Group decision-making based on heterogeneous preference relations with self-confidence

The file attached to this record is the author's final peer reviewed version. The Publisher's final version can be found by following the DOI link.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

Social network decision making with linguistic trustworthiness based induced OWA operators

The file attached to this record is the authors final peer reviewed version. The publisher's version of record can be found by following the DOI link.Classic aggregation operators in group decision making such as the OWA, IOWA, C-IOWA, P-IOWA and I-IOWA have shown to be successful tools in order to provide flexibility in the aggregation of preferences. However, these operators do not take advantage of information related to the interaction between experts. Experts involved in a group decision making problem may have developed opinions about the reliability of other experts' judgements, either because they have previous history of interaction with each other or because they have knowledge that informs them on the reliability of other colleagues in the group in solving decision making problems in the past. In this paper, and within the framework of social network decision making, we present three new social network analysis based IOWA operators that take advantage of the linguistic trustworthiness information gathered from the experts' social network to aggregate the social group preferences. Their use is analysed with simple but illustrative examples

An Interval Valued K-Nearest Neighbors Classifier

The K-Nearest Neighbors (k-NN) classifier has become a well-known, successful method for pattern classification tasks. In recent years, many enhancements to the original algorithm have been proposed. Fuzzy sets theory has been the basis of several proposed models towards the enhancement of the nearest neighbors rule, being the Fuzzy K-Nearest Neighbors (FuzzyKNN) classifier the most notable procedure in the field. In this work we present a new approach to the nearest neighbor classifier based on the use of interval valued fuzzy sets. The use and implementation of interval values facilitates the membership of the instances and the computation of the votes in a more flexible way than the original FuzzyKNN method, thus improving its adaptability to different supervised learning problems. An experimental study, contrasted by the application of nonparametric statistical procedures, is carried out to ascertain whether the Interval Valued K-Nearest Neighbor (IV-KNN) classifier proposed here is significantly more accurate than k-NN, FuzzyKNN and other fuzzy nearest neighbor classifiers. We conclude that the IV-KNN is indeed significantly more accurate than the rest of classifiers analyzed

On aggregating uncertain information by type-2 OWA operators for soft decision making

Yager's ordered weighted averaging (OWA) operator has been widely used in soft decision making to aggregate experts. individual opinions or preferences for achieving an overall decision. The traditional Yager's OWA operator focuses exclusively on the aggregation of crisp numbers. However, human experts usually tend to express their opinions or preferences in a very natural way via linguistic terms. Type-2 fuzzy sets provide an efpcient way of knowledge representation for modeling linguistic terms. In order to aggregate linguistic opinions via OWA mechanism, we propose a new type of OWA operator, termed type-2 OWA operator, to aggregate the linguistic opinions or preferences in human decision making modeled by type-2 fuzzy sets. A Direct Approach to aggregating interval type-2 fuzzy sets by type-2 OWA operator is suggested in this paper. Some examples are provided to delineate the proposed technique. © 2010 Wiley Periodicals, Inc

Alpha-level aggregation: A practical approach to type-1 OWA operation for aggregating uncertain information with applications to breast cancer treatments

Type-1 Ordered Weighted Averaging (OWA) operator provides us with a new technique for directly aggregating uncertain information with uncertain weights via OWA mechanism in soft decision making and data mining, in which uncertain objects are modeled by fuzzy sets. The Direct Approach to performing type-1 OWA operation involves high computational overhead. In this paper, we define a type-1 OWA operator based on the α-cuts of fuzzy sets. Then, we prove a Representation Theorem of type-1 OWA operators, by which type-1 OWA operators can be decomposed into a series of α-level type-1 OWA operators. Furthermore, we suggest a fast approach, called Alpha-Level Approach, to implementing the type-1 OWA operator. A practical application of type-1 OWA operators to breast cancer treatments is addressed. Experimental results and theoretical analyses show that: 1) the Alpha-Level Approach with linear order complexity can achieve much higher computing efficiency in performing type-1 OWA operation than the existing Direct Approach, 2) the type-1 OWA operators exhibit different aggregation behaviors from the existing fuzzy weighted averaging (FWA) operators, and 3) the type-1 OWA operators demonstrate the ability to efficiently aggregate uncertain information with uncertain weights in solving real-world soft decision-making problems. © 2011 IEEE

Type-1 OWA operators for aggregating uncertain information with uncertain weights induced by type-2 linguistic quantifiers

