The task of finding the crisp critical path has received researcher's attention over the past two decades which has wide range of applications in planning and scheduling the large projects. In most cases of our life, the data obtained for decision makers are only approximate, which gives rise to fuzzy critical path problem. In this paper, new ranking methods are introduced to identify the fuzzy critical path and the fuzzy critical length is presented in the nature of fuzzy membership function. The fuzzified version of the problem has been discussed with the aid of numerical example.

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The field of medicine and decision making are the most fruitful and interesting area of applications of fuzzy set theory. In real life situations, the imprecise nature of medical documentation and uncertain information gathered for decision making requires the use of "fuzzy". In this paper, procedures are presented for medical diagnosis and for fuzzy decision model. Examples are illustrated to verify the proposed approach.

The Shortest path problem is a classical network optimisation problem which has wide range of applications in various fields. In this work, we study the task of finding the shortest path in fuzzy weighted graph (network) i.e., vertices remains crisp, but the edge weights will be of fuzzy numbers. It has been proposed to present new algorithms for finding the shortest path in fuzzy sense where illustrative examples are also included to demonstrate our proposed approach.