Fuzzy multisets and their variants
Mahdi Mollaei Arani
Abstract
This paper, considers the fuzzy topological subsets, fuzzy topological spaces and introduces a novel concept of fuzzy Hausdorff space and fuzzy manifold space in this regards. Based on these concepts, we present a concept of fuzzy metric Hausdorff spaces and fuzzy metric manifold spaces via the notations ...
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This paper, considers the fuzzy topological subsets, fuzzy topological spaces and introduces a novel concept of fuzzy Hausdorff space and fuzzy manifold space in this regards. Based on these concepts, we present a concept of fuzzy metric Hausdorff spaces and fuzzy metric manifold spaces via the notations of KM-fuzzy metric spaces. This study, generalises the concept of fuzzy metric space to union and product of fuzzy metric spaces in classical logic and in this regard investigates the some product of fuzzy metric fuzzy manifold spaces. We apply the notation of valued-level subsets and make a relation between of topological space, Husdorff space, manifold space and fuzzy topological space, fuzzy Husdorff space and fuzzy manifold space. In final, we extended the fuzzy topological space, fuzzy Husdorff space and fuzzy manifold space to fuzzy metric topological space, fuzzy metric Husdorff space and fuzzy metric manifold space Indeed, this study analyses the notation of fuzzy metric manifold based on valued-level subset.
Fuzzy multisets and their variants
Mahmut Dirik
Abstract
Due to developments in printing technology, the number of counterfeit banknotes is increasing every year. Finding an effective method to detect counterfeit banknotes is an important task in business. Finding a reliable method to detect counterfeit banknotes is a crucial challenge in the world of economic ...
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Due to developments in printing technology, the number of counterfeit banknotes is increasing every year. Finding an effective method to detect counterfeit banknotes is an important task in business. Finding a reliable method to detect counterfeit banknotes is a crucial challenge in the world of economic transactions. Due to technological development, counterfeit banknotes may pass through the counterfeit banknote detection system based on physical and chemical properties undetected. In this study, an intelligent counterfeit banknote detection system based on a Genetic Fuzzy System (GFS) is proposed to detect counterfeit banknotes efficiently. GFS is a hybrid system that uses a network architecture to fine-tune the membership functions of a fuzzy inference system. The learning algorithms Fuzzy Classification, Genetic Fuzzy Classification, ANFIS Classification, and Genetic ANFIS Classification were applied to the dataset in the UCI machine learning repository to detect the authenticity of banknotes. The developed model was evaluated based on Accuracy (ACC), Mean Absolute Error (MAE), Root Mean Square Error (RMSE), Error Mean, Error STD, and confusion matrix. The experimental results and statistical analysis showed that the classification performance of the proposed model was evaluated as follows: Fuzzy = 97.64%, GA_Fuzzy = 98.60%, ANFIS = 80.83%, GA_ANFIS = 97.72% accuracy (ACC). This shows the significant potential of the proposed GFS models for fraud detection.
