Special Issue "Applications of Fuzzy Optimization and Fuzzy Decision Making"

A special issue of Mathematics (ISSN 2227-7390). This special issue belongs to the section "Fuzzy Set Theory".

Deadline for manuscript submissions: 30 September 2020.

Special Issue Editor

Prof. Dr. Vassilis C. Gerogiannis
Website
Guest Editor
University of Thessaly, Larissa, Greece
Interests: Fuzzy Decision Making; Software Engineering; Requirements Engineering; Systems Analysis and Design

Special Issue Information

Dear Colleagues,

We invite you to submit your latest applied research in the field of fuzzy optimization and decision making to the Special Issue entitled “Applications of Fuzzy Optimization and Fuzzy Decision Making”. The aim of the Special Issue is to expand the applicability of fuzzy optimization and decision making for solving various types of problems in the areas of economics, business, engineering, management, operations research, etc. Any experimental research or empirical study of theoretical developments in fuzzy optimization and decision making is highly welcome. Additionally, research papers presenting solution methods and/or studying their computational complexity, and proposing new algorithms to solve fuzzy optimization and decision making problems, in an effective and efficient manner, are also welcome. We are looking forward to receive innovative approaches that apply, in practical settings, state-of-the art mathematical/algorithmic techniques from fuzzy technology, computational intelligence and soft-computing methodologies, with the aim to offer robust solutions for complex optimization and decision making problems characterized by non-probabilistic uncertainty, vagueness, ambiguity, and hesitation. Such type of papers will address the suitability, validity, and advantages of using fuzzy technologies and the enhancement of them using intelligent methods to treat real-life problems from various disciplines.

Submissions may present, but are not limited to, applications of the following methods:

fuzzy sets;
fuzzy multi-criteria method;
soft computing methods;
rough sets;
intuitionistic fuzzy sets;
fuzzy data mining;
hybrid fuzzy optimization;
evolutionary and swarm intelligence methods;
genetic algorithms;
bio-inspired intelligent computational methods;
fuzzy cognitive maps;
neural networks;
big data optimization;
fuzzy linear programming;
fuzzy nonlinear programming;
discrete fuzzy optimization;
continuous fuzzy optimization;
fuzzy integer programming;
fuzzy dynamic programming;
fuzzy multi-objective programming;
possibilistic linear programming;
fuzzy optimization control;
fuzzy ranking;
fuzzy set operation;
fuzzy sensitivity analysis;
fuzzy dual theory;
interval-valued probability measures.

Application areas include, but are not limited to, the following:

management;
operations and production management;
economics;
finance;
energy;
agriculture;
environment;
education;
engineering;
systems engineering;
software engineering;
smart cities engineering;
big data analytics;
IoT applications.

Prof. Dr. Vassilis C. Gerogiannis
Guest Editor

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All papers will be peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 100 words) can be sent to the Editorial Office for announcement on this website.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Mathematics is an international peer-reviewed open access monthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 1200 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

Published Papers (7 papers)

