Fuzzy permutation graph (FPG) plays a significant role in solving real-life problems where the scope and application of crisp permutation graph get limited due to the fuzziness involved in real situations. In this article an algorithm is designed to find out all maximal fuzzy cliques of a FPG. A similar algorithm is developed at the same time to find out all maximal fuzzy independent sets of the said graph. The inter-relationship between FPG and its two types of complements is presented based on the facts and theories established on fuzzy cliques and fuzzy independent sets. The importance of fuzzy cliques of FPG is discussed through an application on a daily-life problem. The unique property of a FPG having two types of complement graphs help us to solve many useful problems. Here, we have shown how this property of FPG helps us to overcome a hazardous situation occurred due to disrupted scheduling of trains on a foggy day.

中文翻译：

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模糊置换图最大模糊团的生成及应用

模糊置换图 (FPG) 在解决现实问题中扮演着重要的角色，在这些问题中，清晰置换图的范围和应用由于真实情况中的模糊性而受到限制。在本文中，设计了一种算法来找出 FPG 的所有最大模糊团。同时开发了类似的算法来找出所述图的所有最大模糊独立集。基于模糊团和模糊独立集建立的事实和理论，提出了FPG与其两种补语之间的相互关系。通过一个日常生活问题的应用，讨论了 FPG 模糊团的重要性。具有两种补图的 FPG 的独特性质帮助我们解决了许多有用的问题。这里，