Multi-adjoint fuzzy rough sets: Definition, properties and attribute selection

Abstract

This paper introduces a flexible extension of rough set theory: multi-adjoint fuzzy rough sets, in which a family of adjoint pairs are considered to compute the lower and upper approximations. This new setting increases the number of applications in which rough set theory can be used. An important feature of the presented framework is that the user may represent explicit preferences among the objects in a decision system, by associating a particular adjoint triple with any pair of objects. Moreover, we verify mathematical properties of the model, study its relationships to multiadjoint property-oriented concept lattices and discuss attribute selection in this framework.

Multi‐adjoint intuitionistic fuzzy rough sets

“…Assume the poset has the top element . Let , Comelis et al [12] first introduced a fuzzy generalisation B ‐indiscernibility relation. That is a P ‐fuzzy tolerance relation: , and R B satisfies reflexivity property, ; and symmetric property, .…”

“…These models greatly enriched the theory of concept lattice. 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.…”

An intuitionistic fuzzy graded covering rough set

“…In fuzzy rough sets, a fuzzy similarity relation is employed to describe the degree of similarity between two objects, instead of the equivalence relation used in the classical rough set model. Many extended versions and relative applications have been developed widely apply the fuzzy rough set method [11][12][13]44,50] fuzzy covering rough sets, Li et al [27] constructed two pairs of generalized lower and upper fuzzy rough approximation operators using an implicator and a triangular norm based on a fuzzy covering of a universe of discourse. Feng et al [17] studied the reduction of a fuzzy covering and the fusion of multi-fuzzy covering systems based on evidence theory and rough set theory.…”

On the use of thresholds in multi-adjoint concept lattices

“…This philosophy has successfully been applied to fuzzy rough sets [9,10,27], fuzzy relation equations [12] and fuzzy logic programming [19,31]. Adjoint triples (see [7] for more details) are used as basic operators to carry out the computations in this framework and so a general non-commutative environment which allows different degrees of preference related to the set of objects and attributes can easily be established.…”