Matrix-based reduction approach for one-sided fuzzy three-way concept lattices

The Linguistic Concept’s Reduction Methods under Symmetric Linguistic-Evaluation Information

Knowledge reduction is a crucial topic in formal concept analysis. There always exists uncertain, symmetric linguistic-evaluation information in social life, which leads to high complexity in the process of knowledge representation. In order to overcome this problem, we are focused on studying the linguistic-concept-reduction methods in an uncertain environment with fuzzy linguistic information. Based on three-way decisions and an attribute-oriented concept lattice, we construct a fuzzy-object-induced three-way attribute-oriented linguistic (FOEAL) concept lattice, which provides complementary conceptual structures of a three-way concept lattice with symmetric linguistic-evaluation information. Through the granular concept of the FOEAL lattice, we present the corresponding linguistic concept granular consistent set and granular reduction. Then, we further employ the linguistic concept discernibility matrix and discernibility function to calculate the granular reduction set. A similar issue on information entropy is investigated to introduce a method of entropy reduction for the FOEAL lattice, and the relation between the linguistic concept granular reduction and entropy reduction is discussed. The efficiency of the proposed method is depicted by some examples and comparative analysis.

Construction of Fuzzy Linguistic Approximate Concept Lattice in an Incomplete Fuzzy Linguistic Formal Context

Uncertainty research is one of the critical problems in artificial intelligence. In an uncertain environment, a large quantity of information is expressed in linguistic values. Aiming at the missing linguistic-valued information, we first propose incomplete fuzzy linguistic formal context and then discuss the fuzzy linguistic approximate concept. Our proposal can describe the attributes of objects from two aspects simultaneously. One is an object's essential attributes, and another includes the essential and possible attributes. As a result, more object-related information can be obtained to reduce information loss effectively. We design a similarity metric for correcting the errors caused by the initial complement operation. We then construct a corresponding fuzzy linguistic approximate concept lattice for the task of approximate information retrieval. Finally, we illustrate the applicability and feasibility of the proposed approach with concrete examples, which clearly show that our approach can better deal with the linguistic-valued information in an uncertain environment.