This paper studies the allocation of indivisible items to agents, when each agent’s preferences are expressed by means of a directed acyclic graph. The vertices of each preference graph represent the ...subset of items approved of by the respective agent. An arc (a,b) in such a graph means that the respective agent prefers item a over item b. We introduce a new measure of dissatisfaction of an agent by counting the number of non-assigned items which are approved of by the agent and for which no more preferred item is allocated to the agent. Considering two problem variants, we seek an allocation of the items to the agents in a way that minimizes (i) the total dissatisfaction over all agents or (ii) the maximum dissatisfaction among the agents. For both optimization problems we study the status of computational complexity and obtain NP-hardness results as well as polynomial algorithms with respect to natural underlying graph structures, such as stars, trees, paths, and matchings. We also analyze the parameterized complexity of the two problems with respect to various parameters related to the number of agents, the dissatisfaction threshold, the vertex degrees of the preference graphs, and the treewidth.
As is known, the problem of finding a three-dimensional stable matching with cyclic preferences (3DSM-CYC) always has a solution, if the number of objects of each type (i.e., the problem size n) does ...not exceed 5. According to the conjecture proposed by Eriksson et al. (2006), this is true for any n. However, Lam and Plaxton (2019) have proposed an algorithm for constructing preference lists in 3DSM-CYC which has allowed them to disprove the mentioned conjecture. The size of the initially constructed counterexample equals 90; however, according to the results obtained by us recently for the problem with incomplete preference lists, one can use the same construction for getting a counterexample of size 45. The main contribution of this paper consists of reducing the size of the counterexample to n=20. We summarize results of the application of the technique developed by us for constructing counterexamples for 3DSM-CYC. In the final section of the paper we discuss a new variant of 3DSM, whose solution always exists and can be found within the same time as that required for solving 2DSM.
This paper presents consensus based multi-person decision making (MPDM) using consistency graphs (additive consistent and order consistent) in a fuzzy environment. At the first level, consistency ...analysis is put forward after defining consistent fuzzy preference graph (CFPG) with the help of additive transitivity. This analysis further leads us to determine priority weights vector of the decision-makers (DMRs) after evaluation consistency weights. At the second level, the consensus analysis helps us to determine whether the selection process should be initiated or not. If the consensus degree amongst DMRs does not reach a minimum acceptable level, then the enhancement mechanism plays a central role to improve the consensus level by giving suitable suggestions to DMRs. In the end, the weighted sum operator (WSO) is used to get aggregated consistency fuzzy preference graph (AgCFPG) and the order consistency property provides us sufficient information to rank the alternatives.
•A new preference aggregation method is proposed based on the preference graph.•An application to voting and to the group decision in general is given.•The method generalizes the Borda count and the ...Condorcet approach as well.•The properties of monotonicity, clone independence and consistency are discussed.•Applications to Eurovision Song Contest and Cookie type election are given.
Pairwise comparison of various objects (alternatives) is common in many procedures related to decision making. Potential Method (PM) uses a (weighted) preference graph as the basic structure generated by such comparisons to obtain a value function (potential) on the set of alternatives. The potential is calculated as a solution of a system of equations involving the Laplacian matrix of the preference graph. In multiple-criteria decision analysis or group decision making, each criterion or decision maker is represented by its preference graph. A multigraph obtained by joining these graphs aggregates the individual preferences and generates the group potential. Moreover, the influence (weight) of each criterion or decision maker on the group potential may be adjusted. In this article the aggregation of preference graphs is applied to voting systems. Many different forms of voting ballots can generate preference graphs, which gives us a universal (ballot-independent) voting system. As an illustration of the PM in the voting context we have chosen the Eurovision Song Contest and the analysis of the cookie-type ballots where the voters allocate a certain number of points (cookies) to the candidates.
Additive manufacturing (AM) or 3D printing, as an enabling technology for mass customization or personalization, has been developed rapidly in recent years. Various design tools, materials, machines ...and service bureaus can be found in the market. Clearly, the choices are abundant, but users can be easily confused as to which AM process they should use. This paper first reviews the existing multi-attribute decision-making methods for AM process selection and assesses their suitability with regard to two aspects,
preference rating flexibility
and
performance evaluation objectivity
. We propose that an approach that is capable of handling incomplete attribute information and objective assessment within inherent data has advantages over other approaches. Based on this proposition, this paper proposes a weighted preference graph method for personalized preference evaluation and a rough set based fuzzy axiomatic design approach for performance evaluation and the selection of appropriate AM processes. An example based on the previous research work of AM machine selection is given to validate its robustness for the priori articulation of AM process selection decision support.
As an emerging topic on preference learning, aiming at deducting the linear order of alternatives from the partial ranking, preference completion is to complete the preference of the target agent to ...form a linear order from the preferences of other agents under certain complex requirements. In order to improve the effectiveness and efficiency of preference completion in Big Data environments, firstly the preference graph is introduced to represent the collective preference of the agents over the alternatives with a certain consensus algorithm following the preference of the target agent. This preference graph can preserve rich information between agents. In addition, with the introduction of fuzzy ranking, it can illustrate the fuzziness of the target agent that can include several ranking options of the target agent over alternatives. Then, the satisfied preference can be matched from the preference graph with the fuzzy ranking requested by the target agent via isomorphism-based graph pattern matching. With the matched preference, the preference of the target agent can be completed. If the completed preference is not satisfied, the target agent can modify the fuzzy ranking, process the graph pattern rematching and complete the preference again. The experimental results show that with several real datasets the effectiveness and efficiency of the fuzzy ranking-based preference completion via graph pattern matching can be validated.
