*Article* **Symmetric Triangular Interval Type-2 Intuitionistic Fuzzy Sets with Their Applications in Multi Criteria Decision Making**

#### **Sukhveer Singh and Harish Garg** *∗*

School of Mathematics, Thapar Institute of Engineering & Technology (Deemed University), Patiala 147004, India; sukhveer.singh@thapar.edu

**\*** Correspondence: harish.garg@thapar.edu; Tel.: +91-86990-31147

Received: 26 August 2018; Accepted: 11 September 2018; Published: 14 September 2018

**Abstract:** Type-2 intuitionistic fuzzy set (T2IFS) is a powerful and important extension of the classical fuzzy set, intuitionistic fuzzy set to measure the vagueness and uncertainty. In a practical decision-making process, there always occurs an inter-relationship among the multi-input arguments. To deal with this point, the motivation of the present paper is to develop some new interval type-2 (IT2) intuitionistic fuzzy aggregation operators which can consider the multi interaction between the input argument. To achieve it, we define a symmetric triangular interval T2IFS (TIT2IFS), its operations, Hamy mean (HM) operator to aggregate the preference of the symmetric TIT2IFS and then shows its applicability through a multi-criteria decision making (MCDM). Several enviable properties and particular cases together with following different parameter values of this operator are calculated in detail. At last a numerical illustration is to given to exemplify the practicability of the proposed technique and a comparative analysis is analyzed in detail.

**Keywords:** type-2 fuzzy set; multi criteria decision-making; triangular interval type-2 intuitionistic fuzzy set; Hamy mean; aggregation operator
