In variational analysis, Γ-convergence proved its importance because almost all other convergences can be expressed as Γ-convergence. The discussion about maximization and minimization is also fundamental in variational analysis. In this paper, we define three topologies on the collection of intuitionistic fuzzy sets based on maxima operator. Furthermore, convergences in these topologies are proved to be compatible with Γ-, Γ+, Γ convergences when intuitionistic fuzzy sets are upper semicontinuous with locally compact Hausdroff domain.
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