提出了一类新的向量值映射-$D$-$E$-半预不变真拟凸映射, 它是$D$-半预不变真拟凸映射和$D$-$E$-预不变真拟凸映射的真推广. 首先, 举例验证了$D$-$E$-半预不变真拟凸映射的存在性; 其次, 说明了$D$-$E$-半预不变真拟凸映射的水平集是$E$-半不变凸集, 讨论了$D$-$E$-严格半预不变真拟凸映射和$D$-$E$-半严格半预不变真拟凸映射的关系; 再次, 在$D$-$E$-半严格(严格)半预不变真拟凸性下, 得出了向量优化问题的$E$-局部有效解 为$E$-全局有效解, $E$-局部弱有效解为$E$-全局弱有效解, 并举例验证了所得结果; 最后, 在$D$-$E$- 严格半预不变真拟凸性下, 建立了向量优化问题的$E$-全局弱有效 解和$E$-局部弱有效解的唯一性刻画.

In this paper, a class of new vector-valued mapping-$D$-$E$-properly semi-prequasi-invex mapping is put forward, it is true generalization of $D$-properly semi-prequasi-invex mapping and $D$-$E$-properly prequasi-invex mapping. Firstly, examples are given to verified the existence of $D$-$E$-properly semi-prequasi-invex mappings; Secondly, it is illustrated that the level set of $D$-$E$-properly semi-prequasi-invex mapping is an $E$-semi-invex set, the equivalent relation between $D$-$E$-properly semi-strictly semi-prequasi-invex mapping and $D$-$E$-properly strictly semi-prequasi-invex mapping is discussed. Thirdly, two results are obtained, that is, the $E$-local efficient solution of vector optimization problem is the $E$-global efficient solution and the $E$-local weak efficient solution of vector optimization problem is the $E$-global weak efficient solution under $D$-$E$-properly semistrictly (strictly) semi-prequasi-invexity, they are verified with two examples; Lastly, the unicity is established about the $E$-global weak efficient solution and the $E$-local weak efficient solution of vector optimization problem under $D$-$E$-properly strictly semi-prequasi-invexity.