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The early diagnosis of the glaucoma disease in the eye is crucial to avoid vision loss. This paper proposes an efficient computer-aided detection (CAD) system for diagnosing glaucoma based on fundus images, deep transfer learning and fuzzy aggregation operators. Specifically, the proposed CAD system includes three stages: (1) Detection of the region of interest of the optic disc using an efficient deep learning network, (2) Classification of images based on different pre-trained deep convolutional neural networks and support vector machines, and (3) Use of fuzzy aggregation operators to fuse the predictions of glaucoma classifiers. We used three popular yet robust aggregators: ordered weighted averaging (OWA) operator, weighted power mean (WPM), and exponential mean (EXM). We assessed the efficacy of the proposed glaucoma CAD system on three public datasets: DRISHTI-GS1, RIM-ONE, and REFUGE. The proposed conjunctive OWA aggregation method (Conj-OWA) achieves the best glaucoma classification results. Specifically, it achieves accuracy values of 90.2%, 97.8%, and 94.3% and area under the curve (AUC) values of 95.3%, 99.8%, and 96.2%, respectively, on DRISHTI-GS1, RIM-ONE, and REFUGE databases.

The VIKOR-F method has been developed to solve fuzzy multicriteria problem with conflicting and noncommensurable (different units) criteria. It determines the compromise solution that is the "closest" to the ideal. Imprecision in multicriteria decision making can be modelled using fuzzy set theory to define criteria and the importance of criteria. This method solves problem in a fuzzy environment where both criteria and weights could be fuzzy sets. The triangular fuzzy numbers are used to handle imprecise numerical quantities. It is based on the aggregating fuzzy merit that represents distance of an alternative to the ideal solution. The fuzzy operations and procedures for ranking fuzzy numbers are used in developing the VIKOR-F algorithm. A numerical example illustrates an application of the VIKOR-F method.

In many real-life decision making (DM) situations, the available information is vague or imprecise. To adequately solve decision problems with vague or imprecise information, fuzzy set theory and aggregation operator theory have become powerful tools. In last three decades, DM theories and methods under fuzzy aggregation operator have been proposed and developed for effectively solving the DM problems and numerous applications have been reported in the literature. While various aggregation operators have been suggested and developed, there is a lack of research regarding systematic literature review and classification of study in this field. Regarding this, Web of Science database has been nominated and systematic and meta-analysis method called “PRISMA” has been proposed. Accordingly, a review of 312 published articles appearing in 33 popular journals related to fuzzy set theory, aggregation operator theory and DM approaches between July 1986 and June 2017 have been attained to reach a comprehensive review of DM methods and aggregation operator environment. Consequently, the selected published articles have been categorized by name of author(s), the publication year, technique, application area, country, research contribution and journals in which they appeared. The findings of this study found that, ordered weighted averaging (OWA) has been the highest frequently accessed more than other areas. This systematic review shows that the DM theories under fuzzy aggregation operator environment have received a great deal of interest from researchers and practitioners in many disciplines.

For decreasing service centers’ selection risks in emergency facility location selection, it is crucial to have selected candidate service centers within deeply detailed facility location selection model. To achieve this, a new approach developed in this article involves two stages. In the first stage, the fuzzy multi-attribute group decision making (MAGDM) model for evaluation of the selection of candidate service centers is created. For the aggregation of experts’ assessments of candidate service centers (with respect to attributes) aggregation operators’ approach is used. Experts’ assessments are presented in fuzzy terms with semantic form of triangular fuzzy numbers. For the deeply detailed facility location selection modeling and for the intellectual activity of experts in their evaluations, pairwise interactions between attributes of MAGDM model are considered in the construction of the second-order additive triangular fuzzy valued fuzzy measure (TFVFM). The associated triangular fuzzy probability averaging (As-TFPA) aggregation operators’ family is constructed with respect to TFVFM. Analytical properties of the As-TFPA operators are studied. The new operators are certain extensions of the well-known Choquet integral operator. The extensions, in contrast to the Choquet aggregation, consider all possible pair-wise interactions of the attributes by introducing associated fuzzy probabilities of a TFVFM. At the end of the first stage, a candidate service center’s selection index is defined as As-TFPA operator’s aggregation value on experts’ assessments with respect to attributes.

At the second stage, fuzzy multi-objective facility location set covering problem (MOFLSCP) is created for facility location selection optimal planning with new criteria: (1) maximization of candidate service centers selection index and classical two criteria, (2) minimization of the total cost needed to open service centers and (3) minimization of number of agents needed to operate the opened service centers.

For the constructed two-stage methodology a simulation example of emergency service facility location planning for a city is considered. The example gives the Pareto fronts obtained by As-TFPA operators, the Choquet integral-TFCA operator and well-known TOPSIS approach, for optimal selecting candidate sites for the servicing of demand points. The comparative analysis identifies that the differences in the Pareto solutions, obtained by using As-TFPA operators and TFCA operator or TOPSIS aggregation, are also caused by the fact that TFCA operator or TOPSIS approach considers the pair interaction indexes for only one consonant structure of attributes. While new As-TFPA aggregations provide all pairwise interactions for all consonant structures.