Abstract
The combination of fuzzy information systems (ISs) and multi-adjoint theory has become a hot issue in the study and applications of artificial intelligence. An intuitionistic fuzzy set has more flexible and practical ability to represent information and is better in dealing with ambiguity and uncertainty when compared with the fuzzy set. Multi- adjoint intuitionistic fuzzy rough sets are constructed by using adjoint triples under intuitionistic fuzzy IS. For this purpose, the authors propose intuitionistic fuzzy indiscernibility relation and multi-adjoint approximation operators. The basic results in the multi-adjoint fuzzy rough set model are generalised to multi-adjoint intuitionistic fuzzy rough set model. The analogous results are also verified. After that, a novel approach of attribute reduction is proposed. First, a kind of approximate reduction to keep the dependence of the positive region to a degree α is formulated. Second, they propose a heuristic algorithm to compute the attribute reduction. At last, they employ an example to describe the processing of the algorithm.
Highlights
The rough set was originated by Pawlak [1]
An example is employed to illustrate the processing of the algorithm
Considering the context U, U, RB, τ, τ maps all pairs of elements in U × U to particular adjoint triples in the context above. ∀g ∈ F(U), the multi-adjoint upper and lower approximation operators denoted by g ↑ π and g ↑ N, respectively, are defined as follows: J
Summary
The rough set was originated by Pawlak [1]. As an important generalisation of the classical set theory, it has been a powerful mathematical tool for modelling and handing incomplete information in relational databases, and widely used in machine learning, data mining etc. Combined with the rough set theory, Comelis et al [12] introduced multi-adjoint fuzzy rough set Those models increase the flexibility of the approximation operators in the considered data set. By using the operators formed by an adjoint triple, we define the multi-adjoint IF rough set model, which can increase the flexibility of handling uncertainty in a very effective manner by combining two effective tools, i.e. adjoint triple theory and IF set theory. This model has retained the main features of adjoint triples, that is, explicit preferences among the objects may be represented by using different adjoint triples.
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