Intuitionistic Fuzzy Probabilistic Aggregation Operators Based on the Choquet Integral: Application in Multicriteria Decision-Making

Gia Sirbiladze () and Otar Badagadze
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Gia Sirbiladze: Department of Computer Sciences, Iv. Javakhishvili Tbilisi State University, 13, University St., Tbilisi 0186, Georgia, USA
Otar Badagadze: Department of Computer Sciences, Iv. Javakhishvili Tbilisi State University, 13, University St., Tbilisi 0186, Georgia, USA

International Journal of Information Technology & Decision Making (IJITDM), 2017, vol. 16, issue 01, 245-279

Abstract: Associated Intuitionistic Fuzzy Probabilistic Averaging (As-IFPA) and Associated Intuitionistic Fuzzy Probabilistic Geometric (As-IFPG) operators based on the Choquet integral and an associated probability class of a fuzzy measure are constructed. Propositions on the correctness of the extensions are proved: (1) The As-IFPA (As-IFPG) operator for the fuzzy measure — capacity of order two coincides with the Intuitionistic Fuzzy Choquet Averaging (Intuitionistic Fuzzy Choquet Geometric) operator; (2) The As-IFPA (As-IFPG) operator coincides with the Intuitionistic Fuzzy Probabilistic Averaging (Intuitionistic Fuzzy Probabilistic Geometric) operator when a probability measure is used in the role of a fuzzy measure. Connections between the constructed operators and the compositions of dual triangular norms (Tp,Sp) and (Tmin,Smax) are constructed. The conjugate connections between the constructed operators are shown. Two illustrative examples on the applicability of the As-IFPA and As-IFPG operators are presented. Several variants of the new operators (1) for the decision-making problem regarding the fiscal policy of a country; (2) for the decision-making problem regarding the best global supplier selection according to the core competencies of suppliers for a manufacturing company are used. Interactions and dependencies among all the combinations of the criteria in the decision-making process are considered.

Keywords: Associated probabilities of a fuzzy measure; Choquet integral; intuitionistic fuzzy set; intuitionistic fuzzy aggregation operator; fuzzy multicriteria decision-making (search for similar items in EconPapers)
Date: 2017
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Citations: View citations in EconPapers (3)

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DOI: 10.1142/S0219622016500449

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