Nowadays, the world is in turmoil, climate and environmental problems are prominent, the import and export of fresh agricultural products are restricted, etc. The impact of the growing demand for fresh agricultural products and healthy lifestyle choices, and fresh agricultural products are essential for people's daily life, which are perishable, fragile, seasonal, and other unstable factors. Therefore, when the fresh produce supply chain faces various pressures and difficulties, how to enhance the resilience of the supply chain against various problems and risks with flexible and multi-dimensional strategies and methods has become the focus of extensive attention. This kind of problem is a typical contradictory problem, and previous studies have failed to achieve good results. In this paper, based on extenics, we are able to one-dimensionalise the multi-dimensional contradictory problems and multi-dimensionalise the one-dimensional contradictory problems to solve such problems in a scientific and effective way. Firstly, taking fresh agricultural products supply chain enterprise M as the research object, we constructed the fresh agricultural products supply chain enterprise toughness system and identified the toughness state of each index. Secondly, we found the low-evaluation toughness indexes that need to be solved and constructed a extension model of incompatible problems of enterprise toughness. Thirdly, we analysed the objectives and conditions of toughness incompatible problems of fresh agricultural products supply chain enterprises numerically and quantitatively, and then, with the objective of toughness improvement, we analyzed the correlation of the condition basic-elements of incompatible problems and carried out extension transformations. Again, the objectives and conditions of the incompatible problems of fresh produce supply chain enterprises are analysed numerically and quantitatively, and with toughness enhancement as the objective, the correlation analysis and extension transformation of the condition basic-elements of the incompatible problems are implemented to generate the set of toughness enhancement strategies that can solve the incompatible problems in a multidimensional and scientific way. Finally, the optimal toughness enhancement strategies are selected through the superiority evaluation and composed into a new strategy to enhance the toughness of the fresh produce supply chain. Combined with extenics calculations and screening, a new strategy for supply chain resilience enhancement of fresh agricultural products was finally formed. The existing problems are solved from six aspects: product supply type, product demand, product supply efficiency, human resource quantity, production and processing equipment, and logistics guarantee ability. It provides a certain reference significance for the fresh agricultural products supply chain toughness enhancement, and helps enterprises to strengthen their competitiveness and sustainability through the enhancement of toughness.