Group Ranking Problem Research Articles

Consistency of total fuzzy relations: New algorithms to detect and repair inconsistent judgments

Fuzzy orders, especially T-preorders, can express the vague priority over a list of alternatives. The cardinal consistency of such relations is achieved through the T-transitivity condition, while the ordinal consistency of the final decision at a given threshold α∈(0,1] is not guaranteed by the T-consistency. This paper investigates the problem of ordinal consistency, as the minimum requirement for a reliable judgment, of a partial preference induced by a fuzzy relation at a given level α∈(0,1], so-called α-preference relation. We first define new concepts of T−L-cyclic and T-consistency at a given level α for fuzzy relations. Based on digraph theory, a new methodology is designed for finding the locations of all consistent and inconsistent L-cycles of an α-preference. An algorithm is proposed to eliminate the ordinal inconsistency through the TM-transitivity. Meanwhile, a new T-consistency index is introduced to measure the acceptable consistency level of fuzzy relations. Furthermore, some results concerning the ordinal consistency of T-preorders are applied to design another algorithm for creating a consistent collective judgment based on initial fuzzy assessments of alternatives in a group ranking problem. The proposed method constructs the consistent fuzzy order matrix for each case (expert), then calculates the group consensus by aggregating these matrices. The collective fuzzy order is then checked for consistency level. Finally, a numerical example with a real dataset is given to illustrate the application of the proposed method in a ranking problem.

A new consensus mining approach to group ranking problems involving different intensities of preferences

Discovering the group priority from a set of user preferences plays an important role in group decision making because of its extensive applications in practice. In most group ranking problems, users are supposed to input a ranking of alternatives regardless of the intensities of preference. However, if two users specify that they prefer A to B, the intensities of preference may be quite different. In addition, most researchers have tried to determine a total ranking list by minimizing total differences among user preferences, but users might have little consensus on the final results. This study aims to propose a new consensus-based approach for group ranking problems involving different intensities of preference. Stemming from the concept of consensus mining, consensus relationships are discovered by three accumulation matrices and consensus thresholds. An optimization model incorporating the consensus relationships and the concept of Borda majority count is then developed to derive a total ranking list. Compared to previous studies, the proposed approach can treat group ranking problems involving different intensities of preference, reduce the occurrence of ties, and achieve a total ranking list reflecting the consensus preference of the majority of users.

Discovering Consensus Preferences Visually Based on Gower Plots

Group-ranking problems are widely encountered decision problems which combine personal preferences to form an integrated group priority; however, providing support to solve group-ranking problems is difficult because each person has his/her own viewpoint regarding how such decisions should be made. In addition, many researchers have shown that visual aids are useful in helping users comprehend decision backgrounds. Therefore, determining how to support the group-ranking process and providing visual aids is an important issue. This study proposes a novel graphical approach to discover group consensus sequences. First, a counting-based data mining approach is constructed to discover a consensus preference matrix. Second, an ordinal Gower plot can be drawn whereby group consensus sequences can be directly observed. Unlike previous methods, the proposed approach can discover group consensus sequences without involving tedious candidate generation and exhaustive search processes, derive a total ranking list, as well as provide visual aids to users.

Identifying conflict patterns to reach a consensus – A novel group decision approach

In recent years, the group ranking problem has become an important subject of study. In most group ranking problems, the focus is on identifying consensuses. No previous research has involved identifying conflicting opinions, called conflict patterns in this paper, among decision-makers. We define conflict patterns as orderings of alternatives that have roughly the same numbers of advantages and disadvantages. Conflict patterns can reveal the ranking of which alternatives are the most controversial among decision-makers and who the supporters and opponents are. Using conflict pattern data, decision-makers can communicate with people with differing opinions and attempt to resolve the differences.In this study, an algorithm, Mining Conflict Patterns, was developed to identify conflict patterns from users’ partial ranking data. Extensive experiments were conducted using synthetic and real data sets. The results indicate that the proposed method is computationally efficient and can effectively identify conflict patterns among all users.

