Mónica Sánchez

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.

Relative and absolute order-of-magnitude models unified

The aim of this paper is to analyze under which conditions Absolute Order-of-Magnitude and Relative Order-of-Magnitude models may be concordant and to determine the constraints which guarantee concordance. A graphical interpretation of the constraints is provided, bridging the absolute qualitative labels of two quantities into their corresponding relative relation(s), and conversely. The relative order of magnitude relations are then characterized in the absolute order-of-magnitude world.

Decision making under uncertainty using a qualitative TOPSIS method for selecting sustainable energy alternatives

Multi-criteria decision-making methods support decision makers in all stages of the decision-making process by providing useful data. However, criteria are not always certain as uncertainty is a feature of the real world. MCDM methods under uncertainty and fuzzy systems are accepted as suitable techniques in conflicting problems that cannot be represented by numerical values, in particular in energy analysis and planning. In this paper, a modified TOPSIS method for multi-criteria group decision-making with qualitative linguistic labels is proposed. This method addresses uncertainty considering different levels of precision. Each decision maker’s judgment on the performance of alternatives with respect to each criterion is expressed by qualitative linguistic labels. The new method takes into account linguistic data provided by the decision makers without any previous aggregation. Decision maker judgments are incorporated into the proposed method to generate a complete ranking of alternatives. An application in energy planning is presented as an illustrative case example in which energy policy alternatives are ranked. Seven energy alternatives under nine criteria were evaluated according to the opinion of three environmental and energy experts. The weights of the criteria are determined by fuzzy AHP, and the alternatives are ranked using qualitative TOPSIS. The proposed approach is compared with a modified fuzzy TOPSIS method, showing the advantages of the proposed approach when dealing with linguistic assessments to model uncertainty and imprecision. Although the new approach requires less cognitive effort to decision makers, it yields similar results.

Modeling group assessments by means of hesitant fuzzy linguistic term sets

Hesitant linguistic term sets have been introduced to capture the human way of reasoning using linguistic expressions involving different levels of precision. In this paper, a lattice structure is provided to the set of hesitant fuzzy linguistic term sets by means of the operations intersection and connected union. In addition, in a group decision making framework, hesitant fuzzy linguistic descriptions are defined to manage situations in which decision makers are assessing different alternatives by means of hesitant fuzzy linguistic term sets. Based on the introduced lattice structure, two distances between hesitant fuzzy linguistic descriptions are defined. These metric structures allow distances between decision makers to be computed. A centroid of the decision making group is proposed for each distance to model group representatives in the considered group decision making framework.

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.

Consensus, dissension and precision in group decision making by means of an algebraic extension of hesitant fuzzy linguistic term sets

Abstract Present measures of the degree of agreement in group decision-making using hesitant fuzzy linguistic term sets allow consensus or agreement measurement when decision makers’ assessments involve hesitance. Yet they do not discriminate with different degrees of consensus among situations with discordant or polarized assessments. The visualization of differences among groups for which there is no agreement but different possible levels of disagreement is an important issue in collective decision-making situations. In this paper, we propose new collective and individual consensus measures that explicitly consider the hesitance of the decision makers’ hesitance in giving an opinion and also the gap between non-overlapping assessments, thus allowing the measurement of the polarization present within the group’s opinions. In addition, an expert’s profile is defined by considering the expert’s behavior in previous assessments in group decision-making processes in terms of precision and dissension.

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.

Analysis of Tensions in a Population Based on the Adequacy Concept

The concept of similarity between objects has traditionally been taken as the criterion for recognising their membership of a given class. This paper considers how well an object fits into a class by using the concept of adequacy introduced by the LAMDA learning system [6],[9]. The Global Adequacy Degree (GAD) is a function of the objects class membership. An adequacy threshold is associated with a non-informative class (NIC). Objects falling below this threshold value are not considered to belong to any significant class. In this research, the tensions produced by a classification scheme are defined by means of the adequacy of an object in a class. This allows us to analyse the stability orbalance of the scheme. An example is given in the form of the adequacy and the tension of a classification scheme for a group of customers patronising an imaginary shop.

Absolute order-of-magnitude reasoning applied to a social multi-criteria evaluation framework

A social multi-criteria evaluation framework for solving a real-case problem of selecting a wind farm location in the regions of Urgell and Conca de Barberá in Catalonia (northeast of Spain) is studied. This paper applies a qualitative multi-criteria decision analysis approach based on linguistic labels assessment able to address uncertainty and deal with different levels of precision. This method is based on qualitative reasoning as an artificial intelligence technique for assessing and ranking multi-attribute alternatives with linguistic labels in order to handle uncertainty. This method is suitable for problems in the social framework such as energy planning which require the construction of a dialogue process among many social actors with high level of complexity and uncertainty. The method is compared with an existing approach, which has been applied previously in the wind farm location problem. This approach, consisting of an outranking method, is based on Condorcets original method. The results obtained by both approaches are analysed and their performance in the selection of the wind farm location is compared in aggregation procedures. Although results show that both methods conduct to similar alternatives rankings, the study highlights both their advantages and drawbacks.