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Research

Open AccessArticle
Supportiveness of Low-Carbon Energy Technology Policy Using Fuzzy Multicriteria Decision-Making Methodologies
Mathematics 2020, 8(7), 1178; https://doi.org/10.3390/math8071178 - 17 Jul 2020
Abstract
The deployment of low-carbon energy (LCE) technologies and management of installations represents an imperative to face climate change. LCE planning is an interminable process affected by a multitude of social, economic, environmental, and health factors. A major challenge for policy makers is to [...] Read more.
The deployment of low-carbon energy (LCE) technologies and management of installations represents an imperative to face climate change. LCE planning is an interminable process affected by a multitude of social, economic, environmental, and health factors. A major challenge for policy makers is to select a future clean energy strategy that maximizes sustainability. Thus, policy formulation and evaluation need to be addressed in an analytical manner including multidisciplinary knowledge emanating from diverse social stakeholders. In the current work, a comparative analysis of LCE planning is provided, evaluating different multicriteria decision-making (MCDM) methodologies. Initially, by applying strengths, weaknesses, opportunities, and threats (SWOT) analysis, the available energy alternative technologies are prioritized. A variety of stakeholders is surveyed for that reason. To deal with the ambiguity that occurred in their judgements, fuzzy goal programming (FGP) is used for the translation into fuzzy numbers. Then, the stochastic fuzzy analytic hierarchical process (SF-AHP) and fuzzy technique for order performance by similarity to ideal solution (F-TOPSIS) are applied to evaluate a repertoire of energy alternative forms including biofuel, solar, hydro, and wind power. The methodologies are estimated based on the same set of tangible and intangible criteria for the case study of Thessaly Region, Greece. The application of FGP ranked the four energy types in terms of feasibility and positioned solar-generated energy as first, with a membership function of 0.99. Among the criteria repertoire used by the stakeholders, the SF-AHP evaluated all the criteria categories separately and selected the most significant category representative. Finally, F-TOPSIS assessed these criteria ordering the energy forms, in terms of descending order of ideal solution, as follows: solar, biofuel, hydro, and wind. Full article
(This article belongs to the Special Issue Applications of Fuzzy Optimization and Fuzzy Decision Making)
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Open AccessArticle
Three-Way Decisions Making Using Covering Based Fractional Orthotriple Fuzzy Rough Set Model
Mathematics 2020, 8(7), 1121; https://doi.org/10.3390/math8071121 - 09 Jul 2020
Abstract
On the basis of decision-theoretical rough sets (DTRSs), the three-way decisions give new model of decision approach for deal with the problem of decision. This proposed model of decision method is based on the loss function of DTRSs. First, the concept of fractional [...] Read more.
On the basis of decision-theoretical rough sets (DTRSs), the three-way decisions give new model of decision approach for deal with the problem of decision. This proposed model of decision method is based on the loss function of DTRSs. First, the concept of fractional orthotriple fuzzy β -covering (FOF β -covering) and fractional orthotriple fuzzy β -neighborhood (FOF β -neighborhood) was introduced. We combined loss feature of DTRSs with covering-based fractional orthotriple fuzzy rough sets (CFOFSs) under the fractional orthotriple fuzzy condition. Secondly, we proposed a new FOF-covering decision-theoretical rough sets model (FOFCDTRSs) and developed related properties. Then, based on the grade of positive, neutral and negative membership of fractional orthotriple fuzzy numbers (FOFNs), five methods are established for addressing the expected loss expressed in the form of FOFNs and the corresponding three-way decisions are also derived. Based on this, we presented a FOFCDTRS-based algorithm for multi-criteria decision making (MCDM). Then, an example verifies the feasibility of the five methods for solving the MCDM problem. Finally, by comparing the results of the decisions of five methods with different loss functions. Full article
(This article belongs to the Special Issue Applications of Fuzzy Optimization and Fuzzy Decision Making)
Open AccessArticle
Modeling an Uncertain Productivity Learning Process Using an Interval Fuzzy Methodology
Mathematics 2020, 8(6), 998; https://doi.org/10.3390/math8060998 - 18 Jun 2020
Abstract
Existing methods for forecasting the productivity of a factory are subject to a major drawback—the lower and upper bounds of productivity are usually determined by a few extreme cases, which unacceptably widens the productivity range. To address this drawback, an interval fuzzy number [...] Read more.
