A Regret Theory and Frank Aggregation Operator-Based Spherical Cubic Fuzzy CoCoSo Decision Method

Yuan Rong; Huiyi Qiu; Qian Zhang; Wenxue Zhang

Authors

Yuan Rong School of medical information and engineering, Ningxia Medical University, 750004, Yinchuan, China Author https://orcid.org/0000-0001-7576-5276
Huiyi Qiu School of medical information and engineering, Ningxia Medical University, 750004, Yinchuan, China Author https://orcid.org/0009-0007-1000-1372
Qian Zhang School of medical information and engineering, Ningxia Medical University, 750004, Yinchuan, China Author https://orcid.org/0009-0006-0036-1860
Wenxue Zhang School of medical information and engineering, Ningxia Medical University, 750004, Yinchuan, China Author https://orcid.org/0000-0001-8925-539X

Keywords:

Spherical cubic fuzzy set, Frank t-norm and s-norm, LOPCOW, CoCoSo

Abstract

As an extension of spherical fuzzy sets, spherical cubic fuzzy (SCF) sets can more effectively handle uncertain data represented by cubic fuzzy numbers. Nevertheless, existing research on SCF sets is primarily focused on algebraic operations and rarely considers the psychological behavior of experts in decision-making. To address these limitations, this study proposes a novel decision-making method based on Frank aggregation operators and a regret theory-based Combined Compromise Solution (CoCoSo) model in a spherical cubic fuzzy environment. Specifically, SCF sets are used to represent uncertain preference information by combining the advantages of spherical fuzzy sets and cubic sets. We then define new SCF operations based on Frank norms and propose four SCF aggregation operators to obtain collective assessments from multiple experts. Subsequently, the criteria weights are determined using an enhanced logarithmic percentage change-driven objective weighting (LOPCOW) method incorporating the SCF score function. To rank the alternatives while considering the psychological behavior of decision-makers, we develop an improved CoCoSo model by integrating regret theory with the proposed SCF aggregation operators. The proposed decision-making method is applied to the diagnosis of patients with cardiovascular disease under uncertainty. Sensitivity and comparative analyses are conducted to evaluate the robustness and effectiveness of the proposed regret theory-based spherical cubic fuzzy CoCoSo decision-making method.

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