A comprehensive study of implicator-conjunctor based and noise-tolerant fuzzy rough sets: definitions, properties and robustness analysis

© 2014 Elsevier B.V. Both rough and fuzzy set theories offer interesting tools for dealing with imperfect data: while the former allows us to work with uncertain and incomplete information, the latter provides a formal setting for vague concepts. The two theories are highly compatible, and since the late 1980s many researchers have studied their hybridization. In this paper, we critically evaluate most relevant fuzzy rough set models proposed in the literature. To this end, we establish a formally correct and unified mathematical framework for them. Both implicator-conjunctor-based definitions and noise-tolerant models are studied. We evaluate these models on two different fronts: firstly, we discuss which properties of the original rough set model can be maintained and secondly, we examine how robust they are against both class and attribute noise. By highlighting the benefits and drawbacks of the different fuzzy rough set models, this study appears a necessary first step to propose and develop new models in future research.Lynn D’eer has been supported by the Ghent University Special Research Fund, Chris Cornelis was partially supported by the Spanish Ministry of Science and Technology under the project TIN2011-28488 and the Andalusian Research Plans P11-TIC-7765 and P10-TIC-6858, and by project PYR-2014-8 of the Genil Program of CEI BioTic GRANADA and Lluis Godo has been partially supported by the Spanish MINECO project EdeTRI TIN2012-39348-C02-01Peer Reviewe

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

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

Multiverse Predictions for Habitability: Fraction of Planets that Develop Life

In a multiverse context, determining the probability of being in our particular universe depends on estimating its overall habitability compared to other universes with different values of the fundamental constants. One of the most important factors in determining this is the fraction of planets that actually develop life, and how this depends on planetary conditions. Many proposed possibilities for this are incompatible with the multiverse: if the emergence of life depends on the lifetime of its host star, the size of the habitable planet, or the amount of material processed, the chances of being in our universe would be very low. If the emergence of life depends on the entropy absorbed by the planet, however, our position in this universe is very natural. Several proposed models for the subsequent development of life, including the hard step model and several planetary oxygenation models, are also shown to be incompatible with the multiverse. If any of these are observed to play a large role in determining the distribution of life throughout our universe, the~multiverse hypothesis will be ruled out to high significance.Comment: 29 pages, 6 figures, v2: matches published vresio

Observational Bounds on Cosmic Doomsday

Recently it was found, in a broad class of models, that the dark energy density may change its sign during the evolution of the universe. This may lead to a global collapse of the universe within the time t_c ~ 10^{10}-10^{11} years. Our goal is to find what bounds on the future lifetime of the universe can be placed by the next generation of cosmological observations. As an example, we investigate the simplest model of dark energy with a linear potential V(\phi) =V_0(1+\alpha\phi). This model can describe the present stage of acceleration of the universe if \alpha is small enough. However, eventually the field \phi rolls down, V(\phi) becomes negative, and the universe collapses. The existing observational data indicate that the universe described by this model will collapse not earlier than t_c > 10 billion years from the present moment. We show that the data from SNAP and Planck satellites may extend the bound on the "doomsday" time to t_c > 40 billion years at the 95% confidence level.Comment: 11 pages, 6 figures, revtex