Existing methods for forecasting the productivity of a factory are subject to a major drawback—the lower and upper bounds of productivity are usually determined by a few extreme cases, which unacceptably widens the productivity range. To address this drawback, an interval fuzzy number (IFN)-based mixed binary quadratic programming (MBQP)–ordered weighted average (OWA) approach is proposed in this study for modeling an uncertain productivity learning process. In the proposed methodology, the productivity range is divided into the inner and outer sections, which correspond to the lower and upper membership functions of an IFN-based fuzzy productivity forecast, respectively. In this manner, all actual values are included in the outer section, whereas most of the values are included within the inner section to fulfill different managerial purposes. According to the percentages of outlier cases, a suitable forecasting strategy can be selected. To derive the values of parameters in the IFN-based fuzzy productivity learning model, an MBQP model is proposed and optimized. Subsequently, according to the selected forecasting strategy, the OWA method is applied to defuzzify a fuzzy productivity forecast. The proposed methodology has been applied to the real case of a dynamic random access memory factory to evaluate its effectiveness. The experimental results indicate that the proposed methodology was superior to several existing methods, especially in terms of mean absolute error, mean absolute percentage error, and root mean square error in evaluating the forecasting accuracy. The forecasting precision achieved using the proposed methodology was also satisfactory. Full article
(This article belongs to the Special Issue Applications of Fuzzy Optimization and Fuzzy Decision Making)
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Open AccessArticle
Using a Fuzzy Inference System to Obtain Technological Tables for Electrical Discharge Machining Processes
Mathematics 2020, 8(6), 922; https://doi.org/10.3390/math8060922 - 05 Jun 2020
Abstract
Technological tables are very important in electrical discharge machining to determine optimal operating conditions for process variables, such as material removal rate or electrode wear. Their determination is of great industrial importance and their experimental determination is very important because they allow the [...] Read more.
Technological tables are very important in electrical discharge machining to determine optimal operating conditions for process variables, such as material removal rate or electrode wear. Their determination is of great industrial importance and their experimental determination is very important because they allow the most appropriate operating conditions to be selected beforehand. These technological tables are usually employed for electrical discharge machining of steel, but their number is significantly less in the case of other materials. In this present research study, a methodology based on using a fuzzy inference system to obtain these technological tables is shown with the aim of being able to select the most appropriate manufacturing conditions in advance. In addition, a study of the results obtained using a fuzzy inference system for modeling the behavior of electrical discharge machining parameters is shown. These results are compared to those obtained from response surface methodology. Furthermore, it is demonstrated that the fuzzy system can provide a high degree of precision and, therefore, it can be used to determine the influence of these machining parameters on technological variables, such as roughness, electrode wear, or material removal rate, more efficiently than other techniques. Full article
(This article belongs to the Special Issue Applications of Fuzzy Optimization and Fuzzy Decision Making)
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Open AccessArticle
EA/AE-Eigenvectors of Interval Max-Min Matrices
Mathematics 2020, 8(6), 882; https://doi.org/10.3390/math8060882 - 01 Jun 2020
Cited by 1
Abstract
Systems working in discrete time (discrete event systems, in short: DES)—based on binary operations: the maximum and the minimum—are studied in so-called max–min (fuzzy) algebra. The steady states of a DES correspond to eigenvectors of its transition matrix. In reality, the matrix (vector) [...] Read more.
Systems working in discrete time (discrete event systems, in short: DES)—based on binary operations: the maximum and the minimum—are studied in so-called max–min (fuzzy) algebra. The steady states of a DES correspond to eigenvectors of its transition matrix. In reality, the matrix (vector) entries are usually not exact numbers and they can instead be considered as values in some intervals. The aim of this paper is to investigate the eigenvectors for max–min matrices (vectors) with interval coefficients. This topic is closely related to the research of fuzzy DES in which the entries of state vectors and transition matrices are kept between 0 and 1, in order to describe uncertain and vague values. Such approach has many various applications, especially for decision-making support in biomedical research. On the other side, the interval data obtained as a result of impreciseness, or data errors, play important role in practise, and allow to model similar concepts. The interval approach in this paper is applied in combination with forall–exists quantification of the values. It is assumed that the set of indices is divided into two disjoint subsets: the E-indices correspond to those components of a DES, in which the existence of one entry in the assigned interval is only required, while the A-indices correspond to the universal quantifier, where all entries in the corresponding interval must be considered. In this paper, the properties of EA/AE-interval eigenvectors have been studied and characterized by equivalent conditions. Furthermore, numerical recognition algorithms working in polynomial time have been described. Finally, the results are illustrated by numerical examples. Full article
