Granular Space Reduction to a β

Multigranulation rough set is an extension of classical rough set, and optimistic multigranulation and pessimistic multigranulation are two special cases of it. β multigranulation rough set is a more generalized multigranulation rough set. In this paper, we first introduce fuzzy rough theory into β multigranulation rough set to construct a β multigranulation fuzzy rough set, which can be used to deal with continuous data; then some properties are discussed. Reduction is an important issue of multigranulation rough set, and an algorithm of granular space reduction to β multigranulation fuzzy rough set for preserving positive region is proposed. To test the algorithm, experiments are taken on five UCI data sets with different values of β. The results show the effectiveness of the proposed algorithm

Similarity Measure: An Intuitionistic Fuzzy Rough Set Approach

‎In fuzzy set theory‎, ‎the concept of a non-membership function and the hesitation margin were not considered while these two concepts have been included along with the membership function for intuitionistic fuzzy sets‎. ‎It is also to be noted that the intuitionistic fuzzy set is reflected as an extension of the fuzzy set accommodating both membership and non-membership functions together with a hesitation margin‎. ‎In the intuitionistic fuzzy set theory‎, ‎the sum of the membership function and the non-membership function is a value between 0 and 1‎. ‎In recent times‎, ‎intuitionistic fuzzy rough set theory has emerged as a powerful tool for dealing with imprecision and uncertain information in relational database theory‎. ‎Measures of similarity between fuzzy rough sets as well as intuitionistic fuzzy rough sets provide wide applications in real-life problems and that is why many researchers paid more attention to this concept‎. ‎Intuitionistic fuzzy rough set theory behaves like an excellent tool to tackle impreciseness or uncertainties‎. ‎In this paper‎, ‎we propose a new approach of similarity measure on an intuitionistic fuzzy rough set based on a set-theoretic approach‎. ‎The proposed measure is able to give an exact result‎. ‎In the application part‎, ‎we consider a real-life problem for selecting a fair play award-winning team in a cricket tournament and describe the algorithm‎

Intertemporal Choice of Fuzzy Soft Sets

This paper first merges two noteworthy aspects of choice. On the one hand, soft sets and fuzzy soft sets are popular models that have been largely applied to decision making problems, such as real estate valuation, medical diagnosis (glaucoma, prostate cancer, etc.), data mining, or international trade. They provide crisp or fuzzy parameterized descriptions of the universe of alternatives. On the other hand, in many decisions, costs and benefits occur at different points in time. This brings about intertemporal choices, which may involve an indefinitely large number of periods. However, the literature does not provide a model, let alone a solution, to the intertemporal problem when the alternatives are described by (fuzzy) parameterizations. In this paper, we propose a novel soft set inspired model that applies to the intertemporal framework, hence it fills an important gap in the development of fuzzy soft set theory. An algorithm allows the selection of the optimal option in intertemporal choice problems with an infinite time horizon. We illustrate its application with a numerical example involving alternative portfolios of projects that a public administration may undertake. This allows us to establish a pioneering intertemporal model of choice in the framework of extended fuzzy set theorie

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