A Novel Approach to Generalized Intuitionistic Fuzzy Sets Based on Interpolative Boolean Algebra

Abstract

One of the main issues in IFS theory are generalizations of intuitionistic fuzzy set (IFS) definition as well as IFS operations. In this paper, we present the LBIFS-IBA approach by applying operations based on interpolative Boolean algebra (IBA) on generalized IFS. Namely, LBIFS are defined as a special case of Liu's generalized IFS with the maximal interpretational surface. By extending the interpretational surface, the descriptive power of the approach is enhanced, and therefore the problematic situations when (mu)A+nu(A)>1 can be modeled. In addition, IBA-based algebra secures Boolean properties of the proposed approach. Considerable attention is given to comprehension of uncertainty within LBIFS-IBA, i.e., we propose a novel manner of uncertainty interpretation by treating values from [-1,1] interval. In order to prove its importance, we compare LBIFS-IBA with several well-known IFS generalizations, showing that only our approach offers meaningful uncertainty interpretation is all selected cases. Additionally, we illustrate the practical benefits of LBIFS-IBA by applying it to an example of modeling Japanese candlesticks for price charting and paying special attention to uncertainty interpretation.