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Huchang Liao - One of the best experts on this subject based on the ideXlab platform.
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the stably multiplicative consistency of fuzzy Preference Relation and interval valued hesitant fuzzy Preference Relation
IEEE Access, 2019Co-Authors: Yuling Zhai, Huchang LiaoAbstract:Preference Relations are generally used to cope with multi-attribute group decision making (MAGDM), which express the experts’ Preference information through pairwise comparisons. To make decision rationale, one of the vital issues related to Preference Relations is how to make the Preference information logical. The logicality level of Preference information is usually described by the consistency of Preference Relation. Thus, developing methods to check and improve the consistency of Preference Relations is necessary and significant. In this paper, we give a general description of multiplicative transitivity property for fuzzy Preference Relation (FPR). Then, based on the new multiplicative transitivity function which can repair some counterintuitive cases of the traditional one, we define the stably multiplicative consistency, the stably mean multiplicative consistency (SMMC), and the acceptable SMMC for interval-valued hesitant FPR (IVHFPR). Additionally, several algorithms are developed to improve the SMMC of IVHFPR. A practical example concerning the respiratory illness diagnosis is given to demonstrate the applicability of IVHFPR with SMMC.
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consistent fuzzy Preference Relation with geometric bonferroni mean a fused Preference method for assessing the quality of life
Applied Intelligence, 2019Co-Authors: Fatin Mimi Anira Alias, Enrique Herreraviedma, Huchang Liao, Lazim Abdullah, Xunjie GouAbstract:Fuzzy Preference Relation (FPR) is commonly used in solving multi-criteria decision making problems because of its efficiency in representing people’s perceptions. However, the FPR suffers from an intrinsic limitation of consistency in decision making. In this regard, many researchers proposed the consistent fuzzy Preference Relation (CFPR) as a decision-making approach. Nevertheless, most CFPR methods involve a traditional aggregation process which does not identify the interRelationship between the criteria of decision problems. In addition, the information provided by individual experts is indeed related to that provided by other experts. Therefore, the interRelationship of information on criteria should be dealt with. Based on this motivation, we propose a modified approach of CFPR with Geometric Bonferroni Mean (GBM) operator. The proposed method introduces the GBM as an operator to aggregate information. The proposed method is applied to a case study of assessing the quality of life among the population in Setiu Wetlands. It is shown that the best option derived by the proposed method is consistent with that obtained from the other methods, despite the difference in aggregation operators.
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an ordinal consistency based group decision making process with probabilistic linguistic Preference Relation
Information Sciences, 2018Co-Authors: Yixin Zhang, Zeshui Xu, Huchang LiaoAbstract:Abstract The probabilistic linguistic Preference Relation (PLPR) reflects different Preference degrees (or weights) of experts over possible linguistic terms and improves the flexibility for experts in expressing linguistic Preference information. Ordinal consistency is the minimum condition to guarantee that experts would not give some self-contradictory Preferences. The ranking result of alternatives based on ordinal inconsistent Preference Relations is unreliable. This study investigates the ordinal consistency for PLPRs and the identification and modification of ordinal inconsistent PLPRs. To do so, this paper first defines the ordinal consistency of PLPR and presents the Preference graph associated with the PLPR. Then, we present theorems about ordinal consistency of PLPR and define an ordinal consistency index to measure the ordinal consistency level from the perspective of Preference graph. Moreover, we put forward an algorithm to check whether a PLPR is ordinal consistent and further identify the inconsistent elements for the inconsistent PLPR. Another algorithm based on three modification principles is further developed to modify the ordinal inconsistent PLPR and obtain the ordinal consistent one. Furthermore, we introduce new aggregation operators and present the whole decision-making procedure based on the ordinal consistency. Finally, a case study about water resource management is illustrated. Discussions of results and comparison analysis are also provided.
