A new linguistic scale for Interval Type-2 Trapezoidal Fuzzy Number based Multiple Criteria Decision Making method

Decision making is a process for managing the decision problem for human beings that use linguistic information. However, it is sometimes limited by the fact that the linguistic models use only positive linguistic terms, which may not reflect exactly what the experts mean. The previous studies neglected the equilibrium concept (i.e., two sides of a matter) that takes its roots from the Yin Yang theory. The Yin Yang theory philosophically deals with two sides of things in the universe, and focuses on the balance of the two sides. Thus, the purpose of this paper is to introduce the new linguistic scales of positive and negative Interval Type-2 Trapezoidal Fuzzy Number (IT2TrFN) to the decision environment of interval type-2 fuzzy context for solving Interval Type-2 Fuzzy Technique for Order Preference by Similarity to Ideal Solution (IT2FTOPSIS) problems. This new linguistic scales reacts to the subjective judgments from the experts where the lowest of the scale and the highest of the scale are equally strong. In decision making, it is rare to find the negative scale, where it actually does not mean wrong or corrupt. Here, the negative data represents a hypothesis that can make it well-separated. The positive and negative are relatives. Along with considering the context of the new linguistic scale, this paper employs a hybrid averaging approach with ambiguity method and type-reduction method to formulate a collective decision environment. This hybrid averaging approach helps to reduce values of Interval Type-2 Fuzzy Sets (IT2FS) to a crisp number. The feasibility and applicability of the proposed methods are illustrated with an example.