Solving the problem of preliminary partitioning of heterogeneous data into classes in conditions of limited volume

In the context of the formation of heterogeneous data that differ significantly in nature, even of a small volume, it becomes necessary to analyze them for decision-making. This is typical for many high-tech industrial fields of human activity. The problem can be solved by bringing heterogeneous data to a single view and then dividing it into clusters. Instead of searching for a solution for each data element, it is proposed to use the division of the entire set of normalized data into clusters, and thereby simplify the process of isolating the cluster and making a decision on it. The essence of the proposed solution is the automatic grouping of objects with similar data into clusters. This allows you to reduce the amount of analyzed information by combining a lot of data and perform mathematical operations already for the cluster. When splitting, it is proposed to use the theory of fuzzy logic. The possibility of such an approach is due to the fact that different objects always have several characteristics by which they can be combined. These signs are often not obvious and are poorly formalized. A hierarchical modification of the AFC fuzzy clustering method based on the operation (maxmin) of the fuzzy similarity ratio is proposed. The basic concepts and definitions of the proposed method of automatic partitioning of a set of input data, a step-by-step scheme of the corresponding cluster procedure are considered. The efficiency of the proposed method is demonstrated by the example of solving the problem of forming a traffic flow. A numerical experiment has shown that the developed algorithm allows you to automatically analyze heterogeneous data and stably divide them into classes. The application of the proposed modification allows for the preliminary partitioning of data into clusters and allows reducing the volume of analyzed data in the future. There is no need to consider the objects in each case separately

Application of Fuzzy-Neural Network in Classification of Soils using Ground-penetrating Radar Imagery

Errors associated with visual inspection and interpretation of radargrams often inhibits the intensive surveying of widespread areas using ground-penetrating radar (GPR). To automate the interpretive process, this paper presents an application of a fuzzy-neural network (F-NN) classifier for unsupervised clustering and classification of soil profile using GPR imagery. The classifier clusters and classifies soil profiles strips along a traverse based on common pattern similarities that can relate to physical features of the soil (e.g., number of horizons; depth, texture and structure of the horizons; and relative arrangement of the horizons, etc). This paper illustrates this classification procedure by its application on GPR data, both simulated and actual real-world. Results show that the procedure is able to classify the profile into zones that corresponded with those obtained by visual inspection and interpretation of radargrams. Results indicate that an F-NN model can supply real-time soil profile clustering and classification during field surveys

Application of Fuzzy-Neural Network in Classification of Soils using Ground-penetrating Radar Imagery

Errors associated with visual inspection and interpretation of radargrams often inhibits the intensive surveying of widespread areas using ground-penetrating radar (GPR). To automate the interpretive process, this paper presents an application of a fuzzy-neural network (F-NN) classifier for unsupervised clustering and classification of soil profile using GPR imagery. The classifier clusters and classifies soil profiles strips along a traverse based on common pattern similarities that can relate to physical features of the soil (e.g., number of horizons; depth, texture and structure of the horizons; and relative arrangement of the horizons, etc). This paper illustrates this classification procedure by its application on GPR data, both simulated and actual real-world. Results show that the procedure is able to classify the profile into zones that corresponded with those obtained by visual inspection and interpretation of radargrams. Results indicate that an F-NN model can supply real-time soil profile clustering and classification during field surveys

An Algorithm for Detecting the Principal Allotment among Fuzzy Clusters and Its Application as a Technique of Reduction of Analyzed Features Space Dimensionality

This paper describes a modification of a possibilistic clustering method based on the concept of allotment among fuzzy clusters. Basic ideas of the method are considered and the concept of a principal allotment among fuzzy clusters is introduced. The paper provides the description of the plan of the algorithm for detection principal allotment. An analysis of experimental results of the proposed algorithm’s application to the Tamura’s portrait data in comparison with the basic version of the algorithm and with the NERFCM-algorithm is carried out. A methodology of the algorithm’s application to the dimensionality reduction problem is outlined and the application of the methodology is illustrated on the example of Anderson’s Iris data in comparison with the result of principal component analysis. Preliminary conclusions are formulated also