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nature disaster risk evaluation with a group decision making method based on incomplete hesitant fuzzy linguistic Preference Relations
International Journal of Environmental Research and Public Health, 2018Co-Authors: Ming Tang, Huchang LiaoAbstract:Because the natural disaster system is a very comprehensive and large system, the disaster reduction scheme must rely on risk analysis. Experts' knowledge and experiences play a critical role in disaster risk assessment. The hesitant fuzzy linguistic Preference Relation is an effective tool to express experts' Preference information when comparing pairwise alternatives. Owing to the lack of knowledge or a heavy workload, information may be missed in the hesitant fuzzy linguistic Preference Relation. Thus, an incomplete hesitant fuzzy linguistic Preference Relation is constructed. In this paper, we firstly discuss some properties of the additive consistent hesitant fuzzy linguistic Preference Relation. Next, the incomplete hesitant fuzzy linguistic Preference Relation, the normalized hesitant fuzzy linguistic Preference Relation, and the acceptable hesitant fuzzy linguistic Preference Relation are defined. Afterwards, three procedures to estimate the missing information are proposed. The first one deals with the situation in which there are only n-1 known judgments involving all the alternatives; the second one is used to estimate the missing information of the hesitant fuzzy linguistic Preference Relation with more known judgments; while the third procedure is used to deal with ignorance situations in which there is at least one alternative with totally missing information. Furthermore, an algorithm for group decision making with incomplete hesitant fuzzy linguistic Preference Relations is given. Finally, we illustrate our model with a case study about flood disaster risk evaluation. A comparative analysis is presented to testify the advantage of our method.
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consistency based risk assessment with probabilistic linguistic Preference Relation
Soft Computing, 2016Co-Authors: Yixin Zhang, Zeshui Xu, Hai Wang, Huchang LiaoAbstract:Display Omitted Propose the probabilistic linguistic Preference Relation (PLPR).Discuss the consistency of PLPR from the perspective of digraph.Present the consistency and acceptable consistency measures of PLPR.Establish an optimization model to improve the consistency of PLPR.Apply the proposed method to risk assessment. In recent years, the Belt and Road has aroused great attention of international society. It not only produces opportunities for China but also brings challenges: when Chinese investors invest to other countries, they will analyze the present situation of alternative countries and then assess the investment risk of these countries. Hence, how to assess the risk level of alternative countries correctly is pivotal. Moreover, affected by many factors such as decision makers (DMs) lacking of knowledge and the complexity of decision making problems, the DMs usually cannot use precise numbers to describe their Preference information. Therefore, the use of linguistic variables is practical. As a type of linguistic term set, the probabilistic linguistic term set (PLTS) can reflect different importance degrees or weights of all possible evaluation values of a specific object. Whats more, when the DMs use linguistic variables to express their judgements, they sometimes cannot give their evaluation values for attributes directly. In such a case, the DMs usually provide their judgements by pairwise comparison of alternatives. In this paper, we introduce the concept of probabilistic linguistic Preference Relation (PLPR) to present the DMs Preferences. The additive consistency of the PLPR is discussed from the perspective of the Preference Relation graph. Then, the consistency index of the PLPR is defined to measure the consistency. We also introduce the acceptable consistency of the PLPR. Moreover, as for the unacceptable consistent PLPR, an automatic optimization method is proposed to improve its consistency until acceptable. Once all the PLPRs are of acceptable consistency, we directly use the aggregation operators to obtain the comprehensive Preference values of alternatives and then rank the alternatives according to the derived Preference values. Finally, an application example involving the Belt and Road is given and the discussion about the results is conducted.
Yujie Wang - One of the best experts on this subject based on the ideXlab platform.
