Preference Mining Using Neighborhood Rough Set Model on Two Universes

Preference mining plays an important role in e-commerce and video websites for enhancing user satisfaction and loyalty. Some classical methods are not available for the cold-start problem when the user or the item is new. In this paper, we propose a new model, called parametric neighborhood rough set on two universes (NRSTU), to describe the user and item data structures. Furthermore, the neighborhood lower approximation operator is used for defining the preference rules. Then, we provide the means for recommending items to users by using these rules. Finally, we give an experimental example to show the details of NRSTU-based preference mining for cold-start problem. The parameters of the model are also discussed. The experimental results show that the proposed method presents an effective solution for preference mining. In particular, NRSTU improves the recommendation accuracy by about 19% compared to the traditional method

Fuzzy-rough set models and fuzzy-rough data reduction

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

A Novel Rough Set Model in Generalized Single Valued Neutrosophic Approximation Spaces and Its Application

In this paper, we extend the rough set model on two different universes in intuitionistic fuzzy approximation spaces to a single-valued neutrosophic environment

Parameter Selection and Uncertainty Measurement for Variable Precision Probabilistic Rough Set

In this paper, we consider the problem of parameter selection and uncertainty measurement for a variable precision probabilistic rough set. Firstly, within the framework of the variable precision probabilistic rough set model, the relative discernibility of a variable precision rough set in probabilistic approximation space is discussed, and the conditions that make precision parameters α discernible in a variable precision probabilistic rough set are put forward. Concurrently, we consider the lack of predictability of precision parameters in a variable precision probabilistic rough set, and we propose a systematic threshold selection method based on relative discernibility of sets, using the concept of relative discernibility in probabilistic approximation space. Furthermore, a numerical example is applied to test the validity of the proposed method in this paper. Secondly, we discuss the problem of uncertainty measurement for the variable precision probabilistic rough set. The concept of classical fuzzy entropy is introduced into probabilistic approximation space, and the uncertain information that comes from approximation space and the approximated objects is fully considered. Then, an axiomatic approach is established for uncertainty measurement in a variable precision probabilistic rough set, and several related interesting properties are also discussed. Thirdly, we study the attribute reduction for the variable precision probabilistic rough set. The definition of reduction and its characteristic theorems are given for the variable precision probabilistic rough set. The main contribution of this paper is twofold. One is to propose a method of parameter selection for a variable precision probabilistic rough set. Another is to present a new approach to measurement uncertainty and the method of attribute reduction for a variable precision probabilistic rough set

Explaining Low Entropy: An Examination of the Efficacy of Cosmological Explanations for the Second Law of Thermodynamics

Given a low-entropy past state, statistical mechanics purportedly explains the Second Law of Thermodynamics. Modern cosmology furnishes this account with a low-entropy early universe. However, what explains this past state? One approach simply postulates this initial condition as a contingent fact or law. Alternatively, one can seek a dynamical solution. This paper assesses the explanatory efficacy some popular proposals. In particular, Carroll's multiverse hypothesis is critiqued and shown to be subject to similar problems faced by Boltzmann

Quantum Computation and Many Worlds

An Everett (`Many Worlds') interpretation of quantum mechanics due to Saunders and Zurek is presented in detail. This is used to give a physical description of the process of a quantum computation. Objections to such an understanding are discussed.Comment: This paper has been superceded by arXiv:0802.2504v1 [quant-ph