New transitivity of Atanassov`s intuitionistic fuzzy sets in a decision making model - Pękala, Barbara; Grochowalski, Piotr; Szmidt, Eulalia (Zielona Góra: Uniwersytet Zielonogórski)
Atanassov`s intuitionistic fuzzy sets and especially his intuitionistic fuzzy relations are tools that make it possible to model effectively imperfect information that we meet in many real-life situations. In this paper, we discuss the new concepts of the transitivity problem of Atanassov`s intuitionistic fuzzy relations in an epistemic aspect. The transitivity property reflects the consistency of a preference relation. Therefore, transitivity is important from the point of view of real problems appearing, e.g., in group decision making in preference procedures. We propose a new type of optimistic and pessimistic transitivity among the alternatives (options) considered and their use in the procedure of ranking the alternatives in a group decision-making problem.
Keywords: optimistic and pessimistic transitivity; preference relations; optimistic and pessimistic intuitionistic fuzzy negations