Attribute Normalization Approaches to Group Decision-making and Application to Software Reliability Assessment

Because of the complexity of decision-making environment, the uncertainty of fuzziness and the uncertainty of grey maybe coexist in the problems of multi-attribute group decision making. In this paper, we study the problems of multi-attribute group decision making with hybrid grey attribute data (the precise values, interval numbers and linguistic fuzzy variables coexist, and each attribute value has a certain grey degree), and present a new grey hybrid multi-attribute group decision making method based on grey linguistic 2-tuple. Concretely, the concept of grey linguistic 2-tuple is defined based on the traditional linguistic 2-tuple, and the transformation methods of transforming the precise values, interval numbers and linguistic fuzzy variables into the grey linguistic 2-tuples are presented respectively. Further, a new grey linguistic 2-tuple weighted averaging (emph{GLTWA}) operator is presented to aggregate multiple decision makers' individual decision information into comprehensive decision information, and then a ranking method based on grey 2-tuple correlation degree is presented to rank all alternatives and to select the winners. An application decision making example of supplier selection is also given to validate the method developed and to highlight the implementation, practicality and effectiveness of the presented method.

In the problem of group decision-making, the information about the decision makers' preferences is not complete due to factors of the quality of human resource and the influence of environment. The information gained by decision making can be loss or hazy. When it is hazy the values of the objects to be appraised are interval grey numbers. The group decision making problems including the grey number are called the grey group decision-making problems. Combining the thoughts and methods of the grey system with the classic group decision-making theory, the grey group decision making problems are discussed. In this paper, we develop a GREY DEMATEL method for group decision-making to gather group ideas and analyze the cause-effect relationship of complex problems in grey environments. Procedures of the GREY DEMATEL method are then proposed. Using the GREY DEMATEL procedures, the involved criteria of a system (or subsystem) are separated into the cause and effect groups for helping decision-makers focus on those criteria that provide great influence. Finally, a practical example is used to show feasibility and effectiveness of the proposed approach.

Consistency and consensus reaching process for group decision making based on complete interval distributed preference relations under social network analysis

Group decision-making, in which a collective decision needs to be derived from individual agents’ preferences has been an active area of research. In group decisionmaking, autonomous agents need some procedures or mechanisms that can collect preference information from them and make a decision; or some protocols that enable them to be involved in the decision process, to interact with each other and to jointly make a collective decision. Examples include preference aggregation mechanisms, negotiation protocols, voting procedures, and auctions. This thesis studies the problem of agent-based group decision-making in various problem settings, proposing several efficient approaches to support multiple agents in reaching efficient and fair collective decisions overmultiple issues. The research work in this thesis can be divided into two parts, addressing the agent-based group decision-making problem in circumstances in which there is, respectively, complete and incomplete information available. The first part of this thesis focuses on preference aggregation in combinatorial domains, provided all agents’ preferences. Structured preferences Conditional Preference Network (CP-nets) and its variant Trade-off enhanced CP-nets (TCP-nets) are used as formal models for representing the agents’ preferences in group decision-making. Before going into the problem of making a group decision from a collection of CP-nets or TCP-nets, the problem of individual preference reasoning is studied and a computationally efficient heuristic algorithm for dominance testing in CP-nets, which forms the basis for many group decision-making mechanisms, is introduced. Subsequently, we consider the group decision-making problem with multiple agents’ CP-nets and TCP-nets. As the space of possible outcomes in combinatorial domains has a size exponential in the number of variables, computational complexity in group decision-making will be one of the issues that need to be addressed. Two computationally efficient approaches are proposed in order to support agent-based group decisionmaking in combinatorial domains with different decision criteria: (i) an approach that converts the qualitative preferences derived from CP-nets or TCP-nets into numerical penalty scoring functions, and then searches for an optimal collective decision based on the individual penalty scores; and (ii) an approach that focuses on combinatorial vote and computes the winners (i.e., winning alternatives) from a collection of CP-nets according to Majority voting rule. The second part of this thesis is concerned with the disadvantage of disclosing preference information in group decision-making and considers the incomplete information setting. Two negotiation approaches are presented in order to support agent-based group decision-making in, respectively, combinatorial domains and in domains with multiple continuous issues. Firstly, a negotiation protocol in combinatorial domains is proposed, which enables agents to distributively make decisions and leads them to Pareto-optimal agreements under incomplete information setting. Then for the domains with multiple continuous issues, a cooperative mediated negotiation approach is proposed to support the agents searching for joint utility gains and reaching an efficient and fair agreement. For every approach introduced in this thesis, experiments are carried out and the results are presented and analysed in order to provide insights into the performance of these approaches.