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interval valued fuzzy multi criteria decision making based on simple additive weighting and relative Preference Relation
Information Sciences, 2019Co-Authors: Yujie WangAbstract:Abstract To encompass imprecise messages, traditional multi-criteria decision-making (MCDM) was generalized into fuzzy multi-criteria decision-making(FMCDM) in solving decision-making problems. In numerous MCDM methods, simple additive weighting(SAW) is the simplest one, but fuzzy multiplication for generalizing SAW under fuzzy environment is still complicated, especially interval-valued fuzzy numbers. In the past, Wang proposed a model based on SAW and relative Preference Relation to resolve fuzzy multiplication tie. Practically, Wang's model is useful to fuzzy generalization of SAW. However, the model is only used in triangular fuzzy numbers. Recently, more and varied messages are obtained and processed for decision-making problems. Triangular fuzzy numbers are insufficient to express the variance, whereas interval-valued fuzzy numbers are suitable. Therefore, SAW had to be generalized under interval-valued fuzzy environment. In this paper, we combine SAW with a relative Preference Relation into interval-valued FMCDM to avoid fuzzy multiplication and grasp more messages. Our proposed relative Preference Relation improved from Lee's fuzzy Preference Relation is similar to Wang's relative Preference Relation. The main difference is that the proposed Relation is utilized in interval-valued fuzzy numbers, whereas Wang's is used in triangular fuzzy numbers. To sum up, we provide the FMCDM to solve decision-making problems with interval-valued fuzzy numbers easily and quickly.
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a fuzzy multi criteria decision making model based on simple additive weighting method and relative Preference Relation
Applied Soft Computing, 2015Co-Authors: Yujie WangAbstract:In this article, we combine SAW with relative Preference Relation in a FMCDM model to solve FMCDM problems.The FMCDM model avoids multiplying two fuzzy numbers into a pooled fuzzy number, and reserves fuzzy information.The FMCDM model based on SAW and relative Preference Relation to resolve the ties of fuzzy multiplication, aggregation and ranking. In the past, approaches often generalized classical multi-criteria decision-making (MCDM) methods under fuzzy environment to solve fuzzy multi-criteria decision-making (FMCDM) problems and encompass decision-making messages uncertainty and vagueness. These MCDM methods included analytic hierarchy process (AHP), simple additive weighting method (SAW), technique for order Preference by similarity to ideal solution (TOPSIS), etc. In the MCDM methods, SAW is a famous method that is applied in fuzzy environment, but fuzzy multiplication is a drawback to generalize SAW under fuzzy environment. To resolve the multiplication drawback, we utilize a relative Preference Relation that is from fuzzy Preference Relation in fuzzy generalized SAW. Generally, fuzzy Preference Relation is an option to reserve lots of messages. However, pair-wise comparison for fuzzy Preference Relation is complex on operation. Through the description above, the relative Preference Relation is improved form fuzzy Preference Relation to avoid comparing fuzzy numbers on pair-wise and reserving fuzzy messages. Through the relative Preference Relation, we can generalize SAW under fuzzy environment. It is said that we propose a FMCDM model based on SAW and the relative Preference Relation to easily and quickly solve FMCDM problems.
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ranking triangle and trapezoidal fuzzy numbers based on the relative Preference Relation
Applied Mathematical Modelling, 2015Co-Authors: Yujie WangAbstract:Abstract In this paper, we first propose a fuzzy Preference Relation with membership function representing Preference degree to compare two fuzzy numbers. Then a relative Preference Relation is constructed on the fuzzy Preference Relation to rank a set of fuzzy numbers. Since the fuzzy Preference Relation is a total ordering Relation satisfying reciprocal and transitive laws on fuzzy numbers, the relative Preference Relation satisfies a total ordering Relation on fuzzy numbers as well. Normally, utilizing Preference Relation is more reasonable than defuzzification on ranking fuzzy numbers, because defuzzification does not present Preference degree between two fuzzy numbers and loses some messages. However, fuzzy pair-wise comparison by Preference Relation is complex and difficult. To avoid above shortcomings, the relative Preference Relation adopts the strengths of defuzzification and fuzzy Preference Relation. That is to say, the relative Preference Relation expresses Preference degrees of several fuzzy numbers over average as similar as the fuzzy Preference Relation does, and ranks fuzzy numbers by relative crisp values as defuzzification does. Thus utilizing the relative Preference Relation ranks fuzzy numbers easily and quickly, and is able to reserve fuzzy information.
