Educational Technology Assessment Using Bipolar Complex Pythagorean Neutrosophic Hamacher Aggregation Operators

Authors

  • M Kaviyarasu Department of Mathematics, SRM Institute of Science and Technology, Ramapuram, Chennai-600089, Tamil Nadu, India
  • Akbota Nurgaliyeva Department of Mathematics, Korkyt Ata Kyzylorda University. Aiteke Bi Street 29A, 120000, Kyzylorda, Kazakhstan
  • R Venitha Department of Mathematics, SRM Institute of Science and Technology, Ramapuram, Chennai-600089, Tamil Nadu, India
  • Nasreen Kausar Department of Mathematics, Faculty of Arts and Science, Balikesir University, 10145 Balikesir, Turkey & Department of Computer Engineering, Biruni University, 34010, Istanbul, Turkey
  • Hasan Dincer School of Business, Istanbul Medipol University, Istanbul, Turkey & Clinic of Economics, Azerbaijan State University of Economics (UNEC), Baku, Azerbaijan & University College, Korea University, Seoul, Republic of Korea
  • Serhat Yuksel School of Business, Istanbul Medipol University, Istanbul, Turkey & Clinic of Economics, Azerbaijan State University of Economics (UNEC), Baku, Azerbaijan & Department of Economics and Management, Khazar University, Baku, Azerbaijan

Keywords:

Bipolar Complex Pythagorean Neutrosophic set; Hamacher Aggregation Operator; Multi Criteria Decision Making; Educational System; Decision Support System, AI-Based Educational Techniques

Abstract

Multiple-Criteria Decision-Making (MCDM) problems frequently involve uncertainty, incomplete information and inconsistent evaluations, particularly when alternatives are assessed simultaneously from favourable and unfavourable perspectives. To address these complexities, this study develops an integrated decision-making framework based on Bipolar Complex Pythagorean Neutrosophic Sets (BCPNSs) and Hamacher Aggregation Operators (HAOs). The proposed framework incorporates bipolar evaluations, complex-valued membership degrees, Pythagorean characteristics and neutrosophic representations of truth, indeterminacy and falsity within a unified mathematical structure. Three aggregation mechanisms are formulated within this framework: the BCPNS Hamacher Weighted Averaging (BCPNHWA), BCPNS Hamacher Ordered Weighted Averaging (BCPNHOWA) and BCPNS Hamacher Hybrid Averaging (BCPNHHA) operators. Their fundamental mathematical properties, including idempotency, monotonicity and boundedness, are subsequently examined. The applicability of the proposed methodology is demonstrated through an educational technology selection problem comprising three candidate alternatives evaluated against three criteria. The BCPNHWA operator is employed to synthesise criterion-specific BCPNS assessments, after which a score function determines the relative preference ordering of the alternatives. The resulting scores are 0.3972, 0.4539 and 0.4569 for ⅁_1, ⅁_2 and ⅁_3, respectively, establishing the ranking ⅁_3 > ⅁_2 > ⅁_1. Accordingly, ⅁_3, representing artificial intelligence (AI)-based adaptive assessment, emerges as the most preferable educational technology among the alternatives considered. By integrating complementary representations of uncertainty with flexible aggregation procedures, the proposed framework provides a mathematically versatile approach for managing ambiguity, conflicting assessments and imprecise information in educational decision-making and broader MCDM applications.

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Published

2026-06-30

How to Cite

M Kaviyarasu, Akbota Nurgaliyeva, R Venitha, Nasreen Kausar, Hasan Dincer, & Serhat Yuksel. (2026). Educational Technology Assessment Using Bipolar Complex Pythagorean Neutrosophic Hamacher Aggregation Operators. Decision Making: Applications in Management and Engineering, 9(1), 558–585. Retrieved from https://dmame-journal.org/index.php/dmame/article/view/1884

Issue

Vol. 9 No. 1 (2026): Decision Making: Applications in Management and Engineering

Section

Regular articles

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Copyright (c) 2026 Decision Making: Applications in Management and Engineering

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