T-spherical fuzzy Hamacher Heronian mean geometric operators for multiple criteria group decision making using SMART based TODIM method

Abstract

T-spherical fuzzy set studied in this paper adequately defines the uncertain information of any decision making situations. This paper aims to provide a solution approach to a multiple criteria group decision making situation under T-spherical fuzzy context. Every group decision making process utilizes aggregation operators to combine the different expert’s opinions. This paper aims to construct several aggregation operators such as T-spherical fuzzy Hamacher Heronian mean-geometric, weighted geometric, ordered geometric, and hybrid geometric operators. The fundamental properties of the proposed operators are thoroughly investigated. The introduced operators are more potent in considering the criteria interrelationships. Criteria weights play an essential role while aggregating different criteria during multiple criteria decision making processes. This work adopts the simple multi-attribute rating technique (SMART) to compute the criteria weights. Utilizing the proposed operators and SMART technique, a multiple criteria group decision making approach called the TODIM (an acronym in Portuguese for Iterative Multi-Criteria Decision Making) is defined based on the Euclidean distance between the T-spherical fuzzy numbers. A decision making situation of selecting the most deserving one from a set of lecturers based on their research capacity is solved using the proposed TODIM approach to show its applicability. Sensitivity analysis is carried out to reveal the effect of parameters on the decision results. A comparative study is made to exhibit the feasibility of the proposed approach.

Keywords

• -spherical fuzzy set
• Hamacher geometric operators
• Heronian mean function
• TODIM
• SMART
• Group decision making