2-tuple linguistic intuitionistic preference relation and its application in sustainable location planning voting system

Sustainability has increasingly become a major consideration in location planning, directing urban distribution, and regional development. This scenario can be regarded as a group decision making (GDM) voting system case. Taking into account artificial thinking and the characteristics of the case, this paper introduces the 2-tuple linguistic intuitionistic preference relation (LIPR) to resolve the GDM voting system circumstance. Firstly, the Archimedean t-norm and t-conorm based operational laws and the 2-tuple linguistic intuitionistic fuzzy weighted geometric (ATS-2TLIFWG) operator are developed to aggregate and rank linguistic intuitionistic fuzzy numbers (LIFNs). Secondly, various concepts related to the 2-tuple LIPR and geometric consistency are extended for further analysis, including the completely geometrically consistent 2-tuple LIPR, the acceptably geometrically consistent 2-tuple LIPR, and the consistency index. Thirdly, motivated by the adverse impact of contradictory individual comparisons, we investigate a consistency modification algorithm to approximate the acceptable geometric consistency. Fourthly, we consider a consensus reaching algorithm as a unanimous elimination technique in the GDM procedure. A GDM algorithm, involving a consistency modification process as well as a consensus reaching process, and overall value aggregation process, is embedded into the GDM voting system. Finally, we conduct an illustrative example concerning smart city location planning, and employ the proposed algorithms in a comparison analysis to illustrate their feasibility and applicability.