Research On Dominance Relaion In Incomplete Information System

Rough set theory, proposed by Pawlak, is an effective mathematical toolto conceptualize and analyze various types of data. Classical rough set theoryis based on the indiscernibility relation, and mainly studies the completeinformation system, that is, all attribute values in the information system areknown and single. But in many practical issues, the information system isalways incomplete, i.e., some attribute values may be unknown. Furthermore,one important characteristic of multi-attribute decision making is thatinformation is always preference ordering. According to the influence ofdecision maker's preference, there exists a dominance relation among attributevalues. Therefore, in order to process incomplete information systems withpreference-ordered domains (scales), it is necessary to extend the classicalrough set theory.The unknown attribute values in incomplete informations can besummarized as two categories: missing and absent. The unknown attributevalues in incomplete informations, in which all unknown attribute values areconsidered as missing, can be represented by using a set or interval of allpossible values of each attribute, i.e., the incomplete information system ischanged into the set-valued information system or the interval-valuedinformation system. Set-valued information systems and interval-valuedinformation systems are generalized models of single-valued informationsystems. Consequently, to stuty dominance relations in set-valued informationsystems and interval-valued information systems has more significance toexpand the application of rough set.In this thesis, based on the rough set theory, and with a main clue that isresearching the dominance relation, we analyze some key issues in detail,such as constructing extended rough set model, studying sorting-objectsapproach, and discussing the attribute reduction method. The maincontributions are listed as follows:Through analyzing the limitations of four existing dominance relations indisjunctive set-valued information systems, a variable precision dominancerelation is proposed and a disjunctive set-valued ordered information system based on the variable precision dominance relation is defined. It is anextension of the classical rough set theory. Then, an approach for sortingobjects is introduced to the disjunctive set-valued ordered informationsystems, which is based on the whole dominance degree of an object in aninformation system. Furthermore, a discernibility matrix is defined and anattribute reduction method by using the discernibility matrix is developed.Four dominance relations are introduced to interval-valued informationsystem, the important properties and relationships among the four dominancerelations are analyzed. Furthermore, based on limitations of the fourdominance relations, a dominance relation—α-dominance relation isproposed. And then, an extended rough set model based onα-dominancerelation is defined. Finally, an attribute reduction method with respect to theα-dominance relation in interval-valued information system is presented.