Fuzzy hierarchical cross-classification of Greek muds

Abstract

In this paper we analyze the set of Greek muds from eight different locations given in ref 16 using a divisive fuzzy hierarchical cross-classification algorithm. We consider the fuzzy clustering algorithms are capable to eliminate the disfunctionalities of the hard clustering algorithms as well as to provide information obtained from a metrical analysis of the data. The fuzzy hierarchical cross-classification algorithm presented here produces not only a fuzzy partition of the muds in discussion but also a fuzzy partition of the 23 chemical and mineralogical characteristics, so that to each class of muds we may associate the class of characteristics that contributed to the separation of the class of muds.

A Fuzzy Classification of the Chemical Elements

“…3 It deals with the uncertainty and fuzziness arising from interrelated humanistic types of phenomena such as subjectivity, thinking, reasoning, cognition, and perception. 37 Fuzzy Set and Fuzzy Partition. This approach provides a way to translate a linguistic model of the human thinking process into a mathematical framework for developing the computer algorithms for computerized decision-making processes.…”

Assessment of Heart Disease using Fuzzy Classification Techniques

“…In this section we will recall the so-called generalized fuzzy n-means algorithm [3,4,6]. This algorithm is a generalization of the well-known fuzzy n-means algorithm [1,4].…”

“…Among other interesting applications, the fuzzy clustering theory developed in References [3,4,6,8] has been used for the selection and the optimal combination of solvents [7,13], for the classification of Roman pottery [9], for the cross-classification of Greek muds [6], for the development of a fuzzy system of chemical elements [12,14], for producing a performant fuzzy regression algorithm [10], and for the cross-classification of thin layer chromatography data [11].…”

The Fuzzy Hierarchical Cross-Clustering Algorithm. Improvements and Comparative Study

“…In this section we will recall the so-called Generalized Fuzzy n-Means Algorithm. [2][3][4] This algorithm is a generalization of the wellknown Fuzzy n-Means Algorithm. 3,1 Let us consider a set of objects X ) {x 1 , ..., x p } ⊂ R s and let C be a fuzzy set on X.…”

“…Among other interesting applications, the fuzzy clustering theory developed in refs 2-4 and 7 has been used for the selection and the optimal combination of solvents, 5,11 for the classification of Roman pottery, 8 for the cross-classification of Greek muds, 4 for the development of a fuzzy system of chemical elements, 10,12 and for producing a performant fuzzy regression algorithm. 9 In the present paper we will approach the fuzzy hierarchical cross-classification algorithm (see also refs 3 and 4).…”