the observation that higher fuzziness of a fuzzy classifier may imply better generalization aspects of the classifier, especially for classification data exhibiting complex boundaries. This observation is not intuitive with a commonly accepted position in "traditional" pattern recognition. The relationship that obeys the conditional maximum entropy principle is experimentally confirmed. Furthermore, the relationship can be explained by the fact that samples located close to classification boundaries are more difficult to be correctly classified than the samples positioned far from the boundaries. This relationship is expected to provide some guidelines as to the improvement of generalization aspects of fuzzy classifiers.
The paper describes the relation between fuzzy and non-fuzzy description logics. It gives an overview about current research in these areas and describes the difference between tasks for description logics and fuzzy logics. The paper also deals with the transformation properties of description logics to fuzzy logics and backwards. While the process of transformation from a description logic to a fuzzy logic is a trivial inclusion, the other way of reducing information from fuzzy logic to description logic is a difficult task, that will be topic of future work.
Rough sets theory has been considered as a useful method to model the uncertainty and has been applied successfully in many fields. And every rough set is associated with some amount of fuzziness. On the other hand, rough sets theory has been generalized with coverings instead of classical partition. So it is necessary to consider the amount of fuzziness in generalized rough sets induced by a covering. In this paper, a measure of fuzziness in generalized rough sets induced by a covering is proposed. Moreover, some characterizations and properties of this measure are shown by examples, which is every useful in future research works of generalized rough sets induced by a covering.
An integrated approach to truth-gaps and epistemic uncertainty is described, based on probability distributions defined over a set of three-valued truth models. This combines the explicit representation of borderline cases with both semantic and stochastic uncertainty, in order to define measures of subjective belief in vague propositions. Within this framework we investigate bridges between probability theory and fuzziness in a propositional logic setting. In particular, when the underlying truth model is from Kleene's three-valued logic then we provide a complete characterisation of compositional min–max fuzzy truth degrees. For classical and supervaluationist truth models we find partial bridges, with min and max combination rules only recoverable on a fragment of the language. Across all of these different types of truth valuations, min–max operators are resultant in those cases in which there is uncertainty about the relative sharpness or vagueness of the interpretation of the language.
In this paper, we concentrate on the usage of uncertainty associated with the level of fuzziness in determination of the number of clusters in FCM for any data set. We propose a MiniMax -stable cluster validity index based on the uncertainty associated with the level of fuzziness within the framework of interval valued Type 2 fuzziness. If the data have a clustered structure, the optimum number of clusters may be assumed to have minimum uncertainty under upper and lower levels of fuzziness. Upper and lower values of the level of fuzziness for Fuzzy -Mean (FCM) clustering methodology have been found as = 2.6 and 1.4, respectively, in our previous studies. Our investigation shows that the stability of cluster centers with respect to the level of fuzziness is sufficient for the determination of the number of clusters.
In contemporary health science sophisticated apparatus delivers a lot of data on vital processes in patients. All of them are processed as a bulk of numbers not suitable directly for diagnosing or research purposes. Moreover, which is common in biomedical sciences, measured data are intrinsically inaccurate, i.e., fuzzy. In order to overcome these deficiencies a set of visualization methods has been developed as well as dedicated file formats. In the paper authors discuss selected formats and imaging techniques useful for cardiologists. Problems of medical data processing is outlined. Strengthens and weaknesses of raw STL file format are analyzed. Visualization styles of data fuzziness using experimental package ScPovPlot3D based on POVRay are proposed and discussed.
Some decision making applications require to encode statistics and fuzziness. In this work two frameworks are considered: coherent conditional probabilities and possibilities, which allow to give a rigorous interpretation of membership function. A comparison of the two interpretations is given to employ a general Bayesian inferential approach able to embed fuzzy information.
In this study, Fuzzy Cognitive Maps (FCMs), which are powerful tools for graphical representation of knowledge, are analyzed from an ambiguity and fuzziness perspective. In conventional FCMs the causal strengths are represented with singleton (crisp) fuzzy numbers, but recently, other researchers proposed different FCM structures where uniform (interval) or triangular fuzzy numbers are used in causal strength representation. Here, FCMs are analyzed by means of fuzziness and ambiguity measures that are proposed in literature to investigate the capability of models to represent uncertainties. In addition, two new measures, called the average ambiguity measure (AAM) and the average fuzziness measure (AFM), are proposed to indicate uncertainty representation of an FCM. A well-known FCM model of a public health system is used as a case study to show how the fuzzy weights determine the uncertainty representation of FCMs, and then the outcomes are discussed.