The Construction of a Vague Fuzzy Measure Through L1 Parameter Optimization
Abstract
This paper presents a method to construct an aggregation function, reflecting a complex set of initial user preferences, which can be used in the framework of multi-criteria decision making. We consider problems where the decision maker can provide information about the importance and interactions between criteria, as well as a desired portion of criteria to be satisfied. The proposed aggregation process is a vague Choquet integral whose parameters are constructed in two steps. First, we solve a convex constrained L1 optimization problem to obtain a fuzzy measure reflecting the importances and interactions between the criteria. Then the measure is transformed by a monotonic mapping to include vague information on what portion of criteria has to be satisfied. The proposed approach provides an automated construction of an aggregation function, which is completely free of data learning and manual processing. In addition, this method provides a novel fuzzy measure that integrates two different classes of information - importance/interactions of criteria and vague statements.
Document Details
- Document Type
- Technical Report
- Publication Date
- Aug 26, 2012
- Accession Number
- ADA567409
Entities
People
- David Wen
- Evgeni Dimitrov
- Hayden Schaeffer
- Kizza Nandyose
- Olivier Thonnard
- Sandra Rankovic
Organizations
- University of California, Los Angeles