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

A T1OWA Fuzzy Linguistic Aggregation Methodology for Searching Feature-based Opinions.

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.Online services such as Amazon, Tripadvisor, Ebay, etc., allow users to express sentiments about different products or services. Not only that, in some cases it is also possible to express sentiments about the different features characterizing those products or services. Most users express sentiments about individual features by using numerical values, which sometimes do not allow users to reflect properly what they are meaning and therefore they are misleading. To overcome this key issue and make users’ opinions in online services more comprehensive, a new methodology for representing sentiments using linguistic term sets instead of numerical values is presented. In addition, this methodology will allow to implement importance degrees on the different features characterizing users’ opinions. From both sentiments and importance of the features, the most important opinions for each user is derived via an aggregation step based on the Type-1 Ordered Weighted Averaging (T1OWA) operator, which is able to aggregate the corresponding fuzzy set representations of linguistic terms. Furthermore, the final output of the T1OWA based-search process can easily be interpreted by users because it is always of the same type (fuzzy) and defined in the same domain of the original fuzzy linguistic labels. A case study is presented where the T1OWA operator methodology is used to assess different opinions according to different user profiles

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

In decision making, a widely used methodology to manage unbalanced fuzzy linguistic informa- tion 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 draw- backs 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 opera- tor 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 modeled as unbalanced fuzzy linguistic labels.This research work has been supported by the research projects grants (TIN2013-40658-P and TIN2016- 75850-R) from the FEDER funds, and the University of Granada `Strengthening through Short-Visits' (Ref. GENIL-SSV 2015) programme

Type-1 OWA Operators in Aggregating Multiple Sources of Uncertain Information: Properties and Real-World Applications in Integrated Diagnosis.

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.The type-1 ordered weighted averaging (T1OWA) operator has demonstrated the capacity for directly aggregating multiple sources of linguistic information modeled by fuzzy sets rather than crisp values. Yager's ordered weighted averaging (OWA) operators possess the properties of idempotence, monotonicity, compensativeness, and commutativity . This article aims to address whether or not T1OWA operators possess these properties when the inputs and associated weights are fuzzy sets instead of crisp numbers. To this end, a partially ordered relation of fuzzy sets is defined based on the fuzzy maximum ( join ) and fuzzy minimum ( meet ) operators of fuzzy sets, and an alpha-equivalently-ordered relation of groups of fuzzy sets is proposed. Moreover, as the extension of orness and andness of an Yager's OWA operator, joinness and meetness of a T1OWA operator are formalized, respectively. Then, based on these concepts and the representation theorem of T1OWA operators , we prove that T1OWA operators hold the same properties as Yager's OWA operators possess, i.e., idempotence, monotonicity, compensativeness, and commutativity . Various numerical examples and a case study of diabetes diagnosis are provided to validate the theoretical analyses of these properties in aggregating multiple sources of uncertain information and improving integrated diagnosis, respectively