Covering based intuitionistic fuzzy (IF) rough set is a generalization of granular computing and covering based rough sets. By combining covering based rough sets, IF sets and fuzzy rough sets, we introduce three classes of coverings based IF rough set models via IF$$\beta $$-neighborhoods and IF complementary $$\beta $$-neighborhood (IFC$$\beta $$-neighborhood). The corresponding axiomatic systems are investigated, respectively. In particular, the rough and precision degrees of covering based IF rough set models are discussed. The relationships among these types of coverings based IF rough set models and covering based IF rough set models proposed by Huang et al. (Knowl Based Syst 107:155–178, 2016). Based on the theoretical analysis for coverings based IF rough set models, we put forward intuitionistic fuzzy TOPSIS (IF-TOPSIS) methodology to multi-attribute decision-making (MADM) problem with the evaluation of IF information problem. An effective example is to illustrate the proposed methodology. Finally, we deal with MADM problem with the evaluation of fuzzy information based on CFRS models. By comparative analysis, we find that it is more effective to deal with MADM problem with the evaluation of IF information based on CIFRS models than the one with the evaluation of fuzzy information based on CFRS models.

Compatibility measures and consensus models for group decision making with intuitionistic multiplicative preference relations

Evaluation of quality goals is an important issue in process management, which essentially is a multi-attribute decision-making (MADM) problem. The process of assessment inevitably involves uncertain information. The two crucial points in an MADM problem are to obtain weight of attributes and to handle uncertain information. D number theory is a new mathematical tool to deal with uncertain information, which is an extension of evidence theory. The fuzzy analytic hierarchy process (FAHP) provides a hierarchical way to model MADM problems, and the comparison analysis among attributes is applied to obtain the weight of attributes. FAHP uses a triangle fuzzy number rather than a crisp number to represent the evaluation information, which fully considers the hesitation to give a evaluation. Inspired by the features of D number theory and FAHP, a D-FAHP method is proposed to evaluate quality goals in this paper. Within the proposed method, FAHP is used to obtain the weight of each attribute, and the integration property of D number theory is carried out to fuse information. A numerical example is presented to demonstrate the effectiveness of the proposed method. Some necessary discussions are provided to illustrate the advantages of the proposed method.

Picture fuzzy sets (PFSs) can be used to handle real-life problems with uncertainty and vagueness more effectively than intuitionistic fuzzy sets (IFSs). In the process of information aggregation, many aggregation operators under PFSs are used by different authors in different fields. In this article, a multi-attribute decision-making (MADM) problem is introduced utilizing harmonic mean aggregation operators with trapezoidal fuzzy number (TrFN) under picture fuzzy information. Three harmonic mean operators are developed namely trapezoidal picture fuzzy weighted harmonic mean (TrPFWHM) operator, trapezoidal picture fuzzy order weighted harmonic mean (TrPFOWHM) operator and trapezoidal picture fuzzy hybrid harmonic mean (TrPFHHM) operator. The related properties about these operators are also studied. At last, an MADM problem is considered to interrelate among these operators. Furthermore, a numerical instance is considered to explain the productivity of the proposed operators.

Multi-attribute sequential decision problem with optimizing and satisficing attributes

To quantify the influence of decision makers’ psychological factors on the group decision process, this paper develops a new class of aggregation operators based on reference-dependent utility functions (RUs) in multi-attribute group decision analysis. RUs include S-shaped RU and non-S-shaped RU. Each RU affords a framework where the psychological factors explicitly enter the decision problem via the basic utility function, reference point and loss aversion coefficient. Under the general framework, we derive a generalized ordered weighted S-shaped RU proportional averaging (GOSP) operator and a generalized ordered weighted non-S-shaped RU proportional averaging (GONSP) operator, respectively. The GOSP operator implies the risk attitude of the DM for relative losses is risk-seeking, while GONSP operator indicates the risk attitude in this case is risk-averse. As a special case, GONSP operator can degenerate into GOWPA operator which means that the attitude of the DM is risk-neutral. Each operator satisfies the desirable properties of general operator, i.e., monotonicity, commutativity, idempotency and boundedness. Furthermore, we consider hyperbolic absolute risk aversion (HARA) function as the basic utility function, and define an S-shaped HARA and a non-S-shaped HARA utility functions. Based on the two new RUs, we propose GOSP–HARA operator and GONSP–HARA operator. Every operator covers many existing aggregation operators. To ascertain weights of such operators, the paper builds an attribute-deviation weight model and a DMs-deviation weight model. Based on these RU operators and weight models, an approach is addressed for solving multiple attribute group decision-making problem. At last, an example is provided to show the feasible of our approach.

