Llorenç Roselló

Using consensus and distances between generalized multi-attribute linguistic assessments for group decision-making

This paper proposes a mathematical framework and methodology for group decision-making under multi-granular and multi-attribute linguistic assessments. It is based on distances between linguistic assessments and a degree of consensus. Distances in the space of qualitative assessments are defined from the geodesic distance in graph theory and the Minkowski distance. The degree of consensus is defined through the concept of entropy of a qualitatively-described system. Optimal assessments in terms of both proximity to all the expert opinions in the group and the degree of consensus are used to compare opinions and define a methodology to rank multi-attribute alternatives.

Measuring consensus in group decisions by means of qualitative reasoning

This paper presents a mathematical framework to assess the consensus found among different evaluators who use ordinal scales in group decision-making and evaluation processes. This framework is developed on the basis of the absolute order-of-magnitude qualitative model through the use of quantitative entropy. As such, we study the algebraic structure induced in the set of qualitative descriptions given by evaluators. Our results demonstrate that it is a weak partial semi-lattice structure that in some conditions takes the form of a distributive lattice. We then define the entropy of a qualitatively described system. This enables us, on the one hand, to measure the amount of information provided by each evaluator and, on the other hand, to consider a degree of consensus among the evaluation committee. This new approach is capable of managing situations where the assessment given by experts involves different levels of precision. In addition, when there is no consensus regarding the group decision, an automatic process assesses the effort required to achieve said consensus.

A Qualitative Reasoning Approach to Measure Consensus

This chapter introduces a mathematical framework on the basis of the absolute order-of-magnitude qualitative model. This framework allows to develop a methodology to assess the consensus found among different evaluators who use ordinal scales in group decision-making and evaluation processes. The concept of entropy is introduced in this context and the algebraic structure induced in the set of qualitative descriptions given by evaluators is studied. We prove that it is a weak partial semilattice structure that in some conditions takes the form of a distributive lattice. The definition of the entropy of a qualitatively-described system enables us, on one hand, to measure the amount of information provided by each evaluator and, on the other hand, to consider a degree of consensus among the evaluation committee. The methodology presented is able of managing situations where the assessment given by experts involves different levels of precision. In addition, when there is no consensus within the group decision, an automatic process measures the effort necessary to reach said consensus.

Using L-fuzzy sets to introduce information theory into qualitative reasoning

We formally construct the extended set of qualitative labels L over a well-ordered set. The qualitative descriptions of a given set are defined as L-fuzzy sets. In the case where the well-ordered set is finite, a distance between L-fuzzy sets is introduced based on the properties of the lattice L. The concept of the information contained in a qualitative label is introduced, leading to a formal definition of the entropy of an L-fuzzy set as a Lebesgue integral. In the discrete case, this integral becomes a weighted average of the information of the labels, corresponding to the Shannon entropy in information theory.

Using qualitative reasoning to measure discrepancy and consensus in group decision

The measurement of consensus and discrepancy among groups of evaluators is an important issue in group decision systems. These measurements will enable us to analyze the effort that should be made to obtain closer positions among subgroups. This paper presents a new approach, on the basis of the absolute order-of-magnitude qualitative model, to decision-making problems. The concepts of qualitative distance and entropy are defined in the framework of the distributive lattice of qualitativizations over a set of magnitudes or features.

A new approach for Delphi processes based on group consensus with linguistic terms

A new approach for Delphi processes including a measure of consensus based on linguistic terms is introduced in this paper. The measure of consensus involves qualitative reasoning techniques and is based on the concept of entropy. In the proposed approach, consensus is reached automatically without the need for neither a moderator nor a final interaction among panelists. In addition, it permits panelists to answer with different levels of precision depending on their knowledge on each question. An illustrative example considering the opinions of stake holders in neonate health-care to reach a final consensual definition of chronic pain in neonates is presented.