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A consensus model for group decision making problems with unbalanced fuzzy linguistic information
- Int. J. Inform. Technol. Decision Making
"... Most group decision making (GDM) 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 ..."
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Cited by 35 (18 self)
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Most group decision making (GDM) 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 that are not uniformly and symmetrically distributed. The aim of this paper is to present a consensus model for GDM problems with unbalanced fuzzy linguistic information. This consensus model is based on both a fuzzy linguistic methodology to deal with unbalanced linguistic term sets and two consensus criteria, consensus degrees, and proximity measures. To do so, we use a new fuzzy linguistic methodology improving another approach to manage unbalanced fuzzy linguistic information, 1 (Int. J. Intell. Syst. 22(11) (2007) 1197–1214), which uses the linguistic 2-tuple model as representation base of unbalanced fuzzy linguistic information. In addition, the consensus model presents a feedback mechanism to help experts for reaching the highest degree of consensus possible. There are two main advantages provided by this consensus model. First, its ability to cope with GDM problems with unbalanced fuzzy linguistic information overcoming the problem of finding different discrimination levels in linguistic term sets. Second, it supports the consensus process automatically, avoiding the possible subjectivity that the moderator can introduce in this phase.
Cardinal consistency of reciprocal preference relations: a characterization of multiplicative transitivity
- IEEE Trans. Fuzzy Syst
, 2009
"... Abstract-Consistency of preferences is related with rationality, which is associated with the transitivity property. Many properties suggested to model transitivity of preferences are inappropriate for reciprocal preference relations. In this paper, a functional equation is put forward to model the ..."
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Cited by 15 (5 self)
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Abstract-Consistency of preferences is related with rationality, which is associated with the transitivity property. Many properties suggested to model transitivity of preferences are inappropriate for reciprocal preference relations. In this paper, a functional equation is put forward to model the 'cardinal consistency in the strength of preferences' of reciprocal preference relations. We show that under the assumptions of continuity and monotonicity properties, the set of representable uninorm operators is characterized as the solution to this functional equation. Cardinal consistency with the conjunctive representable Cross Ratio uninorm is equivalent to Tanino's multiplicative transitivity property. Because any two representable uninorms are order isomorphic, we conclude that multiplicative transitivity is the most appropriate property for modelling cardinal consistency of reciprocal preference relations. Results towards the characterization of this uninorm consistency property based on a restricted set of (n − 1) preference values, which can be used in practical cases to construct perfect consistent preference relations, are also presented.
Group decision making with incomplete fuzzy linguistic preference relations
- International Journal of Intelligent Systems
, 2009
"... The aim of this paper is to propose a procedure to estimate missing preference values when dealing with incomplete fuzzy linguistic preference relations assessed using a two-tuple fuzzy linguistic approach. This procedure attempts to estimate the missing information in an individual incomplete fuzzy ..."
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Cited by 12 (2 self)
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The aim of this paper is to propose a procedure to estimate missing preference values when dealing with incomplete fuzzy linguistic preference relations assessed using a two-tuple fuzzy linguistic approach. This procedure attempts to estimate the missing information in an individual incomplete fuzzy linguistic preference relation using only the preference values provided by the respective expert. It is guided by the additive consistency property to maintain experts ’ consistency levels. Additionally, we present a selection process of alternatives in group decision making with incomplete fuzzy linguistic preference relations and analyze the use of our estimation procedure in the decision process. C ○ 2008 Wiley Periodicals, Inc. 1.
Managing the consensus in group decision making in an unbalanced fuzzy . . .
- KNOWLEDGE-BASED SYSTEMS
, 2010
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INTEGRATION OF A CONSISTENCY CONTROL MODULE WITHIN A CONSENSUS MODEL
, 2008
"... In group decision making (GDM) processes, prior to the selection of the best alternative(s), it would be desirable that experts achieve a high degree of consensus or agreement between them. Due to the complexity of most decision making problems, individuals’ preferences may not satisfy formal proper ..."
