*Article* **Algorithm for T-Spherical Fuzzy Multi-Attribute Decision Making Based on Improved Interactive Aggregation Operators**

#### **Harish Garg 1,\*, Muhammad Munir 2, Kifayat Ullah 2, Tahir Mahmood 2 and Naeem Jan 2**


Received: 6 November 2018; Accepted: 23 November 2018; Published: 27 November 2018

**Abstract:** The objective of this manuscript is to present some new, improved aggregation operators for the T-spherical fuzzy sets, which is an extension of the several existing sets, such as intuitionistic fuzzy sets, picture fuzzy sets, neutrosophic sets, and Pythagorean fuzzy sets. In it, some new, improved operational laws and their corresponding properties are studied. Further, based on these laws, we propose some geometric aggregation operators and study their various relationships. Desirable properties, as well as some special cases of the proposed operators, are studied. Then, based on these proposed operators, we present a decision-making approach to solve the multi-attribute decision-making problems. The reliability of the presented decision-making method is explored with the help of a numerical example and the proposed results are compared with several prevailing studies' results. Finally, the superiority of the proposed approach is explained with a counter example to show the advantages of the proposed work.

**Keywords:** multi-attribute decision making; aggregation operators; spherical fuzzy sets; interactive geometric operators
