Abstract - We construct two types of alternative-consensus optimization models that concern crisp numbers and intervals for the DMs' opinions. In the alternative-consensus (interval) data envelopment analysis (DEA) model, the optimal alternative is the decision-making unit with the highest output utility, which is also the maximum consensus alternative. The alternative-consensus (interval) optimization model based on the maximum discriminating factor obtains the fixed weights of the DMs on different alternatives. Its essence is to increase the differences in weights among the DMs and improve the differences in the overall output utilities among alternatives by maximizing the discriminating factor, which overcomes the drawback that the optimal alternative is not unique in the alternative-consensus (interval) DEA model.
Abstract - The consensus process plays a decisive role in a group decision making problem. From a perspective of optimization, various consensus models have been presented to help the group reach a predefined consensus level. The aim of this paper is to propose a new primal model and its dual model based on the minimum cost consensus model. In the proposed primal model, different tolerance levels are considered for the decision makers and the group opinion is obtained by the weighted arithmetic average operators. In such a model, the moderator does not need to pay if the changed opinion of a decision maker is still under the tolerance level of that decision maker. The proposed dual consensus model has some significant economic interpretations. Some properties with respect to the two proposed consensus models are analyzed. The validity of the proposed models is illustrated by a numerical example.
Abstract - We define expanded hesitant fuzzy sets, which incorporate all available information of the decision makers that provide the membership degrees that define a hesitant fuzzy set. We show how this notion relates to hesitant fuzzy set and extended hesitant fuzzy set. We define various scores for this setting, which generalize popular scores for hesitant fuzzy elements. Finally, a group decision making procedure is presented and illustrated with an example.
Abstract - Diversity and novelty are appreciated features by users of recommender systems, which alleviate the information overload problem. These features are more important in recommendation to groups because members interests and needs differ from each other or are even in conflict. Various techniques have been used to recommend to groups. However, these techniques apply an aggregation step that imply a loss of information, which negatively affect the recommendation. We aim at avoiding the negative influence of the aggregation step considering the various interests and needs of the group members as the group hesitation, thus, our proposal uses Hesitant Fuzzy Sets to model the group information. A case study is performed to evaluate the proposal, whose results show its performance regarding recommendation diversity, novelty and accuracy.
Abstract - The linguistic distribution is becoming a popular tool to model linguistic expressions in group decision making. Due to the knowledge limitation, it is difficult for decision makers to provide complete linguistic distribution information and partial ignorance exists in practical group decision making problems. Meanwhile, in group decision making it is hoped to find a group opinion whose distribution information is complete and the preference loss between this group opinion and individual opinions is the minimum. To tackle these issues, this paper introduces the concept of incomplete linguistic distributions and proposes a new model called the minimum preference loss model (MPLM), aiming at minimizing the preference loss between the group opinion and individual opinions in the group decision making with incomplete linguistic distributions. Finally, a numerical example is provided to demonstrate our model.
Abstract - In this paper, we investigate the missing elements estimation issue of incomplete fuzzy reciprocal preference relation. Based on the multiplicative consistency property, a constrained nonlinear optimization model (CNOM), which aims for making the induced matrix close to zero, is proposed to estimate the missing elements in the incomplete fuzzy reciprocal preference relation. The numerical example is illustrated to show the correctness and effectiveness of the proposed method. Our method not only estimates the missing elements accurately but also improves the multiplicative consistency, which makes the decision result derived from the incomplete fuzzy reciprocal preference relation could be scientific and effective.