A new group ranking approach for ordinal preferences based on group maximum consensus sequences

Group ranking problems involve aggregating individual rankings to generate group ranking which represents consolidated group preference. Group ranking problems are commonly applied in real-world decision-making problems; however, supporting a group decision-making process is difficult due to the existence of multiple decision-makers, each with his/her own opinions. Hence, determining how to best aid the group ranking process is an important consideration. This study aims to determine a total ranking list which meets group consensus preferences for group ranking problems. A new group consensus mining approach based on the concept of tournament matrices and directed graphs is first developed; an optimization model involving maximum consensus sequences is then constructed to achieve a total ranking list. Compared to previous methods, the proposed approach can generate a total ranking list involving group consensus preferences. It can also determine maximum consensus sequences without the need for tedious candidate generation processes, while also providing flexibility in solving ranking problems using different input preferences that vary in format and completeness. In addition, consensus levels are adjustable.

A novel approach to exploring maximum consensus graphs from users’ preference data in a new age environment

Many methods have been used to produce coherent aggregated results from individual's preference data, such as decision-making support systems, group recommendation systems, and so on. This study proposes a new framework where a graph model is used to represent user preferences and develops a new algorithm for detecting the maximum consensus and majority user group. The maximum consensus graph can be used to illustrate the preferences of the majority of the users. Similarly, discovering the segment of users who belong to the majority is useful information for the decision maker in order to produce consensus opinions and for market mangers to propose the most feasible strategies. In this study we initiate a new approach to the group ranking problem. Experiments using synthetic and real datasets show the model's computational efficiency, scalability, and effectiveness.

A New Approach to the Group Ranking Problem: Finding Consensus Ordered Segments from Users’ Preference Data

ABSTRACTThe group ranking problem involves constructing coherent aggregated results from users’ preference data. The goal of most group ranking problems is to generate an ordered list of all items that represents the user consensus. There are, however, two weaknesses to this approach. First, a complete list of ranked items is always output even when there is no consensus or only a slight consensus. Second, due to similarity of performance, in many practical situations, it is very difficult to differentiate whether one item is really better than another within a set. These weaknesses have motivated us to apply the clustering concept to the group ranking problem, to output an ordered list of segments containing a set of similarly preferred items, called consensus ordered segments. The advantages of our approach are that (i) the list of segments is based on the users’ consensuses, (ii) the items with similar preferences are grouped together in the same segment, and (iii) the relationships between items can be easily seen. An algorithm is developed to construct the consensus of the ordered segments from the users’ total ranking data. Finally, the experimental results indicate that the proposed method is computationally efficient, and can effectively identify consensus ordered segments.

A novel group ranking model for revealing sequence and quantity knowledge

The aggregation of individuals’ preferences into a consensus ranking is a group ranking problem which has been widely utilized in various applications, such as decision support systems, recommendation systems, and voting systems. Gathering the comparison of preferences and aggregate them to gain consensuses is a conventional issue. For example, b>c⩾d⩾a indicates that b is favorable to c, and c (d) is somewhat favorable but not fully favorable to d (a), where>and⩾are comparators, and a, b, c, and d are items. Recently, a new type of ranking model was proposed to provide temporal orders of items. The order, b&c→a, means that b and c can occur simultaneously and are also before a. Although this model can derive the order ranking of items, the knowledge about quantity-related items is also of importance to approach more real-life circumstances. For example, when enterprises or individuals handle their portfolios in financial management, two considerations, the sequences and the amount of money for investment objects, should be raised initially. In this study, we propose a model for discovering consensus sequential patterns with quantitative linguistic terms. Experiments using synthetic and real datasets showed the model’s computational efficiency, scalability, and effectiveness.

Mining consensus preference graphs from users' ranking data

The group ranking problem consists of constructing coherent aggregated results from preference data provided by decision makers. Traditionally, the output of a group ranking problem can be classified into ranking lists and maximum consensus sequences. In this study, we propose a consensus preference graph approach to represent the coherent aggregated results of users' preferences. The advantages of our approach are that (1) the graph is built based on users' consensuses, (2) the graph can be understood intuitively, and (3) the relationships between items can be easily seen. An algorithm is developed to construct the consensus preference graph from users' total ranking data. Finally, extensive experiments are carried out using synthetic and real data sets. The experimental results indicate that the proposed method is computationally efficient, and can effectively identify consensus graphs.

