Variable consistency and variable precision models for dominance-based fuzzy rough set analysis of possibilistic information systems

Abstract

The dominance-based fuzzy rough set approach (DFRSA) is a theoretical framework that can deal with multi-criteria decision analysis of possibilistic information systems. While a set of comprehensive decision rules can be induced from a possibilistic information system by using DFRSA, generation of several intuitively justified rules is sometimes blocked by objects that only partially satisfy the antecedents of the rules. In this paper, we use the variable consistency models and variable precision models of DFRSA to cope with the problem. The models admit rules that are not satisfied by all objects. It is only required that the proportion of objects satisfying the rules must be above a threshold called a consistency level or a precision level. In the presented models, the proportion of objects is represented as a relative cardinality of a fuzzy set with respect to another fuzzy set. We investigate three types of models based on different definitions of fuzzy cardinalities including -counts, possibilistic cardinalities, and probabilistic cardinalities; and the consistency levels or precision levels corresponding to the three types of models are, respectively, scalars, fuzzy numbers, and random variables.

Keywords:

• dominance-based fuzzy rough set approach
• preference-ordered possibilistic information system
• multi-criteria decision analysis
• variable consistency DFRSA
• variable precision DFRSA
• fuzzy cardinality

Acknowledgments

This work was partially supported by the National Science Council of Taiwan under grants NSC 98-2221-E-001-013-MY3 and NSC 100-2410-H-346-002. We wish to thank the guest editors and three anonymous referees for their constructive suggestions.

Notes

This is an extended version of (Fan et al. 2011b).

Also called knowledge representation systems, data tables, or attribute-value systems

For the properties of these operations, see a standard reference on fuzzy logic, such as Hájek (1998)

That is, if and if for any .

In this section, we use the notations , and introduced in Delgado et al. (2002) to denote fuzzy cardinalities. Unfortunately, it is not explicitly mentioned in Delgado et al. (2002) what the acronyms stand for.

A core of a fuzzy set is defined as .