(This article belongs to the Special Issue Applications of Fuzzy Optimization and Fuzzy Decision Making)
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Open AccessArticle
M-CFIS-R: Mamdani Complex Fuzzy Inference System with Rule Reduction Using Complex Fuzzy Measures in Granular Computing
Mathematics 2020, 8(5), 707; https://doi.org/10.3390/math8050707 - 03 May 2020
Abstract
Complex fuzzy theory has strong practical background in many important applications, especially in decision-making support systems. Recently, the Mamdani Complex Fuzzy Inference System (M-CFIS) has been introduced as an effective tool for handling events that are not restricted to only values of a [...] Read more.
Complex fuzzy theory has strong practical background in many important applications, especially in decision-making support systems. Recently, the Mamdani Complex Fuzzy Inference System (M-CFIS) has been introduced as an effective tool for handling events that are not restricted to only values of a given time point but also include all values within certain time intervals (i.e., the phase term). In such decision-making problems, the complex fuzzy theory allows us to observe both the amplitude and phase values of an event, thus resulting in better performance. However, one of the limitations of the existing M-CFIS is the rule base that may be redundant to a specific dataset. In order to handle the problem, we propose a new Mamdani Complex Fuzzy Inference System with Rule Reduction Using Complex Fuzzy Measures in Granular Computing called M-CFIS-R. Several fuzzy similarity measures such as Complex Fuzzy Cosine Similarity Measure (CFCSM), Complex Fuzzy Dice Similarity Measure (CFDSM), and Complex Fuzzy Jaccard Similarity Measure (CFJSM) together with their weighted versions are proposed. Those measures are integrated into the M-CFIS-R system by the idea of granular computing such that only important and dominant rules are being kept in the system. The difference and advantage of M-CFIS-R against M-CFIS is the usage of the training process in which the rule base is repeatedly changed toward the original base set until the performance is better. By doing so, the new rule base in M-CFIS-R would improve the performance of the whole system. Experiments on various decision-making datasets demonstrate that the proposed M-CFIS-R performs better than M-CFIS. Full article
(This article belongs to the Special Issue Applications of Fuzzy Optimization and Fuzzy Decision Making)
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Open AccessArticle
An Integrated Approach of Best-Worst Method (BWM) and Triangular Fuzzy Sets for Evaluating Driver Behavior Factors Related to Road Safety
Mathematics 2020, 8(3), 414; https://doi.org/10.3390/math8030414 - 13 Mar 2020
Cited by 5
Abstract
Driver behavior plays a major role in road safety because it is considered as a significant argument in traffic accident avoidance. Drivers mostly face various risky driving factors which lead to fatal accidents or serious injury. This study aims to evaluate and prioritize [...] Read more.
Driver behavior plays a major role in road safety because it is considered as a significant argument in traffic accident avoidance. Drivers mostly face various risky driving factors which lead to fatal accidents or serious injury. This study aims to evaluate and prioritize the significant driver behavior factors related to road safety. In this regard, we integrated a decision-making model of the Best-Worst Method (BWM) with the triangular fuzzy sets as a solution for optimizing our complex decision-making problem, which is associated with uncertainty and ambiguity. Driving characteristics are different in different driving situations which indicate the ambiguous and complex attitude of individuals, and decision-makers (DMs) need to improve the reliability of the decision. Since the crisp values of factors may be inadequate to model the real-world problem considering the vagueness and the ambiguity, and providing the pairwise comparisons with the requirement of less compared data, the BWM integrated with triangular fuzzy sets is used in the study to evaluate risky driver behavior factors for a designed three-level hierarchical structure. The model results provide the most significant driver behavior factors that influence road safety for each level based on evaluator responses on the Driver Behavior Questionnaire (DBQ). Moreover, the model generates a more consistent decision process by the new consistency ratio of F-BWM. An adaptable application process from the model is also generated for future attempts. Full article
(This article belongs to the Special Issue Applications of Fuzzy Optimization and Fuzzy Decision Making)
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Planned Papers

