Affiliations: [a] Department of Mathematics and Statistics, Riphah International University, Hajj Complex, Islamabad, Pakistan
| [b] Department of Mathematics and Statistics, Bacha Khan University Charsadda, KPK Pakistan
| [c]
Islamabad Model College for Girls F-6/2, Islamabad, Pakistan
| [d]
Polytechnic University of Tirana, Department of Mathematical Engineering, Tirana, Albania
| [e] Department of Mathematics and Computer Science, Faculty of Natural Sciences University of Gjirokastra, Albania
Correspondence:
[*]
Corresponding author. Abbas Ali, Department of Mathematics and Statistics, Riphah International University, Hajj Complex I-14, Islamabad, Pakistan. E-mail: abbas.ali@riphah.edu.pk.
Abstract: The present paper aims to initiate the study of multi attribute group decision making in the presence of incomplete multi attribute and incomplete multi decision while making a decision with preferences in an incomplete information system. The concept of soft preference relation and soft dominance relation corresponding to decision attribute in incomplete multi criteria and incomplete multi decision information system is also presented. The discernibility matrix and discernibility function approach is proposed for decision attribute reduction to find all the reducts in an incomplete information system. A new technique of ranking the feasible alternative is proposed. Using the idea of soft dominance based rough sets, several uncertainty measures, such as approximate precision, rough degree, approximate quality and their mutual relationships are discussed in an incomplete information system. Finally the validity of these concepts are proved by applying these in solving multi-agent conflict analysis problems.
Keywords: Rough set, soft set, preference relation, incomplete information
