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• A second order Takagi-Sugeno (TS2) fuzzy model is proposed. • The proposed model performs better than the original TS fuzzy model in second order nonlinear regression tasks. • Domain adaptation in transfer learning is proved to be effective when optimizing the proposed model. In the regression analysis, Takagi-Sugeno fuzzy model gives a way of exploiting fuzzy logic to tackle nonlinear issues. However, the general Takagi-Sugeno fuzzy model encounters challenges when facing second order regression problems because of its insufficient fitting ability. In this study, the second order Takagi-Sugeno fuzzy model called TS2 fuzzy model is proposed to extend the application scope of the original model. Moreover, domain adaptation in transfer learning is applied to the proposed model by using space transformation. It aims to further reduce the model's cumulative error. The experimental results indicate that the proposed model has a better performance with not much extra processing time when dealing with second order nonlinear regression tasks. [ABSTRACT FROM AUTHOR]

Purpose: The authors consider a dynamic emission-reduction technology investment decision-making problem for an emission-dependent dyadic supply chain consists of a manufacturer and a retailer under subsidy policy for carbon emission reduction. The consumers are assumed to prefer to low-carbon products and formulate a supply chain optimal control problem. Design/methodology/approach: The authors adopt differential game to analyze investment strategies of cost subsidy coefficient with respect to vertical incentive of a manufacturer and a retailer. A comparison analysis under four different decision-making situations, including decentralized decision-making, centralized decision-making, maximizing social welfare, is obtained. Findings: The results show that the economic benefit and environmental pressure have a win–win performance in centralized decision-making. In four different game models, equilibrium strategies, profits and social welfare show changing diversity and have a consistent development trend as time goes on. Research limitations/implications: The authors estimate the demand function is a linear function in this paper. According to the consumers' preference to low-carbon products, consumer's awareness meets the law of diminishing marginal utility like advertising goodwill accumulation. The carbon-sensitive coefficient might be a quadratic expression, which will complicate the problem and be consistent with reality. Practical implications: It captures that there is a necessity to strengthen cooperation and exchange of carbon emission technology among the enterprises by simulation of different decision-makings when government granted cost subsidy. Social implications: The results provide significant guidelines for the supply chain to make decision-makings of emission-reduction technology investment and relevant government departments to determine emission subsidies costs. Originality/value: An endogenous subsidies coefficient is produced by the social welfare function. Distinguished from previous study, it also considered the influences of carbon emission trade policy and consumer preference. [ABSTRACT FROM AUTHOR]