Bipolar method and its modifications

Bipolar is one of the multiple criteria decision analysis methods, proposed by Konarzewska-Gubała (in Archiwum Automatyki i Telemechaniki 32(4):289–300, 1987). The main feature of the method is that alternatives are not compared directly with each other, but they are confronted to the two reference sets of objects: desirable and non-acceptable. Practical application of the method revealed its shortcomings, therefore improvements of the method were desirable. The aim of the paper is to formulate some modifications of the classical Bipolar approach and consider a case where reference sets are numerous. Unified Bipolar procedure which contains classical Bipolar method as well as the modifications described in the paper is given. Numerical illustrations of the modifications and unified approach are also presented

Grey Numbers in Multiple Criteria Decision Analysis and Conflict Resolution

Definitions of grey numbers are adapted for incorporation into Multiple Criteria Decision Analysis and the Graph Model for Conflict Resolution in order to capture uncertainty in decision making. The main objective is to design improved methods for dealing with decision problems under uncertainty, characterized by limited input data and uncertain preferences of decision makers. A literature review is carried out in order to understand the problems of representing uncertainty using grey numbers within two key decision making contexts: comparing alternative solutions within an multiple criteria decision analysis framework, and deciding upon meaningful courses of action by decision makers involved in a conflict. Then two methodologies that rely on grey numbers to represent uncertain information are provided, and relevant definitions, procedures, and solution concepts are presented