245 research outputs found

    Data granulation by the principles of uncertainty

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    Researches in granular modeling produced a variety of mathematical models, such as intervals, (higher-order) fuzzy sets, rough sets, and shadowed sets, which are all suitable to characterize the so-called information granules. Modeling of the input data uncertainty is recognized as a crucial aspect in information granulation. Moreover, the uncertainty is a well-studied concept in many mathematical settings, such as those of probability theory, fuzzy set theory, and possibility theory. This fact suggests that an appropriate quantification of the uncertainty expressed by the information granule model could be used to define an invariant property, to be exploited in practical situations of information granulation. In this perspective, a procedure of information granulation is effective if the uncertainty conveyed by the synthesized information granule is in a monotonically increasing relation with the uncertainty of the input data. In this paper, we present a data granulation framework that elaborates over the principles of uncertainty introduced by Klir. Being the uncertainty a mesoscopic descriptor of systems and data, it is possible to apply such principles regardless of the input data type and the specific mathematical setting adopted for the information granules. The proposed framework is conceived (i) to offer a guideline for the synthesis of information granules and (ii) to build a groundwork to compare and quantitatively judge over different data granulation procedures. To provide a suitable case study, we introduce a new data granulation technique based on the minimum sum of distances, which is designed to generate type-2 fuzzy sets. We analyze the procedure by performing different experiments on two distinct data types: feature vectors and labeled graphs. Results show that the uncertainty of the input data is suitably conveyed by the generated type-2 fuzzy set models.Comment: 16 pages, 9 figures, 52 reference

    Fuzzy-rough set models and fuzzy-rough data reduction

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    Rough set theory is a powerful tool to analysis the information systems. Fuzzy rough set is introduced as a fuzzy generalization of rough sets. This paper reviewed the most important contributions to the rough set theory, fuzzy rough set theory and their applications. In many real world situations, some of the attribute values for an object may be in the set-valued form. In this paper, to handle this problem, we present a more general approach to the fuzzification of rough sets. Specially, we define a broad family of fuzzy rough sets. This paper presents a new development for the rough set theory by incorporating the classical rough set theory and the interval-valued fuzzy sets. The proposed methods are illustrated by an numerical example on the real case

    Quantification of R-Fuzzy sets

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    The main aim of this paper is to connect R-Fuzzy sets and type-2 fuzzy sets, so as to provide a practical means to express complex uncertainty without the associated difficulty of a type-2 fuzzy set. The paper puts forward a significance measure, to provide a means for understanding the importance of the membership values contained within an R-fuzzy set. The pairing of an R-fuzzy set and the significance measure allows for an intermediary approach to that of a type-2 fuzzy set. By inspecting the returned significance degree of a particular membership value, one is able to ascertain its true significance in relation, relative to other encapsulated membership values. An R-fuzzy set coupled with the proposed significance measure allows for a type-2 fuzzy equivalence, an intermediary, all the while retaining the underlying sentiment of individual and general perspectives, and with the adage of a significantly reduced computational burden. Several human based perception examples are presented, wherein the significance degree is implemented, from which a higher level of detail can be garnered. The results demonstrate that the proposed research method combines the high capacity in uncertainty representation of type-2 fuzzy sets, together with the simplicity and objectiveness of type-1 fuzzy sets. This in turn provides a practical means for problem domains where a type-2 fuzzy set is preferred but difficult to construct due to the subjective type-2 fuzzy membership

    Multistage feature selection methods for data classification

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    In data analysis process, a good decision can be made with the assistance of several sub-processes and methods. The most common processes are feature selection and classification processes. Various methods and processes have been proposed to solve many issues such as low classification accuracy, and long processing time faced by the decision-makers. The analysis process becomes more complicated especially when dealing with complex datasets that consist of large and problematic datasets. One of the solutions that can be used is by employing an effective feature selection method to reduce the data processing time, decrease the used memory space, and increase the accuracy of decisions. However, not all the existing methods are capable of dealing with these issues. The aim of this research was to assist the classifier in giving a better performance when dealing with problematic datasets by generating optimised attribute set. The proposed method comprised two stages of feature selection processes, that employed correlation-based feature selection method using a best first search algorithm (CFS-BFS) and as well as a soft set and rough set parameter selection method (SSRS). CFS-BFS is used to eliminate uncorrelated attributes in a dataset meanwhile SSRS was utilized to manage any problematic values such as uncertainty in a dataset. Several bench-marking feature selection methods such as classifier subset evaluation (CSE) and principle component analysis (PCA) and different classifiers such as support vector machine (SVM) and neural network (NN) were used to validate the obtained results. ANOVA and T-test were also conducted to verify the obtained results. The obtained averages for two experimentalworks have proven that the proposed method equally matched the performance of other benchmarking methods in terms of assisting the classifier in achieving high classification performance for complex datasets. The obtained average for another experimental work has shown that the proposed work has outperformed the other benchmarking methods. In conclusion, the proposed method is significant to be used as an alternative feature selection method and able to assist the classifiers in achieving better accuracy in the classification process especially when dealing with problematic datasets

