Determining an estimate of an equivalence relation for moderate and large sized sets
Journal Title: Operations Research and Decisions - Year 2017, Vol 27, Issue 2
Abstract
This paper presents two approaches to determining estimates of an equivalence relation on the basis of pairwise comparisons with random errors. Obtaining such an estimate requires the solution of a discrete programming problem which minimizes the sum of the differences between the form of the relation and the comparisons. The problem is NP hard and can be solved with the use of exact algorithms for sets of moderate size, i.e. about 50 elements. In the case of larger sets, i.e. at least 200 comparisons for each element, it is necessary to apply heuristic algorithms. The paper presents results (a statistical preprocessing), which enable us to determine the optimal or a near-optimal solution with acceptable computational cost. They include: the development of a statistical procedure producing comparisons with low probabilities of errors and a heuristic algorithm based on such comparisons. The proposed approach guarantees the applicability of such estimators for any size of set.
Authors and Affiliations
Leszek KLUKOWSKI
Keywords
Related Articles
- EP ID EP323653
- DOI -
- Views 41
- Downloads 0
Multi-method and multi-criteria decision analysis of objects in a computerized decision support system
A multimethod approach to the multicriteria analysis and assessment of objects (rankings, grouping, econometric assessments) have been presented. This issue is a field of research and engineering associated with the cons...
Advances in antithetic time series analysis: separating fact from artifact
The problem of biased time series mathematical model parameter estimates is well known to be insurmountable. When used to predict future values by extrapolation, even a de minimis bias will even-tually grow into a large...
Barriers to the development of spin-offs. A fuzzy-set-theoretic approach
University spin-offs have idiosyncratic strengths in comparison to other new firms. However, evidence also shows that Polish university spin-offs have a low survival rate, and only a small percent of them grow into susta...
Probabilistic models for analyzing the availability and profit of a deteriorating 2-out-of-4 system
This paper deals with modelling and evaluating the availability and profit of a linear consecutive 2-out-of-4 system exposed to three consecutive stages of deterioration before failure. The system will pass through three...
Are we done with preference rankings? If we are, then what?
Intransitive, incomplete and discontinuous preferences are not always irrational but may be based on quite reasonable considerations. Hence, we pursue the possibility of building a theory of social choice on an alternati...