Dependent type systems are the basis of many proof development environments. In Aspinalland Compagnoni's paper, a system λP≤ is proposed as a subtyping extension of the first orderdependent type system λP (also...Dependent type systems are the basis of many proof development environments. In Aspinalland Compagnoni's paper, a system λP≤ is proposed as a subtyping extension of the first orderdependent type system λP (also called An). λP≤ has nice meta-theoretic properties includingsubject reduction and decidability. In this article, v,e give a reformulation of λP≤ t called λII≤.The advantages of λII< include: type level transitivity elimination property and pretypesbasedsubtyping system. These features considerably faCilitate the met-theoretical study and furtherextensions of this system.展开更多
The multiple attribute group decision making problem in which the input arguments take the form of intuitionistic uncertain linguistic information is studied in the paper.Based on the operational principles of intuiti...The multiple attribute group decision making problem in which the input arguments take the form of intuitionistic uncertain linguistic information is studied in the paper.Based on the operational principles of intuitionistic uncertain linguistic variables and the concept of the expected value and accuracy function,some new dependent aggregation operators with intuitionistic uncertain linguistic information including the dependent intuitionistic uncertain linguistic ordered weighted average(DIULOWA)operator,the dependent intuitionistic uncertain linguistic ordered weighted geometric(DIULOWG)operator,the generalized dependent intuitionistic uncertain linguistic ordered weighted aggregation(GDIULOWA)operator and so on are developed,in which the associated weights only depend on the aggregated arguments.Also,we study some desirable properties of the aggregation operators.Moreover,the approach of multiple attribute group decision making with intuitionistic uncertain linguistic information based on the developed operators is proposed.Finally,an illustrative numerical example is given to show the practicality and effectiveness of the proposed approaches.展开更多
文摘Dependent type systems are the basis of many proof development environments. In Aspinalland Compagnoni's paper, a system λP≤ is proposed as a subtyping extension of the first orderdependent type system λP (also called An). λP≤ has nice meta-theoretic properties includingsubject reduction and decidability. In this article, v,e give a reformulation of λP≤ t called λII≤.The advantages of λII< include: type level transitivity elimination property and pretypesbasedsubtyping system. These features considerably faCilitate the met-theoretical study and furtherextensions of this system.
基金Supported by the National Natural Science Foundation of China(71761027)Ningbo Natural Science Foundation(2015A610161)。
文摘The multiple attribute group decision making problem in which the input arguments take the form of intuitionistic uncertain linguistic information is studied in the paper.Based on the operational principles of intuitionistic uncertain linguistic variables and the concept of the expected value and accuracy function,some new dependent aggregation operators with intuitionistic uncertain linguistic information including the dependent intuitionistic uncertain linguistic ordered weighted average(DIULOWA)operator,the dependent intuitionistic uncertain linguistic ordered weighted geometric(DIULOWG)operator,the generalized dependent intuitionistic uncertain linguistic ordered weighted aggregation(GDIULOWA)operator and so on are developed,in which the associated weights only depend on the aggregated arguments.Also,we study some desirable properties of the aggregation operators.Moreover,the approach of multiple attribute group decision making with intuitionistic uncertain linguistic information based on the developed operators is proposed.Finally,an illustrative numerical example is given to show the practicality and effectiveness of the proposed approaches.
