Laplacian Mixture Modeling for Network Analysis and Unsupervised Learning on Graphs

Laplacian mixture models identify overlapping regions of influence in unlabeled graph and network data in a scalable and computationally efficient way, yielding useful low-dimensional representations. By combining Laplacian eigenspace and finite mixture modeling methods, they provide probabilistic or fuzzy dimensionality reductions or domain decompositions for a variety of input data types, including mixture distributions, feature vectors, and graphs or networks. Provable optimal recovery using the algorithm is analytically shown for a nontrivial class of cluster graphs. Heuristic approximations for scalable high-performance implementations are described and empirically tested. Connections to PageRank and community detection in network analysis demonstrate the wide applicability of this approach. The origins of fuzzy spectral methods, beginning with generalized heat or diffusion equations in physics, are reviewed and summarized. Comparisons to other dimensionality reduction and clustering methods for challenging unsupervised machine learning problems are also discussed.Comment: 13 figures, 35 reference

CAD Software Evaluation for Product Design to Exchange Data in a Supply Chain Network

The sharing information in a supply chain environment, especially CAD models and drawings are so important companies. So, the selection of the most satisfying computer-aided design (CAD) software which enables to exchange data through supply chain network has been major issues for companies in a supply chain. The selection process of CAD software among the raising number of alternatives in the market has been very vital and critical issue for companies that aim to make their design and engineering related activities automated towards computer integrated manufacturing (CIM) environment. Therefore, most companies have used various methods to successfully carry out this difficult and time-consuming process. Of these methods, Analytic Hierarchy Process (AHP) has been widely used for Multiple Criteria Decision Making (MCDM) problems in both academic researches and practices. But, in some cases, due to the vagueness and uncertainty on judgments of the decision-maker(s), the crisp pair wise comparison in the conventional AHP seems to be insufficient and imprecise to capture the right judgments of decision-maker(s). Therefore, a fuzzy logic is introduced in the pair wise comparison of AHP to make up for this deficiency in the conventional AHP, called as fuzzy AHP. In this paper, a fuzzy AHP-based approach is proposed to evaluate a set of CAD software alternatives in the market to reach the best satisfying one based on the needs of company

A review of fuzzy AHP methods for decision-making with subjective judgements

Analytic Hierarchy Process (AHP) is a broadly applied multi-criteria decision-making method to determine the weights of criteria and priorities of alternatives in a structured manner based on pairwise comparison. As subjective judgments during comparison might be imprecise, fuzzy sets have been combined with AHP. This is referred to as fuzzy AHP or FAHP. An increasing amount of papers are published which describe different ways to derive the weights/priorities from a fuzzy comparison matrix, but seldomly set out the relative benefits of each approach so that the choice of the approach seems arbitrary. A review of various fuzzy AHP techniques is required to guide both academic and industrial experts to choose suitable techniques for a specific practical context. This paper reviews the literature published since 2008 where fuzzy AHP is applied to decision-making problems in industry, particularly the various selection problems. The techniques are categorised by the four aspects of developing a fuzzy AHP model: (i) representation of the relative importance for pairwise comparison, (ii) aggregation of fuzzy sets for group decisions and weights/priorities, (iii) defuzzification of a fuzzy set to a crisp value for final comparison, and (iv) consistency measurement of the judgements. These techniques are discussed in terms of their underlying principles, origins, strengths and weakness. Summary tables and specification charts are provided to guide the selection of suitable techniques. Tips for building a fuzzy AHP model are also included and six open questions are posed for future work

Mapping customer needs to engineering characteristics: an aerospace perspective for conceptual design

Designing complex engineering systems, such as an aircraft or an aero-engine, is immensely challenging. Formal Systems Engineering (SE) practices are widely used in the aerospace industry throughout the overall design process to minimise the overall design effort, corrective re-work, and ultimately overall development and manufacturing costs. Incorporating the needs and requirements from customers and other stakeholders into the conceptual and early design process is vital for the success and viability of any development programme. This paper presents a formal methodology, the Value-Driven Design (VDD) methodology that has been developed for collaborative and iterative use in the Extended Enterprise (EE) within the aerospace industry, and that has been applied using the Concept Design Analysis (CODA) method to map captured Customer Needs (CNs) into Engineering Characteristics (ECs) and to model an overall ‘design merit’ metric to be used in design assessments, sensitivity analyses, and engineering design optimisation studies. Two different case studies with increasing complexity are presented to elucidate the application areas of the CODA method in the context of the VDD methodology for the EE within the aerospace secto

