Fuzzy social choice: a selective retrospect

Nurmi, Hannu

doi:10.1007/s00500-007-0196-5

Cited by 30 publications

(18 citation statements)

References 53 publications

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“…As the Nobel laureate Amartya Sen (1970) has noted, "voters opinions can be misrepresented when the preferences are dichotomous in the sense that the collective decision does not take into consideration the intensities of each individual preference". The importance of considering intensities in the individual preferences has also been noted in Cook and Kress (1985); Meek (1975); Nurmi (1981Nurmi ( , 2008; Tanino (1984), and Morales (1797) (see translation in McLean and Urken (1995)), among others.…”

Section: Introductionmentioning

confidence: 86%

Probabilities of Consistent Election Outcomes with Majorities Based on Difference in Support

Diss

Pérez-Asurmendi

2016

Group Decis Negot

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Computer simulations are used to evaluate the likelihood of consistent outcomes under the class of majorities based on difference in support. These majorities require certain consensus in collective preferences to declare an alternative as the winner. More precisely, individuals show preference intensities in the unit interval among each pair of alternatives and it is required that the winner alternative obtains a difference in the sum of the intensities with respect to the loser alternative. This difference is a real number located between 0 and the total number of voters. We introduce the values of the required threshold for which majorities based on difference in support lead to transitive and triple-acyclic collective decisions with a probability of 1. Our results improve the previous theoretical ones since they require softer thresholds to reach consistent collective decisions.

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Section: Introductionmentioning

confidence: 86%

Probabilities of Consistent Election Outcomes with Majorities Based on Difference in Support

Diss

Pérez-Asurmendi

2016

Group Decis Negot

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“…According to the nature of the information expressed for every pair of alternatives, there exist many different representation formats of preference relations [5,8,20,34,35,43,44,47].…”

Section: Incomplete Unbalanced Fuzzy Linguistic Preference Relationsmentioning

confidence: 99%

Managing the consensus in group decision making in an unbalanced fuzzy linguistic context with incomplete information

Cabrerizo

Pérez

Liu

2010

Knowledge-Based Systems

293

114

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To solve group decision making problems we have to take in account different aspects. On the one hand, depending on the problem, we can deal with different types of information. In this way, most group decision making problems based on linguistic approaches use symmetrically and uniformly distributed linguistic term sets to express experts' opinions. However, there exist problems whose assessments need to be represented by means of unbalanced linguistic term sets, i.e., using term sets which are not uniformly and symmetrically distributed. On the other hand, there may be cases in which experts do not have an in-depth knowledge of the problem to be solved. In such cases, experts may not put their opinion forward about certain aspects of the problem and, as a result, they may present incomplete information. The aim of this paper is to present a consensus model to help experts in all phases of the consensus reaching process in group decision making problems in an unbalanced fuzzy linguistic context with incomplete information. As part of this consensus model, we propose an iterative procedure using consistency measures to estimate the incomplete information.In addition, the consistency measures are used together with consensus measures to guided the consensus model.The main novelty of this consensus model is that it supports the management of incomplete unbalanced fuzzy linguistic information and it allows to achieve consistent solutions with a great level of agreement.

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“…. ; e m g; characterized by their own ideas, attitudes, motivations and knowledge, who express their opinions about this set of alternatives to achieve a common solution (Lu et al 2008;Montero 2008;Nurmi 2008). To do this, experts have to express their preferences by means of a set of evaluations over the set of alternatives.…”

Section: Introductionmentioning

confidence: 99%

Analyzing consensus approaches in fuzzy group decision making: advantages and drawbacks

et al. 2009

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Two processes are necessary to solve group decision making problems: a consensus process and a selection process. The consensus process is necessary to obtain a final solution with a certain level of agreement between the experts, while the selection process is necessary to obtain such a final solution. Clearly, it is preferable that the set of experts reach a high degree of consensus before applying the selection process. In order to measure the degree of consensus, different approaches have been proposed. For example, we can use hard consensus measures, which vary between 0 (no consensus or partial consensus) and 1 (full consensus), or soft consensus measures, which assess the consensus degree in a more flexible way. The aim of this paper is to analyze the different consensus approaches in fuzzy group decision making problems and discuss their advantages and drawbacks. Additionally, we study the future trends.

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Fuzzy social choice: a selective retrospect

Cited by 30 publications

References 53 publications

Probabilities of Consistent Election Outcomes with Majorities Based on Difference in Support

Probabilities of Consistent Election Outcomes with Majorities Based on Difference in Support

Managing the consensus in group decision making in an unbalanced fuzzy linguistic context with incomplete information

Analyzing consensus approaches in fuzzy group decision making: advantages and drawbacks

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