type fuzzy

group decision

fuzzy sets

fuzzy preference

fuzzy numbers

soft set

pythagorean fuzzy

Engineering Applications of Artificial Intelligence

All the extensions of ordinary fuzzy sets with three-dimensional membership functions such as intuitionistic fuzzy sets, second type intuitionistic fuzzy sets (or Pythagorean fuzzy sets) and neutrosophic sets aim at defining the judgments of decision makers/ experts with a more detailed description. As a new extension of intuitionistic fuzzy sets of second type, the emerging spherical fuzzy sets (SFS) have been proposed by Kutlu Gündoğdu and Kahraman (2019b). In spherical fuzzy sets, the sum of membership, non-membership and hesitancy degrees must satisfy the condition 0 ≤ μ 2 + v 2 + π 2 ≤ 1 in which these parameters are assigned independently. SFS is an integration of Pythagorean fuzzy sets and neutrosophic sets. In this paper, novel interval-valued spherical fuzzy sets are introduced with their score and accuracy functions; arithmetic and aggregation operations such as interval-valued spherical fuzzy weighted arithmetic mean operator and interval-valued spherical fuzzy geometric mean operator. Later, interval-valued spherical fuzzy sets are employed in developing the extension of TOPSIS under fuzziness. Then, we use the proposed interval-valued spherical fuzzy TOPSIS method in solving a multiple criteria selection problem among 3D printers to verify the developed approach and to demonstrate its practicality and effectiveness. A comparative analysis with single-valued spherical TOPSIS is also performed.

A novel fuzzy TOPSIS method using emerging interval-valued spherical fuzzy sets