Cumulative Prospect Theory: Performance Evaluation of Government Purchases of Home-Based Elderly-Care Services Using the Pythagorean 2-tuple Linguistic TODIM Method

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Abstract
The aging trend of China’s population is increasing, and the pension problem is becoming increasingly prominent. The pension mode provided by the government alone can no longer meet the social demand, and the government’s purchase of home-based care services from social organizations has become a new trend. In order to improve the efficiency and quality of pension services, a reasonable performance evaluation model needs to be established. Performance evaluations of home-based elderly-care services purchased by the government are problematic as a result of multiple-attribute group decision-making (MAGDM), as the problems are not single-attribute or single-expert issues. The extended TODIM not only integrates the advantages of cumulative prospect theory (CPT) into a consideration of the psychological factors of DMs, but also retains the superiority of the classical TODIM in relative dominance. The Pythagorean 2-tuple linguistic sets (P2TLSs) could easily depict qualitative assessment information related to the government’s purchase of home-based care services. Thus, in this paper, we extend the TODIM method based on the cumulative prospect theory (CPT) to the Pythagorean 2-tuple linguistic sets (P2TLSs) and propose a Pythagorean 2-tuple linguistic CPT-TODIM (P2TL-CPT-TODIM) method for MAGDM. The P2TL-CPT-TODIM method was proven superior to the classical one through a case study that included a performance evaluation of a home-based elderly-care service purchased by the government. Meanwhile, a comparison with the P2TL-CPT-TODIM method was performed to demonstrate the stability and effectiveness of the designed method.

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