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a fuzzy multi criteria decision making model by associating technique for order Preference by similarity to ideal solution with relative Preference Relation
Information Sciences, 2014Co-Authors: Yujie WangAbstract:Generally, classical multi-criteria decision-making (MCDM) methods were extended to encompass uncertainty and vagueness of messages under fuzzy environment for solving decision-making problems, especially for technique for order Preference by similarity to ideal solution (TOPSIS). In the fuzzy extension of TOPSIS, fuzzy numbers comparison and aggregation based on fuzzy Preference Relation are important issues to compute distance values between alternatives and ideal (or anti-ideal) solution or rank feasible alternatives, because lots of messages are reserved by fuzzy Preference Relation. However, fuzzy Preference Relation on pair-wise comparison is commonly too complex to calculate. To avoid the drawback, we use a relative Preference Relation improved from fuzzy Preference Relation in the fuzzy extension of TOPSIS for computing distance values between alternatives and ideal (or anti-ideal) solution, or obtaining relative closeness coefficients of alternatives. Thus the relative Preference Relation on fuzzy numbers will be associated with TOPSIS under fuzzy environment to develop a fuzzy multi-criteria decision-making (FMCDM) model. Through the association above, FMCDM problems can be easily solved by the model. Further, we compare the proposed model with other methods to demonstrate the model's feasibility and rationality.
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a criteria weighting approach by combining fuzzy quality function deployment with relative Preference Relation
Applied Soft Computing, 2014Co-Authors: Yujie WangAbstract:In past, fuzzy multi-criteria decision-making (FMCDM) models desired to find an optimal alternative from numerous feasible alternatives under fuzzy environment. However, researches seldom focused on determination of criteria weights, although they were also important components for FMCDM. In fact, criteria weights can be computed through extending quality function deployment (QFD) under fuzzy environment, i.e. fuzzy quality function deployment (FQFD). By FQFD, customer demanded qualities expressing the opinions of customers and service development capabilities presenting the opinions of experts can be integrated into criteria weights for FMCDM. However, deriving criteria weights in FQFD may be complex and different to multiply two fuzzy numbers in real world. To resolve the tie, we will combine FQFD with relative Preference Relation on FMCDM problems. With the relative Preference Relation on fuzzy numbers, it is not necessary multiplying two fuzzy numbers to derive criteria weights in FQFD. Alternatively, adjusted criteria weights will substitute for original criteria weights through relative Preference Relation. Obviously, adjusted criteria weights are clearly determined and then utilized in FMCDM models.
Francisco Chiclana - One of the best experts on this subject based on the ideXlab platform.
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multi stage consistency optimization algorithm for decision making with incomplete probabilistic linguistic Preference Relation
Information Sciences, 2021Co-Authors: Francisco Chiclana, Peng Wang, Peide LiuAbstract:Abstract Incomplete probabilistic linguistic term sets (InPLTSs) can effectively describe the qualitative pairwise judgment information in uncertain decision-making problems, making them suitable for solving real decision-making problems under time pressure and lack of knowledge. Thus, in this study, an optimization algorithm is developed for Preference decision-making with the incomplete probabilistic linguistic Preference Relation (InPLPR). First, to fully investigate the ability of InPLTSs to express uncertain information, they are divided into two categories. Then, a two-stage mathematical optimization model based on an expected multiplicative consistency for estimating missing information is constructed, which can obtain the complete information more scientifically and effectively than some exiting methods. Subsequently, for the InPLPR with unacceptable consistency, a multi-stage consistency-improving optimization model is proposed for improving the consistency of the InPLPR by minimizing the information distortion and the number of adjusted linguistic terms, which can also minimize the uncertainty of the Relationship as small as possible. Afterward, to rank all the alternatives, a mathematical model for deriving the priority weights of the alternatives is constructed and solved, which can obtain the priority weight conveniently and quickly. A decision-making algorithm based on the consistency of the InPLPR is developed, which involves estimating missing information, checking and improving the consistency, and ranking the alternatives. Finally, a numerical case involving the selection of excellent students is presented to demonstrate the application of the proposed algorithm, and a detailed validation test and comparative analysis are presented to highlight the advantages of the proposed algorithm.
