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In this paper, we introduce Interpolative Boolean algebra (IBA) as a suitable algebra for intuitionistic fuzzy sets (IFSs). IBA is [0,1]-valued realization of Boolean algebra, consistent with Boolean axioms and theorems. IFS theory takes into account both membership and non-membership function, so it can be viewed as a generalization of the traditional fuzzy set theory. We propose a realization of IFS conjunction and disjunction operations based on IBA. This may be viewed as a generalized framework for IFS-IBA calculus. Finally, we investigate the validity of the laws of contradiction and excluded middle in our approach.

One of the key issues when it comes to measuring similarity is the discrepancy that exists between the idealized measures and actual human perception. The aim of this paper is to explore the possibility of using logic-based similarity measures for modeling consensus. We propose a soft consensus model for calculating the consensus and proximity degrees on two different levels. The proposed model relies on logic-based similarity measures and the appropriate aggregation functions. It is a fresh approach as it includes logic when perceiving similarity. Several similarity measures based on min, product and Lukasiewicz fuzzy bi-implications are introduced for modeling consensus. We also define a measure of similarity based on interpolative Boolean algebra (IBA) equivalence, and provide its comprehensive theoretical background. In our approach, we analyze how these different logic-based measures treat similarity, and whether they are appropriate to explain the notion of consensus. Finally, we show that IBA equivalence is the only measure that is both appropriate for modeling consensus and interpretable at the same time. The proposed model is illustrated on a problem of project selection in the context of sustainable development and the numerical results are discussed.Keywords Similarity · Interpolative Boolean algebra · Fuzzy bi-implication · IBA equivalence · Logic-based similarity measure · Consensus Communicated by V. Loia.A. Poledica (B) · P. Milošević · I. Dragović · B. Petrović

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