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Cited by 10 (4 self)
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In group decision making (GDM) processes, prior to the selection of the best alternative(s), it would be desirable that experts achieve a high degree of consensus or agreement between them. Due to the complexity of most decision making problems, individuals’ preferences may not satisfy formal properties. ‘Consistency’ is one of such properties, and it is associated with the transitivity property. Obviously, when carrying out a rational decision making, consistent information, i.e. information which does not imply any kind of contradiction, is more appropriate than information containing some contradictions. Therefore, in a GDM process, consistency should also be sought after. In this paper we present a consensus model for GDM problems that proceeds from consistency to consensus. This model integrates a novel consistency reaching module based on consistency measures. In particular, the model generates advice on how experts should change their preferences in order to increase their consistency. Also, the consensus model is considered adaptive because the search for consensus is adapted to the level of agreement achieved at each consensus round.
A Consistency-Based Procedure to Estimate Missing Pairwise Preference Values
"... In this paper, we present a procedure to estimate missing preference values when dealing with pairwise comparison and heterogeneous information. This procedure attempts to estimate the missing information in an expert’s incomplete preference relation using only the preference values provided by that ..."
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Cited by 7 (2 self)
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In this paper, we present a procedure to estimate missing preference values when dealing with pairwise comparison and heterogeneous information. This procedure attempts to estimate the missing information in an expert’s incomplete preference relation using only the preference values provided by that particular expert. Our procedure to estimate missing values can be applied to incomplete fuzzy, multiplicative, interval-valued, and linguistic preference relations. Clearly, it would be desirable to maintain experts ’ consistency levels. We make use of the additive consistency property to measure the level of consistency and to guide the procedure in the estimation of the missing values. Finally, conditions that guarantee the success of our procedure in the estimation of all the missing values of an incomplete preference relation are given. C ○ 2008 Wiley Periodicals, Inc. 1.
A Selection Process Based on Additive Consistency to Deal with Incomplete Fuzzy Linguistic Information
"... Abstract: In group decision making situations, there may be cases in which experts do not have an in-depth knowledge of the problem to be solved and, as a result, they may present incomplete information. In this paper, we present a new selection process to deal with incomplete fuzzy linguistic infor ..."
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Cited by 6 (1 self)
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Abstract: In group decision making situations, there may be cases in which experts do not have an in-depth knowledge of the problem to be solved and, as a result, they may present incomplete information. In this paper, we present a new selection process to deal with incomplete fuzzy linguistic information. As part of it, we use an iterative procedure to estimate the missing information. This procedure is guided by the additive consistency property and only uses the preference values provided by the experts. In addition, the additive consistency property is also used to measure the level of consistency of the information provided by the experts. The main novelties of this selection process are both the possibility to manage decision situations under incomplete fuzzy linguistic information and the importance of the experts ’ preferences in the aggregation processes is modeled by means of the experts ’ consistency. Key Words: group decision making, incomplete information, fuzzy linguistic information, consistency, aggregation
A Note on Two Methods for Estimating Missing Pairwise Preference Values
"... Abstract—This note analyzes two methods for calculating missing values of an incomplete reciprocal fuzzy preference relation. The first method by Herrera-Viedma et al. appeared in the IEEE TRANSACTIONS ON ..."
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Cited by 5 (1 self)
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Abstract—This note analyzes two methods for calculating missing values of an incomplete reciprocal fuzzy preference relation. The first method by Herrera-Viedma et al. appeared in the IEEE TRANSACTIONS ON
A note on the estimation of missing pairwise preference values: a uninorm consistency based method, Int
- J. Uncert., Fuzz. Knowl.-Based Syst
, 2008
"... 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 rep ..."
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Cited by 5 (1 self)
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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.
Consistency of reciprocal preference relations
- in Proc. 2007 IEEE Int. Conf. Fuzzy Systems, 2007
"... Abstract — The consistency of reciprocal preference relations is studied. Consistency is related with rationality, which is associated with the transitivity property. For fuzzy preference relations many properties have been suggested to model transitivity and, consequently, consistency may be measur ..."
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Cited by 2 (2 self)
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Abstract — The consistency of reciprocal preference relations is studied. Consistency is related with rationality, which is associated with the transitivity property. For fuzzy preference relations many properties have been suggested to model transitivity and, consequently, consistency may be measured according to which of these different properties is required to be satisfied. However, we will show that many of them are not appropriate for reciprocal preference relations. We put forward a functional equation to model consistency of reciprocal preference relations, and show that self-dual uninorms operators are the solutions to it. In particular, Tanino’s multiplicative transitivity property being an example of such type of uninorms seems to be an appropriate consistency property for fuzzy reciprocal preferences. I.
