Allelic variation in floral quantitative traits, including the elements of flowers and fruits, is caused by extremely complex regulatory processes. In the genetic improvement of flare tree peony (Paeonia rockii), a unique ornamental and edible oil woody species in the genus Paeonia, a better understanding of the genetic composition of these complex traits related to flowers and fruits is needed. Therefore, we investigated the genetic diversity and population structure of 160 P. rockii accessions and conducted single-marker association analysis for 19 quantitative flower and fruit traits using 81 EST-SSR markers. The results showed that the population had a high phenotypic diversity (coefficients of variation, 11.87–110.64%) and a high level of genetic diversity (mean number of alleles, NA = 6.09). These accessions were divided into three subgroups by STRUCTURE analysis and a neighbor-joining tree. Furthermore, we also found a low level of linkage disequilibrium between these EST-SSRs and, by single-marker association analysis, identified 134 significant associations, including four flower traits with 11 EST-SSRs and 10 fruit traits with 32 EST-SSRs. Finally, based on the sequence alignment of the associated markers, P280, PS2, PS12, PS27, PS118, PS131, and PS145 may be considered potential loci to increase the yield of flare tree peony. These results laid the foundation for further analysis of the genetic structure of some key traits in P. rockii and had an obvious potential application value in marker-assisted selection breeding.
In order to control the systematic divergence among decision makers (DMs) and preserve the original decision preference, this paper proposes a novel decision information fusion framework under the hesitant fuzzy environment. First, a maximum compactness-based normalization method is presented to normalize hesitant fuzzy elements (HFEs) as pretreatment of decision data. Second, prospect theory is introduced to assign the optimal aggregation weights to maximize the efficiency of the preference aggregation process, in which the expected consensus threshold is viewed as a reference point estimated through statistic inference to distinguish DMs’ status. Third, an effective feedback mechanism is designed to improve group consensus, and the dichotomy algorithm is utilized to search optimal feedback weight to preserve original decision information. Finally, a case study and comparison analysis are illustrated to show the efficiency of the proposed hesitant fuzzy information fusion method.
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