Search results for "Codomain"
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The analysis of poverty in Italy. A fuzzy dynamic approach
2004
The commonly used criterion to sharply separate the poor from the non poor on the basis of a poverty threshold appears to be too severe in comparison with the nature of poverty. The latter is multidimensional in its components (domain) and continue in its states (codomain). Moreover an income-based poverty line allows for a remarkable number of spurious transitions below and over that line, which do not correspond to true variations in household’s standard of living. This study starts from the analysis of common (with crisp states) transition matrices; then a fuzzy multidimensional poverty indicator is built. In conclusion, fuzzy states transition matrices synthesize interpretative content …
Some Generalizations of a Simion Schmidt Bijection
2007
In 1985, Simion and Schmidt gave a constructive bijection φ from the set of all length (n-1) binary strings having no two consecutive 1s to the set of all length n permutations avoiding all patterns in {123,132,213}. In this paper, we generalize φ to an injective function from {0,1}n-1 to the set Sn of all length n permutations and derive from it four bijections φ : P →Q where P⊆{0,1}n-1 and Q ⊂ Sn. The domains are sets of restricted binary strings and the codomains are sets of pattern-avoiding permutations. As a particular case we retrieve the original Simion–Schmidt bijection. We also show that the bijections obtained are actually combinatorial isomorphisms, i.e. closeness-preserving bije…