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A Consistency Based Procedure to Estimate Missing Pairwise Preference Values
2020Co-Authors: S Alonso, Francisco Chiclana, Francisco Herrera, E Herrera-viedma, J Alcalá-fernádez, Carlos PorcelAbstract:Abstract In this paper, we present a procedure to estimate missing Preference values when dealing with pairwise comparison and heterogeneous information. The 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 provided
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group decision making based on heterogeneous Preference Relations with self confidence
Fuzzy Optimization and Decision Making, 2017Co-Authors: Wenqi Liu, Francisco Chiclana, Yucheng Dong, Francisco Javier Cabrerizo, Enrique HerreraviedmaAbstract:Preference Relations are very useful to express decision makers’ Preferences over alternatives in the process of group decision-making. However, the multiple self-confidence levels are not considered in existing Preference Relations. In this study, we define the Preference Relation with self-confidence by taking multiple self-confidence levels into consideration, and we call it the Preference Relation with self-confidence. Furthermore, we present a two-stage linear programming model for estimating the collective Preference vector for the group decision-making based on heterogeneous Preference Relations with self-confidence. Finally, numerical examples are used to illustrate the two-stage linear programming model, and a comparative analysis is carried out to show how self-confidence levels influence on the group decision-making results.
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a consistency based procedure to estimate missing pairwise Preference values
Journal of intelligent systems, 2008Co-Authors: S Alonso, Francisco Chiclana, Francisco Herrera, Enrique Herreraviedma, Jesus Alcalafdez, Carlos PorcelAbstract: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. © 2008 Wiley Periodicals, Inc.
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integrating multiplicative Preference Relations in a multipurpose decision making model based on fuzzy Preference Relations
Fuzzy Sets and Systems, 2001Co-Authors: Francisco Chiclana, Francisco Herrera, Enrique HerreraviedmaAbstract:The aim of this paper is to study the integration of multiplicative Preference Relation as a Preference representation structure in fuzzy multipurpose decision-makingproblems. Assumingfuzzy multipurpose decision-makingproblems under di4erent Preference representation structures (ordering, utilities and fuzzy Preference Relations) and using the fuzzy Preference Relations as uniform representation elements, the multiplicative Preference Relations are incorporated in the decision problem by means of a transformation function between multiplicative and fuzzy Preference Relations. A consistency study of this transformation function, which demonstrates that it does not change the informative content of multiplicative Preference Relation, is shown. As a consequence, a selection process based on fuzzy majority for multipurpose decision-makingproblems under multiplicative Preference Relations is presented. To design it, an aggregation operator of information, called ordered weighted geometric operator, is introduced, and two choice degrees, the quanti7er-guided dominance degree and the quanti7er-guided non-dominance degree, are de7ned for multiplicative Preference Relations. c 2001 Elsevier Science B.V. All rights reserved.
Enrique Herreraviedma - One of the best experts on this subject based on the ideXlab platform.
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consistent fuzzy Preference Relation with geometric bonferroni mean a fused Preference method for assessing the quality of life
Applied Intelligence, 2019Co-Authors: Fatin Mimi Anira Alias, Enrique Herreraviedma, Huchang Liao, Lazim Abdullah, Xunjie GouAbstract:Fuzzy Preference Relation (FPR) is commonly used in solving multi-criteria decision making problems because of its efficiency in representing people’s perceptions. However, the FPR suffers from an intrinsic limitation of consistency in decision making. In this regard, many researchers proposed the consistent fuzzy Preference Relation (CFPR) as a decision-making approach. Nevertheless, most CFPR methods involve a traditional aggregation process which does not identify the interRelationship between the criteria of decision problems. In addition, the information provided by individual experts is indeed related to that provided by other experts. Therefore, the interRelationship of information on criteria should be dealt with. Based on this motivation, we propose a modified approach of CFPR with Geometric Bonferroni Mean (GBM) operator. The proposed method introduces the GBM as an operator to aggregate information. The proposed method is applied to a case study of assessing the quality of life among the population in Setiu Wetlands. It is shown that the best option derived by the proposed method is consistent with that obtained from the other methods, despite the difference in aggregation operators.
