International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems

In a previous paper, the authors proposed an alternative approach to classical dimension theory, based upon a general representation of strict preferences not being restricted to partial order sets. Without any relevant restriction, the proposed approach was conceived as a potential powerful tool for decision making problems where basic information has been modeled by means of valued binary preference relations. In fact, assuming that each decision maker is able to consistently manage intensity values for preferences is a strong assumption even when there are few alternatives being involved (if the number of alternatives is large, the same criticism applies to crisp preferences). Any representation tool, as the one proposed by the authors, will in principle play a key role in order to help decision makers to understand their preference structure. In this paper we introduce an alternative approach in order to avoid certain complexity issues of the initial proposal, allowing a close representation easier to be obtained in practice.

Dealing with incomplete information is an important problem in decision making. In this paper, we present a short discussion on this topic and a new estimation method of missing values in an incomplete fuzzy preference relation which is based on the modelling of consistency of preferences via a representable uninorm.

In the e-commerce arena new methods and tools have been recently developed to improve and customize the e-commerce web sites, according to users' necessities and preferences, that are usually vague and uncertain. The most successful tool in this field has been the Recommender Systems. Their aim is to assist e-shops customers to find out the most suitable products by using recommendations. Sometimes, these systems face situations where there is a lack of information or the information is vague or imprecise that yield unsuccessful results. Although several solutions have been proposed, they still present some limitations. In this paper, we present a Knowledge-Based Recommender System that manages and models the uncertainty related to users' preferences by using linguistic information. This system will overcome the problem of lack of information by computing recommendations through completing incomplete linguistic preference relations provided by the users.

In this paper we analyze a group decision procedure that follows a recursive pattern. In the first stage, the members of a group show their opinions on all the individuals of that group, regarding a specific attribute, by means of assessments within an ordered set, e.g. the unit interval or a finite scale. Taking into account this information, some aggregation operators and a family of thresholds, a subgroup of individuals is selected: those members whose collective assessment reach a specific threshold. Now only the opinions of this qualified subgroup are taken into account and a new subgroup emerges in the implementation of the aggregation phase. We analyze how to put in practice this recursive procedure in order to provide a final subgroup of qualified members. We have considered the minimum as aggregation operator. Thus, the collective assessment is just the worst of the individual assessments. This idea corresponds to qualify individuals whenever all the individual assessments reach the fixed threshold.

We propose label semantics as an integrated representation framework for probabilistic uncertainty and fuzziness in multiple-attribute decision making problems. Linguistic attribute hierarchies are then introduced as a means of modelling the complex and often imprecise functional relationships between low-level attributes or measurements and high-level decision or classification variables. Within this framework we introduce linguistic decision trees as a tool for information aggregation in multi-attribute decision problems and describe the process of information propagation through a hierarchy of linked decision trees. In addition, we consider the ranking of different alternatives or examples based on their linguistic descriptions of a high-level utility variable. Finally, we discuss how linguistic decision trees embedded in attribute hierarchies can be learnt from data.

We propose the use of a knowledge based framework for diagnosis in which the knowledge base consists of particular instances of general hierarchical disorder models. We study how to select which manifestation (symptom, malfunction) to query in order to reduce a set of competing diagnosis hypotheses (disorders), none of them completely satisfying, considering only the observed manifestations. We propose to use general information about the order in which competing disorder models should be probed first to guide us on the task of selecting which particular disorder instances to try to confirm first. We propose to then order which manifestation instances to probe, the presence or absence of which will help us to either confirm or eliminate that hypothesis, according to the principle that "(manifestation) instances that share some characteristics with the instance of manifestation that generated the whole process, but which completely disagree in relation to other characteristics" should be probed first.

Bilevel programming deals with hierarchical optimization problems in which the leader at the upper level attempts to optimize his or her objectives, but subject to a set of constraints and the follower's reactions. Typical bilevel programming considers one leader one follower situation and supposes each of them has only one objective. In real world situations, multiple followers may be involved and they may be with different relationships such as sharing decision variables or not, sharing objectives or not. Therefore, the leader's decision will be affected not only by those followers' reactions but also by their relationships. In addition, any of the leader and/or these followers may have multiple conflict objectives that should be optimized simultaneously. Furthermore, the parameters of a bilevel programming model may be described by uncertain values. This paper addresses all these three issues as a whole by particularly focusing on the situation of sharing decision variables among followers. It first proposes a set of fuzzy multi-objective multi-follower bilevel programming (FMMBP) models to describe the complex issue. It then presents an approximation branch-and-bound algorithm to solve the FMMBP problems. Finally, two examples illustrate the proposed models and algorithm.