    Algebraic Structures of Neutrosophic Triplets, Neutrosophic Duplets, or Neutrosophic Multisets

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    Neutrosophy (1995) is a new branch of philosophy that studies triads of the form (, , ), where is an entity {i.e. element, concept, idea, theory, logical proposition, etc.}, is the opposite of , while is the neutral (or indeterminate) between them, i.e., neither nor .Based on neutrosophy, the neutrosophic triplets were founded, which have a similar form (x, neut(x), anti(x)), that satisfy several axioms, for each element x in a given set.This collective book presents original research papers by many neutrosophic researchers from around the world, that report on the state-of-the-art and recent advancements of neutrosophic triplets, neutrosophic duplets, neutrosophic multisets and their algebraic structures – that have been defined recently in 2016 but have gained interest from world researchers. Connections between classical algebraic structures and neutrosophic triplet / duplet / multiset structures are also studied. And numerous neutrosophic applications in various fields, such as: multi-criteria decision making, image segmentation, medical diagnosis, fault diagnosis, clustering data, neutrosophic probability, human resource management, strategic planning, forecasting model, multi-granulation, supplier selection problems, typhoon disaster evaluation, skin lesson detection, mining algorithm for big data analysis, etc

    Uncertain Multi-Criteria Optimization Problems

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    Most real-world search and optimization problems naturally involve multiple criteria as objectives. Generally, symmetry, asymmetry, and anti-symmetry are basic characteristics of binary relationships used when modeling optimization problems. Moreover, the notion of symmetry has appeared in many articles about uncertainty theories that are employed in multi-criteria problems. Different solutions may produce trade-offs (conflicting scenarios) among different objectives. A better solution with respect to one objective may compromise other objectives. There are various factors that need to be considered to address the problems in multidisciplinary research, which is critical for the overall sustainability of human development and activity. In this regard, in recent decades, decision-making theory has been the subject of intense research activities due to its wide applications in different areas. The decision-making theory approach has become an important means to provide real-time solutions to uncertainty problems. Theories such as probability theory, fuzzy set theory, type-2 fuzzy set theory, rough set, and uncertainty theory, available in the existing literature, deal with such uncertainties. Nevertheless, the uncertain multi-criteria characteristics in such problems have not yet been explored in depth, and there is much left to be achieved in this direction. Hence, different mathematical models of real-life multi-criteria optimization problems can be developed in various uncertain frameworks with special emphasis on optimization problems

    Neutrosophic Multi-Criteria Decision Making

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    The notion of a neutrosophic quadruple BCK/BCI-number is considered in the first article (“Neutrosophic Quadruple BCK/BCI-Algebras”, by Young Bae Jun, Seok-Zun Song, Florentin Smarandache, and Hashem Bordbar), and a neutrosophic quadruple BCK/BCI-algebra, which consists of neutrosophic quadruple BCK/BCI-numbers, is constructed. Several properties are investigated, and a (positive implicative) ideal in a neutrosophic quadruple BCK-algebra and a closed ideal in a neutrosophic quadruple BCI-algebra are studied. Given subsets A and B of a BCK/BCI-algebra, the set NQ(A,B), which consists of neutrosophic quadruple BCK/BCInumbers with a condition, is established. Conditions for the set NQ(A,B) to be a (positive implicative) ideal of a neutrosophic quadruple BCK-algebra are provided, and conditions for the set NQ(A,B) to be a (closed) ideal of a neutrosophic quadruple BCI-algebra are given. Techniques for the order of preference by similarity to ideal solution (TOPSIS) and elimination and choice translating reality (ELECTRE) are widely used methods to solve multicriteria decision-making problems. In the second research article (“Decision-Making with Bipolar Neutrosophic TOPSIS and Bipolar Neutrosophic ELECTRE-I”), Muhammad Akram, Shumaiza, and Florentin Smarandache present the bipolar neutrosophic TOPSIS method and the bipolar neutrosophic ELECTRE-I method to solve such problems. The authors use the revised closeness degree to rank the alternatives in the bipolar neutrosophic TOPSIS method. The researchers describe the bipolar neutrosophic TOPSIS method and the bipolar neutrosophic ELECTRE-I method by flow charts, also solving numerical examples by the proposed methods and providing a comparison of these methods. In the third article (“Interval Neutrosophic Sets with Applications in BCK/BCI-Algebra”, by Young Bae Jun, Seon Jeong Kim and Florentin Smarandache), the notion of (T(i,j),I(k,l),F(m,n))-interval neutrosophic subalgebra in BCK/BCI-algebra is introduced for i,j,k,l,m,n infoNumber 1,2,3,4, and properties and relations are investigated. The notion of interval neutrosophic length of an interval neutrosophic set is also introduced, and the related properties are investigated
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