An approach to group ranking decisions in a dynamic environment

The group ranking problem is used to construct coherent aggregate results from preference data provided by decision makers. Although there have been different input formats used to represent user preferences, they share a common weakness, that the input mode is static. In other words, users must provide all the preference data at one time. To overcome this weakness, we propose a framework which allows users to provide partial and/or incomplete preference data at multiple times. Since this is a complicated issue, we specifically focus on a particular aspect as a first attempt at this framework. Accordingly, we reexamine a variant of the group ranking problem, the maximum consensus mining problem, which will give the longest ranking lists of alternatives that agree with the majority and disagree only with the minority, under the dynamic input mode assumption. An algorithm is developed to determine the maximum consensus sequences from the users' partial ranking data. Finally, extensive experiments are carried out using synthetic data sets. The results indicate that the proposed method is computationally efficient, and can effectively identify consensus among all users.

Methodologies and Algorithms for Group-Rankings Decision

The problem of group ranking, also known as rank aggregation, has been studied in contexts varying from sports, to multicriteria decision making, to machine learning, to ranking Web pages, and to behavioral issues. The dynamics of the group aggregation of individual decisions has been a subject of central importance in decision theory. We present here a new paradigm using an optimization framework that addresses major shortcomings that exist in current models of group ranking. Moreover, the framework provides a specific performance measure for the quality of the aggregate ranking as per its deviations from the individual decision-makers’ rankings. The new model for the group-ranking problem presented here is based on rankings provided with intensity—that is, the degree of preference is quantified. The model allows for flexibility in decision protocols and can take into consideration imprecise beliefs, less than full confidence in some of the rankings, and differentiating between the expertise of the reviewers. Our approach relaxes frequently made assumptions of: certain beliefs in pairwise rankings; homogeneity implying equal expertise of all decision makers with respect to all evaluations; and full list requirement according to which each decision maker evaluates and ranks all objects. The option of preserving the ranks in certain subsets is also addressed in the model here. Significantly, our model is a natural extension and generalization of existing models, yet it is solvable in polynomial time. The group-rankings models are linked to network flow techniques.

An agent model based on ideas of concordance and discordance for group ranking problems

Classical decision theory does not provide a suitable theoretical basis for designing group decision agents because the concept of collective preference is not well defined. Here, we propose a model based on fuzzy preferences. A degree of truth is associated with the group preference relation. Fairness, equity, power of majority and compromise with significant minorities are modeled using concordance and discordance principles, reflecting the natural heuristic of collaborative groups making acceptable consensus decisions. Exploitation of the fuzzy group preference relation is performed solving a multiobjective optimization problem with an evolutionary algorithm. The designed agent shows very good performance in some test examples, obtaining better results than Condorcet and Borda methods.

A new method for group decision support based on ELECTRE III methodology

Group decision is usually understood as the reduction of different individual preferences on a given set to a single collective preference. At present, there are few approaches which solve the group ranking problem with multiple criteria in a widely acceptable way. Often, they rest on a poor heuristic which makes a decision about consensus ranking difficult to support. This paper presents an extension of the ELECTRE III multicriteria outranking methodology to assist a group of decision makers with different value systems to achieve a consensus on a set of possible alternatives. Our proposal starts with N individual rankings and N corresponding valued preference functions, and uses the natural heuristic provided by ELECTRE methodology for obtaining a fuzzy binary relation representing the collective preference. A comparison of this method with PROMETHEE II for group decision is carried out. We found that, in this particular application, the proposed heuristic based on majority rules combined with concessions to significant minorities, performs relatively better than a compensatory scheme based on a net flow weighted sum function.

A weak order solution to a group ranking and consistency-driven pairwise comparisons

A novel non-numerical algorithm, based on a partial order, for solving a group ranking problem is compared with the more traditional consistency-driven approach. Both approaches are based on the fundamental concept of pairwise comparisons. Potential applications are discussed.