Three-way decision and granular computing

A trisecting-and-acting model explains three-way decisions (3WD) in terms of two basic tasks. One task is to divide a universal set into three pair-wise disjoint regions called a trisection or a tri-partition of the universal set. The other task is to act upon objects in one or more regions by developing appropriate strategies. 3WD are a class of effective ways and heuristics commonly used in human problem solving and information processing. We argue that 3WD are built on solid cognitive foundations and offer cognitive advantages and benefits. We demonstrate the flexibility and general applicability of 3WD by using examples from across many fields and disciplines.

Three-Way Decisions and Cognitive Computing

Three-way cognitive concept learning via multi-granularity

Incomplete decision contexts: Approximate concept construction, rule acquisition and knowledge reduction

Three-way granular computing, rough sets, and formal concept analysis

The model of three-way concept lattices, a novel model for widely used three-way decisions, is an extension of classical concept lattices in formal concept analysis. This paper systematically analyses the connections between two types of three-way concept lattices (object-induced and attribute-induced three-way concept lattices) and classical concept lattices. The relationships are discussed from the viewpoints of elements, sets and orders, respectively. Furthermore, the necessary and sufficient conditions used to construct three-way concepts on the basis of classical concepts are proved, the algorithms building three-way concept lattices on the basis of classical concept lattices are presented. The obtained results are finally demonstrated and verified by examples.

The connections between three-way and classical concept lattices

Three-way concept analysis is a newly proposed area of formal concept analysis from which one can obtain both the inclusion decision and the exclusion decision. In general, given a context, some attributes may not be essential in three-way concept analysis, such as forming three-way concept lattice. So in this paper, we study the attribute reductions of three-way concept lattices in order to make the data easily be understood. Firstly, based on different criteria generated from object-induced three-way concept (OE-concept), four kinds of attribute reductions are proposed. The four reductions together embody different characteristics of a formal context and can be used in different occasions. Secondly, we discuss their relationships, including their advantages and disadvantages and the relationships among consistent sets and among the cores. Thirdly, based on attribute-induced three-way concept (AE-concept), we also give four attribute-induced three-way attribute reductions and discuss their relationships. Finally, the approaches to computing these attribute reductions are presented and the obtained results are demonstrated and verified by an empirical case. In this paper, we systematically investigate the attribute reductions of three-way concept lattices which enriches the study of formal concept analysis.

The attribute reductions of three-way concept lattices

In this paper, a novel concept formation and novel concept lattices are developed with respect to a binary information table to support three-way decisions. The three-way operators and their inverse are defined and their properties are given. Based on these operators, two types of three-way concepts are defined and the corresponding three-way concept lattices are constructed. Three-way concept lattices provide a new kind of model to make three-way decisions.

Three-Way Formal Concept Analysis

One of the key problems of knowledge discovery is knowledge reduction. Rough set theory and the theory of concept lattices are two efficient tools for knowledge discovery. Attribute reduction based on rough set theory and the theory of concept lattices both have been researched. Since an information system, the data description of rough set theory, and a formal context, the data description of concept lattice theory, can be taken as the other one, the attribute reduction based on the same data base can be studied from these two perspectives, and researching their relation is significant. This paper mainly discusses the relation between concept lattice reduction and rough set reduction based on classical formal context, which will be meaningful for the relation research between these two theories, and for their knowledge discovery.

Ling Wei

Papers

The connections between three-way and classical concept lattices

The attribute reductions of three-way concept lattices

Three-Way Formal Concept Analysis

Relation between concept lattice reduction and rough set reduction

Three-way dual concept analysis