With respect to the multiattribute decision-making (MADM) problem in which the attributes have interdependent or interactive phenomena under the interval-valued intuitionistic fuzzy environment, we propose a group decision-making approach based on the interval-valued intuitionistic fuzzy Einstein geometric Choquet integral operator (IVIFEGC). Firstly, the Einstein operational laws and some basic principle on interval-valued intuitionistic fuzzy sets are introduced. Then, the IVIFEGC is developed and some desirable properties of the operator are studied. Further, an approach to multiattribute group decision-making with interval-valued intuitionistic fuzzy information is developed, where the attributes have interdependent phenomena. Finally, an illustrative example is used to illustrate the developed approach.

Evidential reasoning(ER) is one of the multi-attribute decision making(MADM) approaches that can cope with uncertainties and ambiguities which may caused by the subjective judgments of decision makers. In a MADM problem, many kinds of indicators are always involved, for instance, profit indicator, cost indicator, deviated indicator, fixed indicator and so on. The present ER approach only considers the first three kinds of indicator, so it limits the application of the ER based assessment approach. In the paper, the ER based MADM approach is extended to deal with fixed indicator. Specifically, we will analyze the frame of discernment of fixed indicator, and the transformation methods from the assessment of fixed indicator to probability assignment on evaluation grades are also given. So we will get the ER approach based on profit indicator, cost indicator and fixed indicator.

Multi-attribute decision making (MADM) methods have been widely used in the strategic planning of electric utilities for selecting the best resource strategy with regard to the chosen attributes. In many MADM problems, however, the information available to the decision-maker (DM) is often imprecise due to inaccurate attribute measurements and inconsistent priority judgments. This paper presents an interval-based MADM approach in support of the decision making process with imprecise information. The proposed MADM methodology is based on the model of lineal additive utility function but extends the problem formulation with the measure of composite utility variance. Its main contribution is to help the DM gain insight into how the imprecise data may affect the choice toward the best solution and how a set of acceptable alternatives may be identified with certain confidence. Sample case studies are provided to illustrate the concepts introduced in this paper.

Neutrosophic theories and methods are suitable for handling a variety of uncertain information, especially in complex decision-making situations. Nowadays, how to study multi-attribute group decision-making (MAGDM) problems in neutrosophic environments is a vital task for scholars and practitioners. Granular computing is a popular mathematical framework for uncertain problems, and it has been proved as a useful tool for solving MAGDM problems. In this chapter, a new neutrosophic multigranulation model for MAGDM is proposed, and some theoretical models and decision-making algorithms are presented. Finally, some case studies and comparative analysis are performed to show the merit of the presented models and algorithms. In general, this chapter is conducive to neutrosophic decision-making communities and intelligent decision-making methods.

Recent studies have identified that multi-criteria group analysis methods should take the concepts of risk and uncertainty into account. In some real-life situations, determining the exact values for the potential alternatives' performances and criteria weights is so difficult. To overcome with these situations, their values should be regarded as fuzzy and fuzzy intervals. In this respect, interval-valued hesitant fuzzy sets (IVHFSs) as a suitable modern fuzzy sets theory can be considered because this theory allows decision makers (DMs) to assign some interval-values membership degrees for an alternative in terms of selected criteria under a set to margin of errors. Hence, this paper proposes a novel soft computing approach, namely IVHF-MCGA, based on new interval-valued hesitant fuzzy complex proportional assessment (IVHF-COPRAS) method that can be applied in solving the multi-criteria group decision-making (MCGDM) problems under uncertainty. In this approach, preference values of potential alternatives versus the selected criteria and weights of each criterion are expressed by linguistic variables and then are transformed to interval-valued hesitant fuzzy elements (IVHFEs). In addition, an interval-valued hesitant fuzzy entropy (IVHF-entropy) method is extended to determine the criteria weights by considering the DMs' opinions about the relative importance. Also, a new interval-valued hesitant fuzzy compromise solution (IVHF-CS) method is introduced to estimate the weight of each DM in the group decision-making process along with the last aggregation for the DMs' judgments to avoid the data loss. Then, three practical applications about the robot selection, industrial site selection and rapid prototyping process selection problems are considered to explain steps of the proposed IVHF-MCGA approach and to indicate its validity and applicability. Finally, a comparative analysis between the proposed approach and fuzzy group TOPSIS method is presented based on four comparison parameters, including adequacy to changes of alternatives and criteria, agility in decision process, influence of DMs' weights and impact of first and last aggregations, to show its suitability.