Applications of Generalized Picture Fuzzy Soft Set in Concept Selection

Muhammad Jabir Khan, Supak Phiangsungnoen, Habib ur Rehman, Wiyada Kumam

Abstract

The incorrect identification of a good concept for a particular product leads to an increase in design modification, which increases the functional cost and generating time, therefore the concept selection is a crucial process in the new product development (NPD). In this paper, we used the generalized picture fuzzy soft set to obtain the optimal design concept. We introduced the b-picture fuzzy soft set $(bPFSS)$ and generalized b-picture fuzzy soft set $(GbPFSS)$ on the basis of the bijective soft set. We introduced the lower-and-substitution and upper-or-substitution operations for $GbPFSS$ and discuss their basic properties. The $GbPFSSs$ are used to illustrate the mapping from customers requirements to design concepts. We proposed an algorithm for choosing best design concept using the upper-or-substitution operations for $GbPFSS$. After we discuss a case study for the design concept of laptops for one and two customers separately.