Chao Fu

Robust evidential reasoning approach with unknown attribute weights

In multiple attribute decision making (MADM), different attribute weights may generate different solutions, which means that attribute weights significantly influence solutions. When there is a lack of sufficient data, knowledge, and experience for a decision maker to generate attribute weights, the decision maker may expect to find the most satisfactory solution based on unknown attribute weights called a robust solution in this study. To generate such a solution, this paper proposes a robust evidential reasoning (ER) approach to compare alternatives by measuring their robustness with respect to attribute weights in the ER context. Alternatives that can become the best with the support of one or more sets of attribute weights are firstly identified. The measurement of robustness of each identified alternative from two perspectives, i.e., the optimal situation of the alternative and the insensitivity of the alternative to a variation in attribute weights is then presented. The procedure of the proposed approach is described based on the combination of such identification of alternatives and the measurement of their robustness. A problem of car performance assessment is investigated to show that the proposed approach can effectively produce a robust solution to a MADM problem with unknown attribute weights.

A method of determining attribute weights in evidential reasoning approach based on incompatibility among attributes

Determine attribute weights in evidential reasoning approach.Combine deviation and decision incompatibilities to generate attribute weights.Use favorable intervals of attribute weights for sensitivity analysis.Use favorable intervals of utilities of assessment grades for sensitivity analysis.Handle subjective constraints on attribute weights and assessment grades. Decisions on attribute weights are important problems in multiple attribute decision making. Many methods have been proposed to create attribute weights which are used to aggregate attributes in a simple additive weighting way. In this paper, a method of deriving attribute weights from incompatibility among attributes and possible constraints on the weights is developed based on the evidential reasoning approach in which attribute aggregation is nonlinear rather than linear. The incompatibility is a flexible combination of deviation incompatibility and decision incompatibility with a relaxation coefficient. The deviation incompatibility measures differences between assessments of alternatives on each attribute and the decision incompatibility quantifies differences between assessments of alternatives on one attribute and the aggregated assessments of the alternatives. For a specific alternative, two pairs of optimization problems with a constraint on the difference between potential weights and the combination of deviation incompatibility and decision incompatibility are designed to generate the favorable intervals of attribute weights and those of utilities of assessment grades. A problem of car performance assessment is investigated to demonstrate the applicability of the proposed method. The method is validated by comparison with other methods of producing attribute weights using the problem.

Integrated evidential reasoning approach in the presence of cardinal and ordinal preferences and its applications in software selection

A combination of cardinal and ordinal preferences in multiple-attribute decision making (MADM) demonstrates more reliability and flexibility compared with sole cardinal or ordinal preferences derived from a decision maker. This situation occurs particularly when the knowledge and experience of the decision maker, as well as the data regarding specific alternatives on certain attributes, are insufficient or incomplete. This paper proposes an integrated evidential reasoning (IER) approach to analyze uncertain MADM problems in the presence of cardinal and ordinal preferences. The decision maker provides complete or incomplete cardinal and ordinal preferences of each alternative on each attribute. Ordinal preferences are expressed as unknown distributed assessment vectors and integrated with cardinal preferences to form aggregated preferences of alternatives. Three optimization models considering cardinal and ordinal preferences are constructed to determine the minimum and maximum minimal satisfaction of alternatives, simultaneous maximum minimal satisfaction of alternatives, and simultaneous minimum minimal satisfaction of alternatives. The minimax regret rule, the maximax rule, and the maximin rule are employed respectively in the three models to generate three kinds of value functions of alternatives, which are aggregated to find solutions. The attribute weights in the three models can be precise or imprecise (i.e., characterized by six types of constraints). The IER approach is used to select the optimum software for product lifecycle management of a famous Chinese automobile manufacturing enterprise.

A belief rule based expert system for predicting consumer preference in new product development

In the decision making process of new product development, companies need to understand consumer preference for newly developed products. A recently developed belief rule based (BRB) inference methodology is used to formulate the relationship between consumer preference and product attributes. However, when the number of product attributes is large, the methodology encounters the challenge of dealing with an oversized rule base. To overcome the challenge, the paper incorporates factor analysis into the BRB methodology and develops a BRB expert system for predicting consumer preference of a new product. Firstly, a small number of factors are extracted from product attributes by conducting both exploratory and confirmatory factor analysis. Secondly, a belief rule base is constructed to model the causal relationships between the characteristic factors and consumer preference for products using experts knowledge. Furthermore, a BRB expert system is developed for predicting consumer preference in new product development, where the factor values transformed from product attributes are taken as inputs. Relevant rules in the system are activated by the input data, and then the activated rules are aggregated using the evidential reasoning (ER) approach to generate the predicted consumer preference for each product. Finally, the BRB expert system is illustrated using the data collected from 100 consumers of several tea stores through a market survey. The results show that the prototype of the BRB expert system has superior fitting capability on training data and high prediction accuracy on testing data, and it has great potential to be applied to consumer preference prediction in new product development.

Determining attribute weights to improve solution reliability and its application to selecting leading industries

In multiple attribute decision analysis, many methods have been proposed to determine attribute weights. However, solution reliability is rarely considered in those methods. This paper develops an objective method in the context of the evidential reasoning approach to determine attribute weights which achieve high solution reliability. Firstly, the minimal satisfaction indicator of each alternative on each attribute is constructed using the performance data of each alternative. Secondly, the concept of superior intensity of an alternative is introduced and constructed using the minimal satisfaction of each alternative. Thirdly, the concept of solution reliability on each attribute is defined as the ordered weighted averaging (OWA) of the superior intensity of each alternative. Fourthly, to calculate the solution reliability on each attribute, the methods for determining the weights of the OWA operator are developed based on the minimax disparity method. Then, each attribute weight is calculated by letting it be proportional to the solution reliability on that attribute. A problem of selecting leading industries is investigated to demonstrate the applicability and validity of the proposed method. Finally, the proposed method is compared with other four methods using the problem, which demonstrates the high solution reliability of the proposed method.

