An approach to Fuzzy clustering of the iris petals by using Ac-means Analysis

This paper proposes a definition of a fuzzy partition element based on the homomorphism between type-1 fuzzy sets and the three-valued Kleene algebra. A new clustering method based on the C-means algorithm, using the defined partition, is presented in this paper, which will be validated with the traditional iris clustering problem by measuring its petals.

Three-Mode Fuzzy Co-Clustering Based on Probabilistic Concept and Comparison with FCM-Type Algorithms

Three-mode fuzzy co-clustering is a promising technique for analyzing relational co-occurrence information among three mode elements. The conventional FCM-type algorithms achieved simultaneous fuzzy partition of three mode elements based on the fuzzy c-means (FCM) concept, and then, they often suffer from careful tuning of three independent fuzzification parameters. In this paper, a novel three-mode fuzzy co-clustering algorithm is proposed by modifying the conventional aggregation criterion of three elements based on a probabilistic concept. The fuzziness degree of three-mode partition can be easily tuned only with a single parameter under the guideline of the probabilistic standard. The characteristic features of the proposed method are compared with the conventional algorithms through numerical experiments using an artificial dataset and are demonstrated in application to a real world dataset of MovieLens movie evaluation data.

A User Recommendation Model for Answering Questions on Brainly Platform

Brainly is a Community Question Answer (CQA) application that allows students or parents to ask questions related to their homework. The current mechanism is that users ask questions, then other users who are in the same subject interest can see and answer it. As a reward for answering questions, Brainly gives points. The number of points varies by question. The greater of total points users have, Brainly will automatically display them in the smartest user leaderboard on the site's front page. But sometimes, some users do not have good activity in answering questions. Thus, it is possible to have an urgent question that has not been answered by anyone. This study implements Fuzzy C-Means cluster method to improve Brainly's feature regarding the speed and accuracy of answers. The idea is to create student clusters by utilizing the smartest students' leaderboard, subjects interest, and answering activities. The stages applied in this research started with Data Extraction, Preprocessing, Cluster Process, and User Recommender. The optimal number of clusters in the answerer recommendation in the Brainly platform is 2 clusters. The value of the fuzzy partition coefficient for two clusters reached 0.97 for Mathematics and 0.93 for Indonesian. Meanwhile, the results of the recommendations were influenced by answer ratings. Many numbers of the answer are not given rating because the possibility of the answers are not appropriate or user's insensitivity in giving ratings.

Dynamic programming based fuzzy partition in fuzzy decision tree induction

Fuzzy decision trees are one of the most popular extensions of decision trees for symbolic knowledge acquisition by fuzzy representation. Among the majority of fuzzy decision trees learning methods, the number of fuzzy partitions is given in advance, that is, there are the same amount of fuzzy items utilized in each condition attribute. In this study, a dynamic programming-based partition criterion for fuzzy items is designed in the framework of fuzzy decision tree induction. The proposed criterion applies an improved dynamic programming algorithm used in scheduling problems to establish an optimal number of fuzzy items for each condition attribute. Then, based on these fuzzy partitions, a fuzzy decision tree is constructed in a top-down recursive way. A comparative analysis using several traditional decision trees verify the feasibility of the proposed dynamic programming based fuzzy partition criterion. Furthermore, under the same framework of fuzzy decision trees, the proposed fuzzy partition solution can obtain a higher classification accuracy than some cases with the same amount of fuzzy items.

Fuzzy Divisive Hierarchical Associative-Clustering Applied to Different Varieties of White Wines According to Their Multi-Elemental Profiles

Wine data are usually characterized by high variability, in terms of compounds and concentration ranges. Chemometric methods can be efficiently used to extract and exploit the meaningful information contained in such data. Therefore, the fuzzy divisive hierarchical associative-clustering (FDHAC) method was efficiently applied in this study, for the classification of several varieties of Romanian white wines, using the elemental profile (concentrations of 30 elements analyzed by ICP-MS). The investigated wines were produced in four different geographical areas of Romania (Transylvania, Moldova, Muntenia and Oltenia). The FDHAC algorithm provided not only a fuzzy partition of the investigated white wines, but also a fuzzy partition of considered characteristics. Furthermore, this method is unique because it allows a 3D bi-plot representation of membership degrees corresponding to wine samples and elements. In this way, it was possible to identify the most specific elements (in terms of highest, smallest or intermediate concentration values) to each fuzzy partition (group) of wine samples. The chemical elements that appeared to be more powerful for the differentiation of the wines produced in different Romanian areas were: K, Rb, P, Ca, B, Na.

Fuzzy Divisive Hierarchical Clustering of Solvents According to Their Experimentally and Theoretically Predicted Descriptors

The present study describes a simple procedure to separate into patterns of similarity a large group of solvents, 259 in total, presented by 15 specific descriptors (experimentally found and theoretically predicted physicochemical parameters). Solvent data is usually characterized by its high variability, different molecular symmetry, and spatial orientation. Methods of chemometrics can usefully be used to extract and explore accurately the information contained in such data. In this order, advanced fuzzy divisive hierarchical-clustering methods were efficiently applied in the present study of a large group of solvents using specific descriptors. The fuzzy divisive hierarchical associative-clustering algorithm provides not only a fuzzy partition of the solvents investigated, but also a fuzzy partition of descriptors considered. In this way, it is possible to identify the most specific descriptors (in terms of higher, smallest, or intermediate values) to each fuzzy partition (group) of solvents. Additionally, the partitioning performed could be interpreted with respect to the molecular symmetry. The chemometric approach used for this goal is fuzzy c-means method being a semi-supervised clustering procedure. The advantage of such a clustering process is the opportunity to achieve separation of the solvents into similarity patterns with a certain degree of membership of each solvent to a certain pattern, as well as to consider possible membership of the same object (solvent) in another cluster. Partitioning based on a hybrid approach of the theoretical molecular descriptors and experimentally obtained ones permits a more straightforward separation into groups of similarity and acceptable interpretation. It was shown that an important link between objects’ groups of similarity and similarity groups of variables is achieved. Ten classes of solvents are interpreted depending on their specific descriptors, as one of the classes includes a single object and could be interpreted as an outlier. Setting the results of this research into broader perspective, it has been shown that the fuzzy clustering approach provides a useful tool for partitioning by the variables related to the main physicochemical properties of the solvents. It gets possible to offer a simple guide for solvents recognition based on theoretically calculated or experimentally found descriptors related to the physicochemical properties of the solvents.