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M¨ obius representation of the bipolar decomposition integrals and its applications | ||
| Iranian Journal of Fuzzy Systems | ||
| دوره 22، شماره 4، مهر و آبان 2025، صفحه 1-15 اصل مقاله (480.1 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22111/ijfs.2025.9334 | ||
| نویسندگان | ||
| J. Abbas* 1؛ R. Mesiar2؛ R. Halas3 | ||
| 1Department of Applied Sciences, University of Technology, Al Sina´ a Street, P. O. Box (19006), Baghdad, Iraq | ||
| 2Faculty of Civil Engineering, Slovak University of Technology, Radlinsk´ eho 11, 810 05 Bratislava, Slovakia | ||
| 3Department of Algebra and Geometry, Palack´y University of Olomouc, 17. listopadu 12, 779 00 Olomouc, Czech Republic | ||
| چکیده | ||
| The bipolar decomposition integral, recently introduced in [5], is a general framework for handling integrals related to aggregation on unipolar and bipolar scales. The M¨obius representation is related to the notion of k-additivity of a monotone set function and allows to derive simple expressions of some nonlinear integrals. In this paper, we propose M¨obius representation for the bipolar decomposition integral, which includes the M¨obius representation of each of the bipolar Choquet integral, bipolar Shilkret integral, and bipolar Pan integral. Then, we introduce the expressions for computing bipolar decomposition integrals concerning a 2-additive bi-capacity. Lastly, a practical numerical example is provided to illustrate the applicability of the proposed results in dealing with aggregation on bipolar scales, and simplicity of calculating the 2-additive bipolar decomposition integrals. | ||
| کلیدواژهها | ||
| 2-additive bi-capacity؛ aggregation functions؛ bipolar decomposition integrals؛ M¨obius transform؛ multi criteria decision-making | ||
| مراجع | ||
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