Relational Demonic Fuzzy Refinement

We use relational algebra to define a refinement fuzzy order called demonic fuzzy refinement and also the associated fuzzy operators which are fuzzy demonic join (⊔fuz), fuzzy demonic meet (⊓fuz), and fuzzy demonic composition (□fuz). Our definitions and properties are illustrated by some examples using mathematica software (fuzzy logic)

Cluster validity for fuzzy criterion clustering

AbstractIn this paper, we define a validity measure for fuzzy criterion clustering which is a novel approach to fuzzy clustering that in addition to being non-distance-based, addresses the cluster validity problem. The model is then recast as a bilevel fuzzy criterion clustering problem. We propose an algorithm for this model that solves both the validity and clustering problems. Our approach is validated via some sample problems

Fuzzy autocatalytic set of fuzzy graph type-3 based on functional analysis theory

Fuzzy Autocatalytic Set (FACS) of fuzzy graph Type-3 is one of the newly capable graphs for a breakthrough of the relationship between fuzzy graph and autocatalytic set. It was successfully used to model an incineration process of a regional clinical waste in 2005. In this research, the mathematical structures of FACS and its properties were explored based on the suitable concept of fuzzy and non-fuzzy metric structure and fuzzy and non-fuzzy normed structure with the structure of its graph. In other words, the possible new structures of FACS have been explored via two new insights of its metric fuzziness and its normed fuzziness. Firstly, a fuzzy detour FT3-distance between vertices in FACS was investigated whereby a quasi-pseudo-FT3-metric fuzziness on FACS which depends on this distance was established, followed by an introduction to the concept FT3-cycle space of FACS as a vector space which is then proven as a normed space. These concepts have led to the visualization of the structure of FACS in a fuzzy norm, hence some propositions and theorems were established. In addition, the study on these structures of FACS was exploited, in particular the connection with functional analysis features and the application of these structures to the clinical incineration process

Fifty years of similarity relations: a survey of foundations and applications

On the occasion of the 50th anniversary of the publication of Zadeh's significant paper Similarity Relations and Fuzzy Orderings, an account of the development of similarity relations during this time will be given. Moreover, the main topics related to these fuzzy relations will be reviewed.Peer ReviewedPostprint (author's final draft

Security Risks to Petroleum Industry: An Innovative Modeling Technique Based on Novel Concepts of Complex Bipolar Fuzzy Information

In today’s world, the countries that have easy access to energy resources are economically strong, and thus, maintaining a better geopolitical position is important. Petroleum products such as gas and oil are currently the leading energy resources. Due to their excessive worth, the petroleum industries face many risks and security threats. Observing the nature of such problems, it is asserted that the complex bipolar fuzzy information is a better choice for modeling them. Keeping the said problem in mind, this article introduces the novel structure of complex bipolar fuzzy relation (CBFR), which is basically used to find out the relationships between complex bipolar fuzzy sets (CBFSs). Similarly, the types of CBFRs are also defined, which is helpful during the process of analyzing and interpreting the problem. Moreover, some useful results and interesting properties of the proposed structures are deliberated. Further, a new modeling technique based on the proposed structures is initiated, which is used to investigate the security risks to petroleum industries. Furthermore, a detailed comparative analysis proves the advantages and supremacy of CBFRs over other structures. Therefore, the results achieved by the proposed methods are substantially reliable, practical and complete

Application of fuzzy theory to pattern recognition

Piecewise curve approximation is used to describe boundaries of objects in pictures and waveforms. The method consists of linear and quadratic piecewise polynomial approximations in which the error must not exceed a predetermined cost threshold. A fuzzy Bayes model is used to determine if a breakpoint exists within an interval In or between intervals In and In+1 and to determine whether these intervals can be merged for data compaction reasons. In order to achieve these objectives a new fast algorithm has been proposed which gives good curve/object fitting. This algorithm uses a technique for generating generalized inverse matrices once an initial generalized inverse matrix has been determined. The continuity requirements at the breakpoints are relaxed such that the only requirement is that the data point for interval In-1 is the starting point for interval In. Results of computer experiments with graphic outlines and radar data are reported