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Number 4 - December 2021
Volume 31 - 2021
New transitivity of Atanassov’s intuitionistic fuzzy sets in a decision making model
Barbara Pękala, Piotr Grochowalski, Eulalia Szmidt
Abstract
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