A multi-item generalized intuitionistic fuzzy inventory model with inventory level dependent demand using possibility mean,variance and covariance

Abstract

Generalized intuitionistic fuzzy numbers (GIFNs), a special kind of intuitionistic fuzzy set (IFSs) on the real number set are useful to deal with ill-known quantities in fuzzy optimization problems. How to measure the value and uncertainty of a GIFN is of eminent importance. The earlier part of the paper describes the concept of the possibility mean, variance and covariance of generalized intuitionistic fuzzy number. Furthermore, we show that possibility mean and variance of linear combination of generalized intuitionistic trapezoidal fuzzy numbers can be computed in a conventional way to those probability theory. Another part of this paper investigates a multi-item inventory model with inventory level dependent demand in generalized intuitionistic fuzzy environment. By employing the possibility mean and variance, the multi-item generalized intuitionistic fuzzy inventory model (MGIFim) is transformed into an equivalent deterministic linear programming problem. Finally, the model is illustrated with the help of numerical example, and to validated the proposed model few sensitivity analyses are also presented under different parameters.