Purpose
Recommender system approaches such as collaborative and content-based filtering rely on user ratings and product descriptions to recommend products. More recently, recommender system research ...has focussed on exploiting knowledge from user-generated content such as product reviews to enhance recommendation performance. The purpose of this paper is to show that the performance of a recommender system can be enhanced by integrating explicit knowledge extracted from product reviews with implicit knowledge extracted from analysis of consumer’s purchase behaviour.
Design/methodology/approach
The authors introduce a sentiment and preference-guided strategy for product recommendation by integrating not only explicit, user-generated and sentiment-rich content but also implicit knowledge gleaned from users’ product purchase preferences. Integration of both of these knowledge sources helps to model sentiment over a set of product aspects. The authors show how established dimensionality reduction and feature weighting approaches from text classification can be adopted to weight and select an optimal subset of aspects for recommendation tasks. The authors compare the proposed approach against several baseline methods as well as the state-of-the-art better method, which recommends products that are superior to a query product.
Findings
Evaluation results from seven different product categories show that aspect weighting and selection significantly improves state-of-the-art recommendation approaches.
Research limitations/implications
The proposed approach recommends products by analysing user sentiment on product aspects. Therefore, the proposed approach can be used to develop recommender systems that can explain to users why a product is recommended. This is achieved by presenting an analysis of sentiment distribution over individual aspects that describe a given product.
Originality/value
This paper describes a novel approach to integrate consumer purchase behaviour analysis and aspect-level sentiment analysis to enhance recommendation. In particular, the authors introduce the idea of aspect weighting and selection to help users identify better products. Furthermore, the authors demonstrate the practical benefits of this approach on a variety of product categories and compare the approach with the current state-of-the-art approaches.
The problem of learning conditional preference networks (CP-nets) from a set of examples has received great attention recently. However, because of the randomicity of the users' behaviors and the ...observation errors, there is always some noise making the examples inconsistent, namely, there exists at least one outcome preferred over itself (by transferring) in examples. Existing CP-nets learning methods cannot handle inconsistent examples. In this work, we introduce the model of learning consistent CP-nets from inconsistent examples and present a method to solve this model. We do not learn the CP-nets directly. Instead, we first learn a preference graph from the inconsistent examples, because dominance testing and consistency testing in preference graphs are easier than those in CP-nets. The problem of learning preference graphs is translated into a 0-1 programming and is solved by the branch-and-bound search. Then, the obtained preference graph is transformed into a CP-net equivalently, which can entail a subset of examples with maximal sum of weight. Examples are given to show that our method can obtain consistent CP-nets over both binary and multivalued variables from inconsistent examples. The proposed method is verified on both simulated data and real data, and it is also compared with existing methods.
Customer requirement preference is an important part of customer satisfaction. In view of similar case retrieval technology for existing product level, in the process of solving similar cases, there ...is no consideration for customer requirement preference. This article proposes a similar case solution method considering customer requirement preference. First, we deal with the expression of customer requirements and transform them into operable parameter forms according to the mapping model. Second, the preference graph is used to analyze the customer’s requirement preference, to determine the preference weight, and to weigh the final weight of the requirement node with the initial weight determined by the fuzzy analytic hierarchy process. Finally, the similarity degree solving model of requirement node and product case attribute parameters is established. By integrating the weights of the above-mentioned nodes, the similarity of the product case is obtained, and a more satisfied case of the customer is obtained. Taking the automated guided vehicle car product as an example, the effectiveness of the proposed method is verified.
Resolving Zeckhauser’s paradox Pawitan, Yudi; Isheden, Gabriel
Theory and decision,
05/2020, Volume:
88, Issue:
4
Journal Article
Peer reviewed
Open access
Zeckhauser’s paradox has puzzled and entertained many rationality enthusiasts for almost half a century. You are forced to play a Russian Roulette with a 6-chamber revolver containing either (A) two ...bullets, or (B) four bullets. Would you pay more to remove the two bullets in (A) than you would to remove one in (B)? Most would say yes, but rational considerations based on the classical utility theory suggest you should not. We discuss a possible solution within the classical framework, by explicitly stating and accounting for more detailed preferences in terms of fewer bullets and smaller debt. To a large extent, the paradox arises due to a surreptitious trespassing of Savage’s Small-World utilities implied by a limited set of preferences to govern a larger world containing potentially conflicting preferences. To avoid logical issues associated with death in the roulette, we also describe a non-fatal game-show version, where you choose one box out of six that could be either empty or contain prize money. Here, the paradox arises when you pay from the prize money, but not when you pay from your own money. In summary, the paradox provides a useful lesson about the normative role of the utility function as a rational guide for our decisions and preferences.
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