TOPSIS with Belief Structure for Group Belief Multiple Criteria Decision Making

The technique for order performance by similarity to ideal solution （TOPSIS） is one of the major techniques in dealing with multiple criteria decision making （MCDM） problems, and the belief structure （BS） model has been used successfully for uncertain MCDM with incompleteness, impreciseness or ignorance. In this paper, the TOPSIS method with BS model is proposed to solve group belief MCDM problems. Firstly, the group belief MCDM problem is structured as a belief decision matrix in which the judgments of each decision maker are described as BS models, and then the evidential reasoning approach is used for aggregating the multiple decision makers＇ judgments. Subsequently, the positive and negative ideal belief solutions are defined with the principle of TOPSIS. To measure the separation from ideal solutions, the concept and algorithm of belief distance measure are defined, which can be used for comparing the difference between BS models. Finally, the relative closeness and ranking index are calculated for ranking the alternatives. A numerical example is given to illustrate the proposed method.

Optimal Insurance with Background Risk under the Ambiguity and Belief Heterogeneity Structure

In this paper, we discuss the optimal insurance in the presence of background risk while the insured is ambiguity averse and there exists belief heterogeneity between the insured and the insurer. We give the optimal insurance contract when maxing the insured’s expected utility of his/her remaining wealth under the smooth ambiguity model and the heterogeneous belief form satisfying the MHR condition. We calculate the insurance premium by using generalized Wang’s premium and also introduce a series of stochastic orders proposed by [1] to describe the relationships among the insurable risk, background risk and ambiguity parameter. We obtain the deductible insurance is the optimal insurance while they meet specific dependence structures.

Synthetic damage effect assessment through evidential reasoning approach and neural fuzzy inference:Application in ship target

The damage effect assessment of anti-ship missiles combines system science and weapon science,which can provide reference for the assessment of battlefield damage situation.In order to solve the difficulty of heterogeneous data aggregation and the difficulty in constructing the mapping between factors and damage effect,this paper analyzes the specific damage process of the anti-ship missile to the ship,and proposes a synthetic Evidential Reasoning(ER)–Adaptive Neural Fuzzy Inference System(ANFIS)to assess the damage effect.To solve the problem of fuzziness and uncertainty of criteria in the assessment process,the belief structure model is used to transform qualitative and quantitative information into a unified mathematical structure,and ER algorithm is used to fuse the information of lower-level criteria.In order to solve the problem of fuzziness and uncertainty of the information contained in the first-level variables,and the strong non-linear characteristics of the mapping between first-level variables and damage effect,the ANFIS with selfadaptation and self-learning is constructed.The map between the three first-level variables and damage effect is established,and the interaction process of the various factors in the damage effect assessment are clear.Sensitivity analysis shows that assessment model has good stability.The result analysis and comparative analysis show that the process proposed in this paper can effectively assess the damage effect of anti-ship missiles,and all criteria data are objective and comparable.

A new structural reliability index based on uncertainty theory

The classical probabilistic reliability theory and fuzzy reliability theory cannot directly measure the uncertainty of structural reliability with uncertain variables, i.e., subjective random and fuzzy variables. In order to simultaneously satisfy the duality of randomness and subadditivity of fuzziness in the reliability problem, a new quantification method for the reliability of structures is presented based on uncertainty theory, and an uncertainty-theory-based perspective of classical Cornell reliability index is explored. In this paper, by introducing the uncertainty theory, we adopt the uncertain measure to quantify the reliability of structures for the subjective probability or fuzzy variables, instead of probabilistic and possibilistic measures. We utilize uncertain variables to uniformly represent the subjective random and fuzzy parameters, based on which we derive solutions to analyze the uncertainty reliability of structures with uncertainty distributions. Moreover, we propose the Cornell uncertainty reliability index based on the uncertain expected value and variance.Experimental results on three numerical applications demonstrate the validity of the proposed method.