The below list represents only planned manuscripts. Some of these manuscripts have not been received by the Editorial Office yet. Papers submitted to MDPI journals are subject to peer-review.

Title: Extending Fuzzy Cognitive Graphs With Tensor-Based Distance Metrics
Authors: Georgios Drakopoulos 1,* , Andreas Kanavos 2 , Phivos Mylonas 1 and Panagiotis Pintelas 3
Affiliation: 1 Humanistic and Social Informatics Lab, Department of Informatics, Ionian University; [email protected]; [email protected] 2 Computer Engineering and Informatics Department, University of Patras; [email protected] 3 Department of Mathematics, University of Patras; [email protected]
Abstract: Cognitive graphs are generalized and high level representations of the key topological attributes of real or abstract spatial environments which are progressively built by a sequence of noisy observations. Higher order relationships are represented in lower dimensions as patterns with similar structure so that salient features are preserved during projection. The latter can be partially attributed to the form of the distance metrics in the original space. Currently cognitive graphs play a crucial role in psychology as it is believed that this is how humans construct inner representations of both actual space and, perhaps more interestingly, complex fields comprising of interconnected notions such as languages with dedicated neurons located at hippocampus. In deep learning cognitive graphs are effective tools for simultaneous dimensionality reduction and visualization with applications to edge prediction, ontology alignment, and transfer learning. Fuzzy edge cognitive graphs have been proposed as an algorithmic way for representing inside the original space locations of incomplete knowledge or errors caused by either noisy or insufficient number of observations. In this graph class a probability denoting how likely is an edge to belong to the graph is mapped to that particular edge. This allows the definition of edge costs based, perhaps non-linearly, on these probabilities. In this article the potential of employing tensor-based distance metrics in order to assess distances dependent on multiple topological features in a locally higher order way is explored. This is consistent both with substantial empirical evidence on how human associative memory works and with the requirement for smooth filling when local information is insufficient. As a concrete example, the Kaggle Myers-Briggs personality type dataset is used with norm- and tensor-based distance metrics. The coherency of the resulting cognitive graphs, compared against the dataset ground truth, indicate that the latter approach achieves higher accuracy and F1 scores.

Title: Supportiveness of Low-Carbon Energy Policy Making via a Comparative Analysis of Fuzzy Multi-Criteria Decision Making Methodologies
Authors: Konstantinos Kokkinos 1 and Vayos Karayannis 2,*
Affiliation: 1 Energy Systems Department, University of Thessaly, Larissa, Greece; [email protected] 2 Chemical Engineering Department, University of Western Macedonia, Kozani, Greece; [email protected]
Abstract: The deployment and management of low-carbon energy (LCE) technologies and installations represents an imperative to face climate change. LCE planning is an interminable process affected by a multitude of anthropogenic, economic, environmental and health factors. A major challenge for policy makers is to select the future energy strategy that maximizes sustainability. Thus, policy formulation and evaluation needs to be addressed in an analytical manner including multidisciplinary knowledge emanating from diverse social stakeholders. In this work, a comparative analysis of the LCE planning is provided, evaluating different multi-criteria decision making methodologies: Initially, by applying SWOT (strengths, weaknesses, opportunities and threats) analysis, the available energy strategy alternatives are prioritized. A variety of stakeholders is surveyed for that reason. To deal with the ambiguity occurred in their judgements, Fuzzy Goal Programming (F-GP) is used for the translation into fuzzy numbers. Then Stochastic Fuzzy Analytic Hierarchical Process (SF-AHP) and Fuzzy Technique for Order Performance by Similarity to Ideal Solution (F-TOPSIS) are applied to evaluate a repertoire of energy alternatives including solar, biofuel, hydro and wind power. The methodologies are estimated based on the same set of tangible and intangible criteria for the case study of Thessaly region, Greece.

Title: Fuzzy Cognitive Maps Optimization for Decision Making and Prediction
Authors: Katarzyna Poczeta 1, Elpiniki Papageorgiou 2,* and Vassilis C. Gerogiannis 3,*
Affiliation: 1 Department of Information Systems, Kielce University of Technology, Kielce, Poland; [email protected] 2 Faculty of Technology, University of Thessaly, Geopolis, Larisa, Greece; [email protected] 3 Department of Digital Systems, University of Thessaly, Geopolis, Larisa, Greece; [email protected]
Abstract: The problem of representing and analyzing complexity of models constructed by data is a difficult one emerging the need for new, more effective techniques, even there are many methodologies proposed to cope with it recently. The main idea of this paper is to systematically create a nested structure based on a Fuzzy Cognitive Map (FCM) in which each element/concept at a higher map level is decomposed into another FCM that provides more detailed and more precise representation of complex time series data. The resulted nested structure is optimized through evolutionary and hybrid learning algorithms. Through applying a dynamic optimization process, the whole nested structure based on FCMs is restructured in order to derive important relationships between map concepts at every nesting level as well as to determine the weights of these relationships on the basis of the available time series. This allows discovering and describing hidden relationships between important map concepts. The paper recommends to apply the proposed nested approach for the forecasting of consumption in energy buildings, as well as for decision making tasks in selected complex problems from the energy domain devoted to energy efficiency.

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