A hybrid hesitant fuzzy N-soft set framework for algebraic modeling of corporate bond evaluation under parameter-induced uncertainty

Ema Carnia; Riaman; Sukono; Zahrahtul Amani Zakaria; Moch Panji Agung Saputra; Audrey Ariij Sya'imaa HS; Mugi Lestari; Astrid Sulistya Azahra; Ema Carnia; Riaman; Sukono; Zahrahtul Amani Zakaria; Moch Panji Agung Saputra; Audrey Ariij Sya'imaa HS; Mugi Lestari; Astrid Sulistya Azahra

doi:10.3934/math.20261060

AIMS Mathematics

2026, Volume 11, Issue 8: 26409-26453. doi: 10.3934/math.20261060

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Research article

A hybrid hesitant fuzzy N-soft set framework for algebraic modeling of corporate bond evaluation under parameter-induced uncertainty

1.
Department of Mathematics, Faculty of Mathematics and Natural Sciences, Universitas Padjadjaran, Jatinangor, Sumedang, Jawa Barat 45363, Indonesia; Email: ema.carnia@unpad.ac.id (E.C.); riaman@unpad.ac.id (R.); sukono@unpad.ac.id (S.); moch16006@mail.unpad.ac.id (M.P.A.S)
2.
Faculty of Informatics and Computing, Universiti Sultan Zainal Abidin, Besut Campus, 22200 Besut, Terengganu, Malaysia; Email: zahrahtulamani@unisza.edu.my (Z.A.Z.)
3.
Master's Program in Mathematics, Faculty of Mathematics and Natural Sciences, Universitas Padjadjaran, Jatinangor, Sumedang, Jawa Barat 45363, Indonesia; Email: audrey19002@mail.unpad.ac.id (A.A.S.HS.); mugi24002@mail.unpad.ac.id (M.L.)
4.
Doctoral Program in Mathematics, Faculty of Mathematics and Natural Sciences, Universitas Padjadjaran, Jatinangor 45363, Sumedang, Indonesia; Email: astrid23002@mail.unpad.ac.id (A.S.A.)

Received: 15 May 2026 Revised: 06 July 2026 Accepted: 24 July 2026 Published: 24 August 2026
MSC : 03E72, 90B50, 91G10

The evaluation of corporate bond yields is a multi-criteria decision-making problem involving parameter-based uncertainty and heterogeneity in expert judgments. Approaches, including N-soft sets, hesitant N-soft sets, and hesitant fuzzy N-soft sets, remain limited in their ability to simultaneously represent uncertainty at the level of discrete grade assignment and fuzzy membership degrees. To address these limitations, we proposed a hybrid hesitant fuzzy N-soft set (HHFNSS) framework integrated with a soft yield structure. The proposed model represented each object-parameter pair as a set of possible grade combinations along with corresponding sets of membership values, thereby accommodating two-layer hesitancy within a unified algebraic structure. A formal reduction mechanism was developed to transform the set-based representation into a reduced fuzzy N-soft set, which was subsequently processed using a soft yield-generating function to produce a scalar evaluative index. Based on this framework, a structured decision-making algorithm was constructed to rank alternatives. An application to corporate bond evaluation demonstrated that the proposed model yields stable and discriminative rankings that are consistent with the fundamental financial characteristics of the evaluated firms. Comparative analysis indicated that the framework provides a more comprehensive representation of uncertainty than existing models. In contrast, sensitivity analysis confirmed the robustness of the ranking results against variations in input parameters. Overall, the proposed HHFNSS-based soft yield framework offers a flexible and effective approach for multicriteria evaluation under complex uncertainty conditions. This research aligns with Decent Work and Economic Growth (SDG) 8, specifically Target 8.10, by contributing to the strengthening of domestic financial institutions' capacity for transparent and replicable corporate bond evaluation. The proposed framework supports more efficient capital allocation, which is foundational to sustained economic growth and the creation of decent work opportunities.
- hybrid hesitant fuzzy N-soft set,
- soft yield,
- hesitant fuzzy soft set,
- soft set,
- N-soft set,
- uncertainty modeling,
- corporate bond evaluation,
- SDG's 8
Citation: Ema Carnia, Riaman, Sukono, Zahrahtul Amani Zakaria, Moch Panji Agung Saputra, Audrey Ariij Sya'imaa HS, Mugi Lestari, Astrid Sulistya Azahra. A hybrid hesitant fuzzy N-soft set framework for algebraic modeling of corporate bond evaluation under parameter-induced uncertainty[J]. AIMS Mathematics, 2026, 11(8): 26409-26453. doi: 10.3934/math.20261060

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Abstract

The evaluation of corporate bond yields is a multi-criteria decision-making problem involving parameter-based uncertainty and heterogeneity in expert judgments. Approaches, including N-soft sets, hesitant N-soft sets, and hesitant fuzzy N-soft sets, remain limited in their ability to simultaneously represent uncertainty at the level of discrete grade assignment and fuzzy membership degrees. To address these limitations, we proposed a hybrid hesitant fuzzy N-soft set (HHFNSS) framework integrated with a soft yield structure. The proposed model represented each object-parameter pair as a set of possible grade combinations along with corresponding sets of membership values, thereby accommodating two-layer hesitancy within a unified algebraic structure. A formal reduction mechanism was developed to transform the set-based representation into a reduced fuzzy N-soft set, which was subsequently processed using a soft yield-generating function to produce a scalar evaluative index. Based on this framework, a structured decision-making algorithm was constructed to rank alternatives. An application to corporate bond evaluation demonstrated that the proposed model yields stable and discriminative rankings that are consistent with the fundamental financial characteristics of the evaluated firms. Comparative analysis indicated that the framework provides a more comprehensive representation of uncertainty than existing models. In contrast, sensitivity analysis confirmed the robustness of the ranking results against variations in input parameters. Overall, the proposed HHFNSS-based soft yield framework offers a flexible and effective approach for multicriteria evaluation under complex uncertainty conditions. This research aligns with Decent Work and Economic Growth (SDG) 8, specifically Target 8.10, by contributing to the strengthening of domestic financial institutions' capacity for transparent and replicable corporate bond evaluation. The proposed framework supports more efficient capital allocation, which is foundational to sustained economic growth and the creation of decent work opportunities.

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