The Analytical Hierarchy Process (AHP) idealistically assumes the independence of the criteria which are often interrelated, conflicting or can be traded-off. It is, therefore, proposed that AHP could be extended by applying fuzzy logic to adequately incorporate the different relationships that may exist among the criteria. It is shown that the conventional and consistent fuzzy approaches could actually lead to different choices and an explanation is provided. Finally, two different application scenarios are illustrated on the web service selection problem.
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
This study proposes implementation of Boolean consistent fuzzy inference system for credit scoring purposes. Fuzzy inference system (FIS) allows domain experts to express their knowledge in the form of fuzzy rules, which enables combination of automatic rating with human judgment. Crucial for this model is that fuzzy rules are being evaluated using Boolean consistent fuzzy logic, which preserves all Boolean axioms. Experimental results show that the Boolean consistent FIS outperforms the conventional FIS in terms of classification accuracy, precision, and recall. Consistent fuzzy logic could contribute to the rightful approval of more loans which in turn would have positive effects on economic growth.
The aim of this paper is to propose a soft consensus model based on interpolative Boolean algebra for group decision making problems. Consensus degrees are calculated on three levels (on pairs of alternatives, alternatives, collective level) by means of pseudo-logical aggregation. The relation of equivalence is employed as a similarity measure among experts' opinions. In fact real-valued realization of equivalence is used as a generalized Boolean polynomial.In the illustrative example of sustainable development problem, we have shown that the proposed model is appropriate to determine the level of agreement among experts.
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