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Shahn Majid - One of the best experts on this subject based on the ideXlab platform.
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q-Fuzzy Spheres and Quantum Differentials on B _ q [SU _2] and U _ q (su _2)
Letters in Mathematical Physics, 2011Co-Authors: Shahn MajidAbstract:We provide a new unified construction of the two-parameter Podleś two-spheres as characterised by a projector e with trace_ q ( e ) = 1 + λ. In our formulation the limit in which q → 1 with λ fixed is the Fuzzy sphere, while the limit λ → 0 with q fixed is the standard q -deformed sphere. We show further that the non-standard Podleś spheres arise geometrically as ‘constant time slices’ of the unit hyperboloid in q -Minkowski space viewed as the braided group B _ q [ SU _2]. Their localisations are then isomorphic to quotients of U _ q ( su _2) at fixed values of the q -Casimir precisely q -deforming the Fuzzy Case. We also use transmutation and twisting theory to introduce a $${C_q[G_\mathbb {C}]}$$ -covariant differential calculus on general B _ q [ G ] and U _ q ( g ), with Ω( B _ q [ SU _2]) and Ω( U _ q ( su _2) given in detail. To complete the picture, we show how the covariant calculus on the 3D bicrossproduct spacetime arises from Ω( C _ q [ SU _2]) prior to twisting.
Dagmar Markechová - One of the best experts on this subject based on the ideXlab platform.
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Rényi entropy of Fuzzy dynamical systems
Chaos Solitons & Fractals, 2019Co-Authors: Zahra Eslami Giski, Abolfazl Ebrahimzadeh, Dagmar MarkechováAbstract:Abstract The present paper is devoted to the study of Renyi entropy in the Fuzzy Case. We define the Renyi entropy of a Fuzzy partition and its conditional version and derive basic properties the suggested entropy measures. In particular, it was shown that the Renyi entropy of a Fuzzy partition is monotonically decreasing. Consequently, using the proposed concept of Renyi entropy, the notion of Renyi entropy of a Fuzzy dynamical system is introduced. Finally, it is proved that the Renyi entropy of a Fuzzy dynamical system is invariant under isomorphism of Fuzzy dynamical systems.
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Rényi Entropy and Rényi Divergence in the Intuitionistic Fuzzy Case
Tatra Mountains Mathematical Publications, 2018Co-Authors: Beloslav Riečan, Dagmar MarkechováAbstract:Abstract Our objective in this paper is to define and study the Rényi entropy and the Rényi divergence in the intuitionistic Fuzzy Case. We define the Rényi entropy of order of intuitionistic Fuzzy experiments (which are modeled by IF-partitions) and its conditional version and we examine their properties. It is shown that the suggested concepts are consistent, in the Case of the limit of q going to 1, with the Shannon entropy of IF-partitions. In addition, we introduce and study the concept of Rényi divergence in the intuitionistic Fuzzy Case. Specifically, relationships between the Rényi divergence and Kullback-Leibler divergence and between the Rényi divergence and the Rényi entropy in the intuitionistic Fuzzy Case are studied. The results are illustrated with several numerical examples.
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Logical Entropy and Logical Mutual Information of Experiments in the Intuitionistic Fuzzy Case
Entropy (Basel Switzerland), 2017Co-Authors: Dagmar Markechová, Beloslav RiečanAbstract:In this contribution, we introduce the concepts of logical entropy and logical mutual information of experiments in the intuitionistic Fuzzy Case, and study the basic properties of the suggested measures. Subsequently, by means of the suggested notion of logical entropy of an IF-partition, we define the logical entropy of an IF-dynamical system. It is shown that the logical entropy of IF-dynamical systems is invariant under isomorphism. Finally, an analogy of the Kolmogorov–Sinai theorem on generators for IF-dynamical systems is proved.
