Critical path method is a network based method premeditated for scheduling and organization of complex project in real world application. In this paper, a novel approach has been made to find the critical path in a directed acyclic graph, whose activity time is uncertain. The indistinguishable parameters in the network are represented by intuitionistic trapezoidal fuzzy numbers, instead of crisp numbers. A new procedure is proposed to find the optimal path, and an illustrative example is provided to validate the proposed approach.Keywords: Intuitionistic trapezoidal fuzzy number, Graded mean integration representation of intuitionistic trapezoidal fuzzy number, Ranking of intuitionistic fuzzy number, Critical path.

In real life, information available on situations/issues/problems is vague, inexact, or insufficient and so the parameters involved therein are grasped in an uncertain way by the decision maker. But in real life such uncertainty is unavoidable. One possible way out is to consider the knowledge of experts about the parameters involved as fuzzy data. In a network, the arc length may represent time or cost. In Relevant literature reports there are several methods to solve such problems in network-flow. This paper proposes an optimized path for use in networks, using trapezoidal intuitionistic fuzzy numbers, assigned to each arc length in a fuzzy environment. It proposes a new algorithm to find the optimized path and implied distance from source node to destination node.

Network analysis is a technique which determines the various sequences of activities concerning a project and the project completion time. The popular methods of this technique which is widely used are the critical path method and program evaluation and review techniques. The aim of this paper is to present an analytical method for measuring the criticality in an (Atanassov) intuitionistic fuzzy project network. Vague parameters in the project network are represented by (Atanassov) intuitionistic trapezoidal fuzzy numbers. A metric distance ranking method for (Atanassov) intuitionistic fuzzy numbers to a critical path method is proposed. (Atanassov) Intuitionistic fuzzy critical length of the project network is found without converting the (Atanassov) intuitionistic fuzzy activity times to classical numbers. The fuzzified conversion of the problem has been discussed with the numerical example. We also apply four different ranking procedures and we compare it with metric distance ranking method. Comparison reveals that the proposed ranking method is better than other raking procedures.

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Hard sets and soft sets must be adopted for several unknown logistical problems. This paper seeks to solve the cluster-based decision-making dilemma effectively based on fumigated soft environments. First of all, we are introducing an adjustable approach to resolution of decisions focused on fuzzy soft solutions. Then, the information and the degree of divergence dependent on a-similarity are introduced to determine the weights of the experts. In addition, with uncertain expert weights, we can create an effective cluster-based decision-making strategy. Finally, sensitivity analysis and comparative analysis was conducted with other established approaches.