Choquet Integral Based On Triangular Norms And Its Application In Multi-criteria Decision Making

The Choquet integral,one of the most important theories and methods for solving decision problems,has attracted much attention from scholars in the field since it was proposed.The focus of research has gradually shifted to its extensions and their applications,with the emergence of various extensions of the Choquet integral.In 2016,Lucca et al.proposed some recent generalised forms of the Cho-quet integral whose main approach is to replace the product operator in the integral expression by some functions with aggregation,pre-aggregation and ordered direc-tion monotonicity to obtain an aggregated or pre-aggregated function or family of functions.One of the lastest extensions is the Choquet integral based on triangular norms.It replaces the product operator in the Choquet integral with triangular norms to obtain a family of functions,called theC_T-integral.In this paper,based on theC_T-integral proposed by Lucca et al,several properties of theC_T-integral are studied and further generalised,and then this new generalised form is applied to solve a multi-criteria decision making problem to verify its validity.First,some properties of the Choquet integral are systematically investigat-ed and proved by checking whether they are satisfied after the extension to theC_T-integral.Among them,mean value,idempotent,translation invariance,posi-tive homogeneity and duality can be satisfied,but theC_T-integral does not satisfy comonotone additivity.It is concluded that theC_T-integral property is more rig-orously established by considering not only the nature of the Choquet integral but also the nature of the trigonometric modes.Therefore,this part of the study be-longs to the cross-fertilisation of the classical properties of Choquet integrals and the properties of triangular norms.Second,further generalised forms of theC_T-integral are investigated,consid-ering that theC_T-integral proposed by Lucca et al.does not make explicit require-ments on the specific form of the fuzzy measure.In this section,we express the fuzzy measure in theC_T-integral as a specific interval-valued Sugeno probability measure in order to obtain aC_T-integral on the interval-valued Sugeno probability measure,which is more convenient to apply.Finally,to demonstrate the validity of applying theC_T-integral to the interval-valued Sugeno probability measure,it is applied to solve such multi-criteria decision making problems for determining the end-of-life（EOL）strategy for refrigerator com-ponents.Compared to the general Choquet integral,the method proposed in this paper not only improves the calculation process,but also makes the calculation simpler and less computationally intensive.