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Kullback-Leibler Divergence and Mutual Information of Experiments in the Fuzzy Case
Axioms, 2017Co-Authors: Dagmar MarkechováAbstract:The main aim of this contribution is to define the notions of Kullback-Leibler divergence and conditional mutual information in Fuzzy probability spaces and to derive the basic properties of the suggested measures. In particular, chain rules for mutual information of Fuzzy partitions and for Kullback-Leibler divergence with respect to Fuzzy P-measures are established. In addition, a convexity of Kullback-Leibler divergence and mutual information with respect to Fuzzy P-measures is studied
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The Lebesgue decomposition theorem for Fuzzy quantum spaces
Fuzzy Sets and Systems, 1994Co-Authors: Dagmar Markechová, Anna TirpákováAbstract:Abstract The present paper is devoted to signed measures of Fuzzy quantum spaces. The Lebesque decomposition theorem is proved for the Fuzzy Case.
Moti Schneider - One of the best experts on this subject based on the ideXlab platform.
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design issues in Fuzzy Case based reasoning
Fuzzy Sets and Systems, 2001Co-Authors: T Y Slonim, Moti SchneiderAbstract:This paper focuses on the aspect of Case representation in Case-based reasoning systems. We introduce an augmentation in which each Case is weighted individually over an independent set of properties. In addition, we encourage the use of Fuzzy-valued properties, and show their incorporation in this representation. Combining these two characteristics, we receive the framework for a versatile Fuzzy CBR system.
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Matching attributes in a Fuzzy Case based reasoning
18th International Conference of the North American Fuzzy Information Processing Society - NAFIPS (Cat. No.99TH8397), 1999Co-Authors: G. Dvir, G. Langholz, Moti SchneiderAbstract:This paper describes a Fuzzy expert Case-based reasoning system. The idea is to combine methodologies from both technologies to come up with a system that utilizes inference procedures with matching algorithms used by Case-based reasoning systems. We describe the system and, with examples, show how it can be utilized to solve problems in a more natural way than some of the existing Case-based reasoning systems.
Christopher Obrien - One of the best experts on this subject based on the ideXlab platform.
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vendor selection and order allocation using an integrated Fuzzy Case based reasoning and mathematical programming model
International Journal of Production Economics, 2009Co-Authors: F Faez, Seyed Hassan Ghodsypour, Christopher ObrienAbstract:A basic part of the logistic management of companies is the purchasing function, and the appropriate selection of vendors and allocating orders among them is one of the prime responsibilities of this function. Many conceptual and analytical models have been developed for addressing the vendor selection problem (VSP). This paper focuses on a Case-based reasoning (CBR) approach which is a recently recommended method for solving the VSP by making use of previous similar situations. Having applied Fuzzy set theory in the proposed model--as a novel innovation--the vague nature of some selection criteria has been incorporated by utilizing the linear membership function of Fuzzy type to quantify the vagueness in decision parameters. Moreover, a mixed integer programming model is employed to simultaneously consider suitable vendor selection and order allocation; due to the purchase situation of vendors derived from the CBR system, and with respect to such realistic constraints as meeting the buyer's demand, vendors' capacity, etc.
Juan M. Corchado - One of the best experts on this subject based on the ideXlab platform.
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Reducing the Memory Size of a Fuzzy Case-Based Reasoning System Applying Rough Set Techniques
IEEE Transactions on Systems Man and Cybernetics Part C (Applications and Reviews), 2007Co-Authors: Florentino Fernández-riverola, Fernando Díaz, Juan M. CorchadoAbstract:Early work on Case-based reasoning (CBR) reported in the literature shows the importance of soft computing techniques applied to different stages of the classical four-step CBR life cycle. This correspondence proposes a reduction technique based on rough sets theory capable of minimizing the Case memory by analyzing the contribution of each Case feature. Inspired by the application of the minimum description length principle, the method uses the granularity of the original data to compute the relevance of each attribute. The rough feature weighting and selection method is applied as a preprocessing step prior to the generation of a Fuzzy rule system, which is employed in the revision phase of the proposed CBR system. Experiments using real oceanographic data show that the rough sets reduction method maintains the accuracy of the employed Fuzzy rules, while reducing the computational effort needed in its generation and increasing the explanatory strength of the Fuzzy rules
