Interval-Valued Picture Uncertain Linguistic Generalized Hamacher Aggregation Operators and Their Application in Multiple Attribute Decision-Making Process

This paper aims to present the concept of interval-valued picture uncertain linguistic set (IVPULS), which composes the grade of truth, abstinence, and falsity in the form of a subset of the unit interval. IVPULS is an extensive capable theory to manage awkward and unreliable information. To explore the theory, we firstly stated some basic operational laws of them and investigated their properties. Based on these stated laws, we defined several weighted and ordered weighted generalized Hamacher aggregation (GHA) operators. Several special cases are deduced from the proposed operators. Furthermore, a multi-attribute decision-making approach algorithm is stated by using the concept of proposed GHA operators under the IVPULSs environment. The presented algorithm has been explored with a numerical example and compares their results with the existing studies to examine and improve the quality and feasibility of the discovered theory.