A Multi-Attribute Decision Making for Investment Decision Based on D Numbers Methods

Investment decision is a traditional multi-attribute decision making (MADM) problem since it has many uncertainty factors and incomplete information such as investment value, cost, sales, etc. D numbers theory is a useful tool to deal with uncertainty factors and incomplete information. In this paper, interval number and D numbers theory are revealed in the uncertain factor and incomplete information of investment decision. The weights of uncertain factors are calculated using entropy weight method. Thus, a new MADM model for investment decision based on D numbers theory is proposed. Numerical example is used to illustrate the efficiency of the proposed method.

Distribution of the Maximum and Minimum of a Random Number of Bounded Random Variables

We study a new family of random variables that each arise as the distribution of the maximum or minimum of a random number N of i.i.d. random variables X1, X2,…, XN, each distributed as a variable X with support on [0, 1]. The general scheme is first outlined, and several special cases are studied in detail. Wherever appropriate, we find estimates of the parameter θ in the one-parameter family in question.

（n, 2n）-Dominating Numbers of Undirected Toroidal Mesh C（3,3,...,3）

The(d,k)-dominating number is a new measure to characterize reliability of resource- sharing in fault tolerant networks.This paper obtains that the(n,2n)-dominating number of the n-dimensional undirected toroidal mesh C(3,3,…,3)is equal to 3(n≥3).

An ECR-PCR rule for fusion of evidences defined on a non-exclusive framework of discernment

In the research of uncertain information processing,Dempster-Shafer Theory(DST)provides a framework for dealing with uncertain information,where evidence is defined on a Frame of Discernment(FOD)consisting of mutually exclusive elements.However,the requirement of exclusiveness on FOD sometimes is not satisfied,as shown in Dezert-Smarandache Theory(DSm T),a derivative of DST.In DSm T,the non-exclusiveness is expressed by propositions’intersection and the fusion of evidence is realized through a Proportional Conflict Redistribution(PCR)rule.In order to handle non-exclusive FODs,a new framework called D Number Theory(DNT)has been proposed recently,which quantifies the non-exclusive degree between propositions different from DSm T.In previous studies,an Exclusive Conflict Redistribution(ECR)rule has been designed in DNT to implement the fusion of evidence defined on a non-exclusive FOD,but there are some deficiencies in the ECR rule.In this paper,a new rule called ECR-PCR rule is proposed by combining the ECR and PCR rules to better implement the fusion of evidence defined on a nonexclusive FOD.Within the proposed rule,the definition of conflict utilizes the idea of ECR’s exclusive conflict,and the disposal of conflict is following the idea of PCR’s proportional redistribution.Properties of the ECR-PCR rule are presented.The effectiveness of the proposed new rule is verified through numerical examples and applications,in comparison with other fusion methods.