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The purpose of this paper is to introduce a novel similarity measure of intuitionistic fuzzy sets (IFSs). The proposed measure is based on the equivalence relation in the IFS-IBA approach. Due to the logic-based background, this measure compares IFS from a different viewpoint than the standard measures, emphasizing comprehension of intuitionism. The IFS-IBA similarity measure has a solid mathematical background and can be combined with various IF aggregation operators. Additionally, we define IFS-IBA distance function as a complement of IFS-IBA similarity. Both IFS-IBA similarity and distance functions may have different realizations that are easy to interpret. Hence, the measures are offering great descriptive power and the ability to model various problems. The benefits of the proposed measure are illustrated on the problem of pattern recognition and classification within k -NN algorithm. Finally, we show that the proposed measure is appropriate for IF hierarchical clustering on the problem of clustering Serbian medium-sized companies according to their financial ratios. Results obtained using the IFS-IBA measure are clear-cut and more meaningful compared to a standard IF distances regardless of the I-fuzzification method used. [ABSTRACT FROM AUTHOR]

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 μ A + ν 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. [ABSTRACT FROM AUTHOR]

Fuzzy inference systems (FIS) enable automated assessment and reasoning in a logically consistent manner akin to the way in which humans reason. However, since no conventional fuzzy set theory is in the Boolean frame, it is proposed that Boolean consistent fuzzy logic should be used in the evaluation of rules. The main distinction of this approach is that it requires the execution of a set of structural transformations before the actual values can be introduced, which can, in certain cases, lead to different results. While a Boolean consistent FIS could be used for establishing the diagnostic criteria for any given disease, in this paper it is applied for determining the likelihood of peritonitis, as the leading complication of peritoneal dialysis (PD). Given that patients could be located far away from healthcare institutions (as peritoneal dialysis is a form of home dialysis) the proposed Boolean consistent FIS would enable patients to easily estimate the likelihood of them having peritonitis (where a high likelihood would suggest that prompt treatment is indicated), when medical experts are not close at hand. [ABSTRACT FROM AUTHOR]