Weighted cautious conjunctive rule for belief functions combination

Denoeux proposed an operator called the cautious conjunctive rule (CCR) to combine non-dogmatic belief functions (i.e., the frame is considered a focal element) from reliable dependent sources, which can occur in practice. However, in cases such as uncertain multiple attribute and group decision analyses, belief functions may denote data that vary in importance. This paper extends CCR as a weighted CCR (WCCR) to combine belief functions in consideration of their relative weights in such situations. Properties of WCCR are analyzed, proven, and demonstrated using numerical examples. In particular, the consideration of relative weights enables WCCR to combine dogmatic belief functions. The normalized WCCR is further constructed and used to assess the trustworthiness of a hospital information system employed in many hospitals in Anhui Province, China.

Constructing confidence belief functions from one expert

It has become a noticeable topic on how to construct belief functions from the quantitative and qualitative opinions of one expert. The existing methods proposed in the literature addressing the topic, however, have paid little attention to the bounded rationality (BR) of the expert. This paper introduces a confidence belief function (BF) qualitatively and quantitatively under the assumption of BR, generated from a set of BFs sampled from the expert by interacting with a number of reliable information providers in a valid time interval. Besides, a procedure for quantitatively producing a confidence BF is presented, which is based on a statistical method mainly involving three steps, dividing the set of BFs into a number of non-conflicting or consistent subsets, forming the confidence interval-valued belief structures (IBSs) of the subsets, and integrating the IBSs into the confidence IBS of the set. A numerical example about a manager in a telecommunications company deciding whether to upgrade a business campaign or not is given to show the procedure for generating a confidence BF. Since the method of generating a confidence BF is on the power set of a frame of discernment, its scalability is also discussed.

Analysis of fuzzy Hamacher aggregation functions for uncertain multiple attribute decision making

As generalizations of algebraic and Einstein t-norms and t-conorms, Hamacher t-norm and t-conorm have been widely applied in fuzzy multiple attribute decision making (MADM) to combine assessments on each attribute, which are generally expressed by Atanassovs intuitionistic fuzzy (AIF) numbers, interval-valued intuitionistic fuzzy (IVIF) numbers, hesitant fuzzy (HF) elements, and dual hesitant fuzzy (DHF) elements. Due to the fact that AIF numbers and HF elements are special cases of IVIF numbers and DHF elements, respectively, two propositions can be established from analyzing numerical examples and real cases concerning MADM with IVIF and DHF assessments in the literature: (1) the monotonicity of alternative scores derived from Hamacher arithmetic and geometric aggregation operators with respect to the parameter r in Hamacher t-norm and t-conorm; and (2) the relationship between alternative scores generated by Hamacher arithmetic and geometric aggregation operators, given the same r. Here, we provide the theoretical proof of these two propositions in the context of MADM with IVIF and DHF assessments. With the theoretical support of these propositions, the meaning of r in MADM is explained, and a new method is proposed to compare alternatives in MADM with consideration of all possible values of r. Two numerical examples are solved by the proposed method and the other two existing methods to demonstrate the applicability and validity of the proposed method and highlight its advantages.

Analyzing the applicability of Dempster's rule to the combination of interval-valued belief structures

To combine interval-valued belief structures (IBSs), it is necessary to investigate the applicability of Dempsters rule to know whether Dempsters rule is adequate to be used and whether other alternatives are needed. This makes it significant to investigate IBSs pairwise relationships (IPRs) since they have an important impact on the applicability of Dempsters rule to the combination of two IBSs. IPRs can be constructed based on beliefs pairwise relationships (BPRs), so this paper proposes a consistency measure to quantitatively divide BPRs into three categories. Using a consistency interval between two IBSs that is obtained by solving a pair of optimization problems constructed based on the consistency measure, IPRs are quantified and divided into six categories on the basis of BPRs. According to IPRs, the applicability of Dempsters rule to the combination of two IBSs is recommended. Finally, the applicability of Dempsters rule to the combination of multiple IBSs is investigated.

A novel evidential reasoning based method for software trustworthiness evaluation under the uncertain and unreliable environment

Highlights? The evidential reasoning approach based software trustworthiness evaluation method. ? Two discounting factor approaches to measuring the reliability degree of trustworthiness evaluations. ? The new description of the software trustworthiness evaluation problem. ? The decision rules for software trustworthiness evaluation. Many software trustworthiness evaluation (STE) problems include both quantitative and qualitative indicators with unreliability and various kinds of uncertainties. In this paper, a novel evidential reasoning (ER) based STE method is developed to model these problems. Considering the reliability of objective and subjective trustworthiness evaluations, two discounting factor estimation approaches to STE are proposed to meet the demands of the unreliable trustworthiness evaluations pretreatment. In order to characterize the degree of evaluation unreliability, the utility theory based trustworthiness evaluation distance is constructed to characterize the degree of evaluation. An intelligent software embedded in the liquid metal detection system is evaluated by the ER based STE method to demonstrate its detailed implementation process, and its validity and applicability.