Fuzzy-probabilistic aggregations in the discrete covering problem

Abstract

In this paper, a new criterion is introduced for the discrete covering problem. In this criterion, the a priori information represented by a fuzzy measure and a misbelief distribution on alternatives are condensed by aggregation instruments. Using the Dempster–Shafer belief structure and representations of fuzzy measures through associated probabilities, several variants of a new criterion for the discrete covering problem are constructed based on aggregations by two types of the most typical value, namely, monotone expectation and fuzzy expected value. A bicriterial problem is obtained using one of the variants of the new criterion and the criterion of average price minimisation. The example on the application of a new criterion is presented, where the possibility distribution on the optimal choice of the candidates (alternatives) is represented by expert valuations.

Keywords:

• minimal fuzzy covering
• fuzzy measure
• associated probabilities
• average misbelief criterion
• most typical value
• Dempster–Shafer belief structure

2000 Mathematics Subject Classification::

• 90C70
• 28E10

Acknowledgements

The designated project has been fulfilled by financial support of the Georgian National Science Foundation (Grant No. GNSF/ST08/1-361). Any idea in this work is of the author and may not represent the opinion of the Georgian National Science Foundation itself.