Abstract
The current chapter lays the foundation for the original axiomatic approach. First, we introduce the last (fourth) axiom on the invariance of preference relation.
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Notes
- 1.
Recall that the inequality \(y^{\prime} \ge y^{\prime\prime}\) means \(y^{\prime}{ \geqq }y^{\prime\prime}\) and \(y^{\prime} \ne y^{\prime\prime}\).
- 2.
The definition of a lexicographic relation can be found in Sect. 1.2.
- 3.
The proof is suggested by O.V. Baskov.
- 4.
Indeed, vectors (2.7) form a linear independent system, since the matrix composed of them has rank m.
- 5.
Recall that, for m-dimensional vectors \(a\) and \(b\), the notation \(\langle a,b\rangle\) gives their scalar product: \(\langle a,b\rangle = \sum\limits_{i = 1}^{m} {a_{i} b_{i} }\).
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Noghin, V.D. (2018). Pareto Set Reduction Based on Elementary Information Quantum. In: Reduction of the Pareto Set. Studies in Systems, Decision and Control, vol 126. Springer, Cham. https://doi.org/10.1007/978-3-319-67873-3_2
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DOI: https://doi.org/10.1007/978-3-319-67873-3_2
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