The evaluation performance for commercial banks by intuitionistic fuzzy numbers: the case of Spain

In a globalized world, the banking sector has been forced to advance not only in financial performance, but also in non-financial performance, especially in sustainability criteria. For this purpose, multicriteria decision methods are especially suited to evaluate efficiency and to make a stable ranking of the most outstanding banks in the Spanish financial system. However, we are aware of the difficulties involved due to the inherent uncertainty and subjectivity of this process. For this reason, the use of fuzzy models is proposed, especially intuitionistic fuzzy numbers combined with the Analytic Hierarchy Process and the TOPSIS. The combination of financial criteria based on the CAMELS rating system with non-financial sustainability criteria makes it possible to order the Spanish banking system based on global efficiency. The most relevant contributions are: first, the use of intuitionistic fuzzy numbers in the performance evaluation process, whereby the quality of the information available can be quantified; and the most important one, a simplification of the process in the implementation of the intuitionistic fuzzy TOPSIS. Finally, through a sensibility analysis, it is possible to isolate the relevance of the sustainability process to obtain the global performance evaluation

COMPARISON OF DIFFERENT FUZZY AHP METHODOLOGIES IN RISK ASSESSMENT

Being able to evaluate risks is an important task in many areas of human activity: economics, ecology, etc. Usually, environmental risk assessment is carried out on the basis of multiple and sometimes conflicting factors. Using multiple criteria decision-making (MCDM) methodology is one of the possible ways to solve the problem. Methodologies of analytic hierarchy process (AHP) are the most commonly used MCDM methods, which combine subjective and personal preferences in risk assessment process. However, AHP involves human subjectivity, which introduces vagueness type of uncertainty and requires the usage of decision making under those uncertainties. In this paper it was considered to deal with uncertainty by using the fuzzy-based techniques. However, nowadays there exist multiple Fuzzy AHP methodologies developed by different authors. In this paper, these Fuzzy AHP methodologies will be compared, and the most appropriate Fuzzy AHP methodology for the application in case of environmental risks assessment will be offered on the basis of this comparison

Decision support model for the selection of asphalt wearing courses in highly trafficked roads

The suitable choice of the materials forming the wearing course of highly trafficked roads is a delicate task because of their direct interaction with vehicles. Furthermore, modern roads must be planned according to sustainable development goals, which is complex because some of these might be in conflict. Under this premise, this paper develops a multi-criteria decision support model based on the analytic hierarchy process and the technique for order of preference by similarity to ideal solution to facilitate the selection of wearing courses in European countries. Variables were modelled using either fuzzy logic or Monte Carlo methods, depending on their nature. The views of a panel of experts on the problem were collected and processed using the generalized reduced gradient algorithm and a distance-based aggregation approach. The results showed a clear preponderance by stone mastic asphalt over the remaining alternatives in different scenarios evaluated through sensitivity analysis. The research leading to these results was framed in the European FP7 Project DURABROADS (No. 605404).The research leading to these results has received funding from the European Union Seventh Framework Programme (FP7/2007–2013) under Grant Agreement No. 605404

Permutation based decision making under fuzzy environment using Tabu search

One of the techniques, which are used for Multiple Criteria Decision Making (MCDM) is the permutation. In the classical form of permutation, it is assumed that weights and decision matrix components are crisp. However, when group decision making is under consideration and decision makers could not agree on a crisp value for weights and decision matrix components, fuzzy numbers should be used. In this article, the fuzzy permutation technique for MCDM problems has been explained. The main deficiency of permutation is its big computational time, so a Tabu Search (TS) based algorithm has been proposed to reduce the computational time. A numerical example has illustrated the proposed approach clearly. Then, some benchmark instances extracted from literature are solved by proposed TS. The analyses of the results show the proper performance of the proposed method