The Intelligence of Octagonal Fuzzy Number to Determine the Fuzzy Critical Path: A New Ranking Method

Abstract

This research paper proposes a modified ranking approach to determine the critical path in fuzzy project network, where the duration of each activity time is represented by an octagonal fuzzy number. In this method, a modified subtraction formula is carried out on fuzzy numbers. This modified method works well on fuzzy backward pass calculations as there will be no negative time. The analysis is expected to show that the fuzzy number which is used in this paper is more effective in determining the critical path in a fuzzy project network and possibility of meeting the project time. A numerical example is given and compared with trapezoidal, triangular fuzzy numbers through proposed ranking method.

Critical Path Method for Z-fuzzy Numbers

“…No single work referring to critical path in the context of Z-fuzzy numbers has been identified. On the other hand, papers referring to critical path methods for fuzzy durations modeled not only by well-known types of fuzzy numbers, but also by less common types, like hexagonal, octagonal, type-2, hesitant, intuitionistic fuzzy numbers [5][6][7][8][9][10][11][12][13][14][15] have been identified, which means that our research fits well into the current trends of research in fuzzy project modelling.…”

On Fuzzy Critical Path Method Based On Ranking Of Various Type-2 Fuzzy Quantities Using Centroid Of Centroids

“…The results of the calculations are presented in the following tables. (19,20,21,30,39,47,48,49), (16,17,18,30,39,50,51,53), (13,14,15,30,39,54,55,56), (10,11,12,30,39,57,58,60), (7,8,9,30,39,61,62,63), (4,5,6,30,39,64,65 26, 27,29,36,37,38,39), (22,23,24,29,36,40,41,43), (19,20,21,29,36,…”

“…In 2010, Sireesha and Ravi Shankar [12] developed a new method based on fuzzy theory to solve the project scheduling problem without computing forward and backward pass calculations under uncertainty. Shakeela Sathish and Ganesan [11] proposed a new approach to critical path analysis in project network based on fuzzy ranking method to determine the fuzzy critical path of project network without converting the fuzzy activity times to classical numbers in 2011. In 2013, Ravi Shankar [10] developed a new fuzzy critical path method by applying a proposed approach of ranking of fuzzy numbers using centroid of centroids of fuzzy number to its distance from original point and Elizabeth and Sujatha [3] proposed a new ranking method based on acceptability and decision maker risk index to identify the fuzzy critical path in which they presented the fuzzy critical length in the nature of fuzzy membership function in the same year.…”

Finding the Critical Path Method for Fuzzy Network with Development Ranking Function

“…Several papers are also presented on a critical path method for solution the fuzzy project network [8] and [9]. Narayanamoorthy and Maheswari [10] obtained a modified classification method for assessing the critical path (CP) of the fuzzy project network (FPN), in which the length of each process time is a fuzzy octagonal number (FON), and an updated formula is implemented on the fuzzy numbers in this process. Researches [11][12][13][14][15][16][17][18][19] have studied the different applications of the ranking function.…”