Fuzzy Critical Path Method Based on a New Approach of Ranking Fuzzy Numbers using Centroid of Centroids

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Fuzzy Basic Definitions

In this section, some basic fuzzy basic definitions on fuzzy sets are presented (Kaufmann & Gupta, 1985):

• Definition 1: Let U be a Universe set. A fuzzy set of U is defined by a membership function where is the grade of x in, ;

• Definition 2: A fuzzy set of universe set U is a fuzzy number if (i)is normal i.e., and (ii) is convex i.e.;

  

and:;

• Definition 3: The membership function of the real fuzzy number is given by:

  

where is a constant, a, b, c, d are real numbers and are two strictly monotonic and continuous functions. It is standard to write a fuzzy number as . If , then is a normalized fuzzy number, otherwise is said to be a generalized or non-normal fuzzy number if ;