Z-relation equation-based decision making

Abstract

Fuzzy relations were a main tool of fuzzy set theory in decision making, control and other fields. However, partial reliability of decision-relevant information is missed in these approaches. To deal with fuzziness and partial reliability of information, Zadeh introduced the concept of Z-number. The purpose of research presented in this paper is to develop an approach to decision making under Z-number-valued information. We introduce a definition of Z-number-valued relation (Z-relation) and some operations. The reason is to use Z-relations for evaluation of alternatives w.r.t. multiple criteria under imperfect information provided by a decision maker. In view of this, a Z-relation equation is formulated and some results on its solvability are given. These results are a basis of solving decision problems starting from multicriteria evaluation till final ranking of alternatives. The major conclusion is that this approach allows to deal with fusion of fuzzy and probabilistic information at a feasible level of computational complexity. The main limitation of the approach is difficulty of identification of a Z-relation. No expert knowledge (as it requires intensive involvement of experts) or data-driven information (when data quality is low) may exist. At the same time, computational complexity will grow with the high increase of a number of alternatives.A numerical example on decision making for project selection is considered to illustrate applicability of the study.