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group decision making based on heterogeneous Preference Relations with self confidence
Fuzzy Optimization and Decision Making, 2017Co-Authors: Wenqi Liu, Francisco Chiclana, Yucheng Dong, Francisco Javier Cabrerizo, Enrique HerreraviedmaAbstract:Preference Relations are very useful to express decision makers’ Preferences over alternatives in the process of group decision-making. However, the multiple self-confidence levels are not considered in existing Preference Relations. In this study, we define the Preference Relation with self-confidence by taking multiple self-confidence levels into consideration, and we call it the Preference Relation with self-confidence. Furthermore, we present a two-stage linear programming model for estimating the collective Preference vector for the group decision-making based on heterogeneous Preference Relations with self-confidence. Finally, numerical examples are used to illustrate the two-stage linear programming model, and a comparative analysis is carried out to show how self-confidence levels influence on the group decision-making results.
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a consistency based procedure to estimate missing pairwise Preference values
Journal of intelligent systems, 2008Co-Authors: S Alonso, Francisco Chiclana, Francisco Herrera, Enrique Herreraviedma, Jesus Alcalafdez, Carlos PorcelAbstract: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. © 2008 Wiley Periodicals, Inc.
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integrating multiplicative Preference Relations in a multipurpose decision making model based on fuzzy Preference Relations
Fuzzy Sets and Systems, 2001Co-Authors: Francisco Chiclana, Francisco Herrera, Enrique HerreraviedmaAbstract:The aim of this paper is to study the integration of multiplicative Preference Relation as a Preference representation structure in fuzzy multipurpose decision-makingproblems. Assumingfuzzy multipurpose decision-makingproblems under di4erent Preference representation structures (ordering, utilities and fuzzy Preference Relations) and using the fuzzy Preference Relations as uniform representation elements, the multiplicative Preference Relations are incorporated in the decision problem by means of a transformation function between multiplicative and fuzzy Preference Relations. A consistency study of this transformation function, which demonstrates that it does not change the informative content of multiplicative Preference Relation, is shown. As a consequence, a selection process based on fuzzy majority for multipurpose decision-makingproblems under multiplicative Preference Relations is presented. To design it, an aggregation operator of information, called ordered weighted geometric operator, is introduced, and two choice degrees, the quanti7er-guided dominance degree and the quanti7er-guided non-dominance degree, are de7ned for multiplicative Preference Relations. c 2001 Elsevier Science B.V. All rights reserved.
Roman Slowinski - One of the best experts on this subject based on the ideXlab platform.
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ordinal regression revisited multiple criteria ranking using a set of additive value functions
European Journal of Operational Research, 2008Co-Authors: Salvatore Greco, Roman Slowinski, Vincent MousseauAbstract:We present a new method, called UTAGMS, for multiple criteria ranking of alternatives from set A using a set of additive value functions which result from an ordinal regression. The Preference information provided by the decision maker is a set of pairwise comparisons on a subset of alternatives ARÂ [subset, double equals]Â A, called reference alternatives. The Preference model built via ordinal regression is the set of all additive value functions compatible with the Preference information. Using this model, one can define two Relations in the set A: the necessary weak Preference Relation which holds for any two alternatives a, b from set A if and only if for all compatible value functions a is preferred to b, and the possible weak Preference Relation which holds for this pair if and only if for at least one compatible value function a is preferred to b. These Relations establish a necessary and a possible ranking of alternatives from A, being, respectively, a partial preorder and a strongly complete Relation. The UTAGMS method is intended to be used interactively, with an increasing subset AR and a progressive statement of pairwise comparisons. When no Preference information is provided, the necessary weak Preference Relation is a weak dominance Relation, and the possible weak Preference Relation is a complete Relation. Every new pairwise comparison of reference alternatives, for which the dominance Relation does not hold, is enriching the necessary Relation and it is impoverishing the possible Relation, so that they converge with the growth of the Preference information. Distinguishing necessary and possible consequences of Preference information on the complete set of actions, UTAGMS answers questions of robustness analysis. Moreover, the method can support the decision maker when his/her Preference statements cannot be represented in terms of an additive value function. The method is illustrated by an example solved using the UTAGMS software. Some extensions of the method are also presented.