The OWA operator proposed by Yager has been widely used to aggregate experts' opinions or preferences in human decision making. Yager's traditional OWA operator focuses exclusively on the aggregation of crisp numbers. However, experts usually tend to express their opinions or preferences in a very natural way via linguistic terms. These linguistic terms can be modelled or expressed by (type-1) fuzzy sets. In this paper, we define a new type of OWA operator, the type-1 OWA operator that works as an uncertain OWA operator to aggregate type-1 fuzzy sets with type-1 fuzzy weights, which can be used to aggregate the linguistic opinions or preferences in human decision making with linguistic weights. The procedure for performing type-1 OWA operations is analysed. In order to identify the linguistic weights associated to the type-1 OWA operator, type-2 linguistic quantifiers are proposed. The problem of how to derive linguistic weights used in type-1 OWA aggregation given such type of quantifier is solved. Examples are provided to illustrate the proposed concepts. Crown Copyright © 2008

On constructing parsimonious type-2 fuzzy logic systems via influential rule selection

Type-2 fuzzy systems are increasing in popularity, and there are many examples of successful applications. While many techniques have been proposed for creating parsimonious type-1 fuzzy systems, there is a lack of such techniques for type-2 systems. The essential problem is to reduce the number of rules, while maintaining the system's approximation performance. In this paper, four novel indexes for ranking the relative contribution of type-2 fuzzy rules are proposed, which are termed values, c-values, ω1-values, and ω2 -values. The R-values of type-2 fuzzy rules are obtained by applying a QR decomposition pivoting algorithm to the firing strength matrices of the trained fuzzy model. The c-values rank rules based on the effects of rule consequents, while the ω1-values and ω2-values consider both the rule-base structure (via firing strength matrices) and the output contribution of fuzzy rule consequents. Two procedures for utilizing these indexes in fuzzy rule selection (termed "forward selection"and "backward elimination") are described. Experiments are presented which demonstrate that by using the proposed methodology, the most influential type-2 fuzzy rules can be effectively retained in order to construct parsimonious type-2 fuzzy models. © 2009 IEEE

On Constructing Parsimonious Type-2 Fuzzy Logic Systems via Influential Rule Selection

Type-2 fuzzy systems are increasing in popularity, and there are many examples of successful applications. While many techniques have been proposed for creating parsimonious type-1 fuzzy systems, there is a lack of such techniques for type-2 systems. The essential problem is to reduce the number of rules, while maintaining the system's approximation performance. In this paper, four novel indexes for ranking the relative contribution of type-2 fuzzy rules are proposed, which are termed R-values, c-values, ω1 -values, and ω2 -values. The R-values of type-2 fuzzy rules are obtained by applying a QR decomposition pivoting algorithm to the firing strength matrices of the trained fuzzy model. The c-values rank rules based on the effects of rule consequents, while the ω1 -values and ω2 -values consider both the rule-base structure (via firing strength matrices) and the output contribution of fuzzy rule consequents. Two procedures for utilizing these indexes in fuzzy rule selection (termed "forward selection" and "backward elimination") are described. Experiments are presented which demonstrate that by using the proposed methodology, the most influential type-2 fuzzy rules can be effectively retained in order to construct parsimonious type-2 fuzzy models

Type-1 OWA Unbalanced Fuzzy Linguistic Aggregation Methodology. Application to Eurobonds Credit Risk Evaluation

The file attached to this record is the author's final peer reviewed version. The Publisher's final version can be found by following the DOI link.In decision making, a widely used methodology to manage unbalanced fuzzy linguistic information is the linguistic hierarchy (LH), which relies on a linguistic symbolic computational model based on ordinal 2-tuple linguistic representation. However, the ordinal 2-tuple linguistic approach does not exploit all advantages of Zadeh's fuzzy linguistic approach to model uncertainty because the membership function shapes are ignored. Furthermore, the LH methodology is an indirect approach that relies on the uniform distribution of symmetric linguistic assessments. These drawbacks are overcome by applying a fuzzy methodology based on the implementation of the Type-1 Ordered Weighted Average (T1OWA) operator. The T1OWA operator is not a symbolic operator and it allows to directly aggregate membership functions, which in practice means that the T1OWA methodology is suitable for both balanced and unbalanced linguistic contexts and with heterogeneous membership functions. Furthermore, the final output of the T1OWA methodology is always fuzzy and defined in the same domain of the original unbalanced fuzzy linguistic labels, which facilitates its interpretation via a visual joint representation. A case study is presented where the T1OWA operator methodology is used to assess the creditworthiness of European bonds based on real credit risk ratings of individual Eurozone member states modelled as unbalanced fuzzy linguistic labels

GDMR A new framework in R to suppot Fuzzy Group Decision Making processes

This is a summary of our article published in Information Science [12] to be part of the MultiConference CAEPIA'15 KeyWorks