Ibrahim Ozkan

Upper and lower values for the level of fuzziness in FCM

The level of fuzziness is a parameter in fuzzy system modeling which is a source of uncertainty. In order to explore the effect of this uncertainty, one needs to investigate and identify effective upper and lower boundaries of the level of fuzziness. For this purpose, Fuzzy c-means (FCM) clustering methodology is investigated to determine the effective upper and lower boundaries of the level of fuzziness in order to capture the uncertainty generated by this parameter. In this regard, we propose to expand the membership function around important information points of FCM. These important information points are, cluster centers and the mass center. At these points, it is known that, the level of fuzziness has no effect on the membership values. In this way, we identify the counter-intuitive behavior of membership function near these particular information points. It will be shown that the upper and lower values of the level of fuzziness can be identified. Hence the uncertainty generated by this parameter can be encapsulated.

MiniMax ε-stable cluster validity index for Type-2 fuzziness

Uncertainty is a central part of many data analysis methodologies. Although quantifying the uncertainty has long been discussed, the research on it is still in progress. The level of fuzziness in fuzzy system modeling is a source of uncertainty which can be classified as a parameter uncertainty. Upper and lower values of the level of fuzziness for Fuzzy C-Mean (FCM) clustering methodology have been found as 2.6 and 1.4 respectively in our previous studies. 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 in any data. We propose MiniMax ε-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. Our investigation shows that the half range of upper and lower levels of fuzziness would be enough to determine the optimum number of clusters.

A fuzzy analysis of country-size argument for the Feldstein-Horioka puzzle

This study aims to analyze the effect of country size, represented by relative Gross National Products (GNP), on the association between domestic investment and saving, using data from a panel of 21 OECD countries. The countries are clustered into four groups with respect to their relative country sizes with an application of Fuzzy c-Means clustering technique. The novelty of this approach is that it is an unsupervised method that generates membership values between zero and one instead of binary values that take values of zero or one only. In addition to this it has the advantages of its tolerance to imprecise data and the ease of understanding. The results show that the saving retention coefficients are greater for larger countries except for the cluster which contains the largest country. Thus, this work presents only partial evidence that the country size affects the relationship of domestic saving and investment.

Uncertainty and Fuzzy Decisions

Uncertainty is the main reason that makes human free to choose. Many actions, strategies are designed to handle or reduce the uncertainty to make decision makers life easier. But there is no common accepted theory in the academia. Researchers still struggling to create a common understanding. There are theories that we may follow to make decisions under uncertainty. Among them, probability theory, fuzzy theory and evidence theory can be given. Decision problem is constructed in with the help of these theories. Fuzzy Logic and Fuzzy theory may be considered as the recent advancement and has been applied in many fields for different type of decision problems.

Uncertainty, Complexity and Fuzzy Logic

We explore the concept of uncertainty, complexity and fuzzy logic in order to provide a grounding of the use of fuzzy logic in human perception and decision making with precisiated natural language expressions. For this purpose, we provide generally accepted notions of uncertainty, its taxonomies, its sources and the need of fuzzy theory that provides a grounding for the handling of uncertainty. Finally a brief introduction is given to fuzzy decision making studies. In particular, we outline perception based decision making with an application of essential concept of fuzzy logic. For this purpose we restated essential concepts related to theoretical inquiry along with its interpretations in classical and fuzzy theories.

MiniMax ε-stable cluster validity index for type-2 fuzziness

Uncertainty is a central part of many data analysis methodologies. Although quantifying the uncertainty has long been discussed, the research on it is still in progress. The level of fuzziness in fuzzy system modeling is a source of uncertainty which can be classified as a parameter uncertainty. Upper and lower values of the level of fuzziness for Fuzzy C-Mean (FCM) clustering methodology have been found as 2.6 and 1.4 respectively in our previous studies. 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 in any data. We propose MiniMax e-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. Our investigation shows that the half range of upper and lower levels of fuzziness would be enough to determine the optimum number of clusters.

A new causal discovery heuristic

Probabilistic methods for causal discovery are based on the detection of patterns of correlation between variables. They are based on statistical theory and have revolutionised the study of causality. However, when correlation itself is unreliable, so are probabilistic methods: unusual data can lead to spurious causal links, while nonmonotonic functional relationships between variables can prevent the detection of causal links. We describe a new heuristic method for inferring causality between two continuous variables, based on randomness and unimodality tests and making few assumptions about the data. We evaluate the method against probabilistic and additive noise algorithms on real and artificial datasets, and show that it performs competitively.

Cooperative hybrid ARQ networks

In this work, the performance contribution of a relay node which cooperates to a source node during the transmission of data packets from source node to destination node is investigated. The effect of diversity gain to the performance of a network consists of correlated flat-faded Rayleigh channels. In this work, the re-transmissions of an individual packet are combined at destination node by employing maximal-ratio combining (MRC) method. To model the packet errors for convolutionally coded packets, an approach to ease the analytic investigation is followed.

A Review of Cluster Validation with an Example of Type-2 Fuzzy Application in R

Interval valued type-2 fuzziness can be represented by means of membership functions obtained with upper and lower values of the level of fuzziness. These upper and lower values for the level of fuzziness in FCM algorithm were obtained in our previous studies. A particular application of Interval valued type-2 fuzziness is shown for cluster validity analysis in this chapter. For this purpose, we introduce a brief taxonomy for cluster validity indices to clarify the contribution of our novel approach. To provide reproducibility of our technique, the source code is written in freely available language ‘R’ and can be found on our web site.