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ordinal regression revisited multiple criteria ranking using a set of additive value functions
European Journal of Operational Research, 2008Co-Authors: Salvatore Greco, Roman Slowinski, Vincent MousseauAbstract:Abstract We present a new method, called UTAGMS, for multiple criteria ranking of alternatives from set A using a set of additive value functions which result from an ordinal regression. The Preference information provided by the decision maker is a set of pairwise comparisons on a subset of alternatives AR ⊆ A, called reference alternatives. The Preference model built via ordinal regression is the set of all additive value functions compatible with the Preference information. Using this model, one can define two Relations in the set A: the necessary weak Preference Relation which holds for any two alternatives a, b from set A if and only if for all compatible value functions a is preferred to b, and the possible weak Preference Relation which holds for this pair if and only if for at least one compatible value function a is preferred to b. These Relations establish a necessary and a possible ranking of alternatives from A, being, respectively, a partial preorder and a strongly complete Relation. The UTAGMS method is intended to be used interactively, with an increasing subset AR and a progressive statement of pairwise comparisons. When no Preference information is provided, the necessary weak Preference Relation is a weak dominance Relation, and the possible weak Preference Relation is a complete Relation. Every new pairwise comparison of reference alternatives, for which the dominance Relation does not hold, is enriching the necessary Relation and it is impoverishing the possible Relation, so that they converge with the growth of the Preference information. Distinguishing necessary and possible consequences of Preference information on the complete set of actions, UTAGMS answers questions of robustness analysis. Moreover, the method can support the decision maker when his/her Preference statements cannot be represented in terms of an additive value function. The method is illustrated by an example solved using the UTAGMS software. Some extensions of the method are also presented.
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mining decision rule Preference model from rough approximation of Preference Relation
Computer Software and Applications Conference, 2002Co-Authors: Roman Slowinski, Salvatore Greco, Benedetto MatarazzoAbstract:Given a ranking of actions evaluated by a set of evaluation criteria, we construct a rough approximation of the Preference Relation known from this ranking. The rough approximation of the Preference Relation is a starting point for mining " if... then" decision rules constituting a symbolic Preference model. The set of rules is induced such as to be compatible with a concordance-discordance Preference model used in well-known multicriteria decision aiding methods. An application of the set of decision rules to a new set of actions gives a fuzzy outranking graph. Positive and negative flows are calculated for each action in the graph, giving arguments about its strength and weakness. Aggregation of both arguments leads to a final ranking, either partial or complete. The approach can be applied to support a multicriteria choice and ranking of actions when the input information is a ranking of some reference actions.
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rough approximation of a Preference Relation by dominance Relations
European Journal of Operational Research, 1999Co-Authors: Salvatore Greco, Benedetto Matarazzo, Roman SlowinskiAbstract:An original methodology for using rough sets to Preference modeling in multi-criteria decision problems is presented. This methodology operates on a pairwise comparison table (PCT), including pairs of actions described by graded Preference Relations on particular criteria and by a comprehensive Preference Relation. It builds up a rough approximation of a Preference Relation by graded dominance Relations. Decision rules derived from the rough approximation of a Preference Relation can be used to obtain a recommendation in multi-criteria choice and ranking problems. The methodology is illustrated by an example of multi-criteria programming of water supply systems.
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rough approximation of a Preference Relation in a pairwise comparison table
1998Co-Authors: Salvatore Greco, Benedetto Matarazzo, Roman SlowinskiAbstract:A methodology for using rough sets for Preference modelling in multi-criteria decision problems is presented. It operates on a pairwise comparison table (PCT), i.e. an information table whose objects are pairs of actions instead of single actions, and whose entries are binary Relations (graded Preference Relations) instead of attribute values. PCT is a specific information table and, therefore, all the concepts of the rough set analysis can be adapted to it. However, the classical rough set approximations based on indiscernibility Relation do not consider the ordinal properties of the criteria in a decision problem. To deal with these properties, a rough approximation based on graded dominance Relations has been recently proposed. The decision rules obtained from these rough approximations can be used to obtain a recommendation in different multi-criteria decision problems. The methodology is illustrated by an example which compares the results obtained when using the rough approximation by indiscernibility Relation and the rough approximation by graded dominance Relations, respectively.
