Soft dominance based multigranulation decision theoretic rough sets and their applications in conflict problems
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Soft dominance based multigranulation decision theoretic rough sets and their applications in conflict problems Noor Rehman1 · Abbas Ali2 · Kostaq Hila3
© Springer Nature B.V. 2020
Abstract The extension of rough set model is a crucial and vast research direction in rough set the‑ ory. Meanwhile decision making can be considered as a mental process in which human beings make a choice among several alternatives. However, with the increasing complex‑ ity of real decision making problems, the decision makers frequently face the challenge of characterizing their preferences in an uncertain context. In the present paper, we ini‑ tiate a multi attribute group decision making problem in the presence of multi attribute and multi decision in decision making with preferences. We further present the concept of soft preference relation and soft dominance relation corresponding to decision attribute in the multi criteria and multi decision information system. Further we put forward the idea of two types of optimistic/pessimistic multigranulation (soft dominance based optimistic/ pessimistic multigranulation decision theoretic) approximations and their applications in solving a multi agent conflict analysis decision problem. The proposed method addresses the limitations of the Pawlak model and Sun’s conflict analysis model and thus improve these models. Finally, the results on labor management negotiation problems show that the proposed algorithms are more effective and efficient for feasible consensus strategy when compared with other techniques. Keywords Rough set · Soft set · Preference relation · Decision theoretic · Soft preference relation
* Kostaq Hila [email protected]
Noor Rehman [email protected]; [email protected]
Abbas Ali [email protected] 1
Department of Mathematics and Statistics, Bacha Khan University Charsadda, Charsadda, KPK, Pakistan
2
Department of Mathematics and Statistics, Riphah International University, Haji Complex I‑14, Islamabad, Pakistan
3
Department of Mathematical Engineering, Polytechnic University of Tirana, Tirana, Albania
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N. Rehman et al.
1 Introduction Most of the theoretical work on decision making under uncertainty takes a certain type of the individual behavior as a primitive and the determines the preference functional that represents the behavior. In general the individual’s behavior is his/her private and profes‑ sional life. The critical problem of decision making under uncertainty is, how to deal with the individual’s behavior and the reach to final optimal objective(s). However, because the complexity, inaccuracy and unstructured of the decision making problems under uncer‑ tainty, and the limitation of knowledge and cognitive for individual decision maker, then it is difficult to acquire a reasonable and scientific decision making with only single deci‑ sion maker under uncertainty in reality. In order to get a reasonable and reliable optimal result, several experts come from different fields with different specialities a
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