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 μA+νA>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.

A New Partial Correlation Coefficient Technique Based on Intuitionistic Fuzzy Information and Its Pattern Recognition Application

“…Our frst assignment is to compute the correlation coefcient between each of the building patterns using the modifed approach (i.e., equation (12)) after computing the hesitation margins of I i for i � 1, 2, 3, 4.…”

“…Te algorithm based on the modifed approach (i.e., equation (12)) for computing the correlation coefcient between the building patterns is made up of the following steps:…”

“…An approach of the cluster algorithm using IFSs was discussed in [9], and decision-making processes were executed using correlation operators on IFSs [10,11]. In fact, assorted application examples have been discussed from the perspective of IFSs [12][13][14][15]. Sundry discussions of decision-making in uncertain frameworks have been presented [16][17][18].…”

A Novel IBA-DE Hybrid Approach for Modeling Sovereign Credit Ratings

“…With the LA being implemented as the weighted sum of structure vectors in the case of mutually dependent attributes, it will be used later in the paper when credit ratings are derived from the predetermined attributes. LA has been used multiple times as a suitable tool for financial problems such as modeling [52], financial analysis [53,54], and credit score forecasting [55].…”