Search results for: Fuzzy Delphi Method

Authors: Mahmood Otadi, Maryam Mosleh

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The hybrid differential equations have a wide range of applications in science and engineering. In this paper, the homotopy analysis method (HAM) is applied to obtain the series solution of the hybrid differential equations. Using the homotopy analysis method, it is possible to find the exact solution or an approximate solution of the problem. Comparisons are made between improved predictor-corrector method, homotopy analysis method and the exact solution. Finally, we illustrate our approach by some numerical example.

Keywords: fuzzy number, fuzzy ODE, HAM, approximate method

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Authors: G. S. Thakur

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In this paper, four new operators (O1, O2, O3, O4) are proposed, defined and considered to study the new properties and identities on hesitant fuzzy sets. These operators are useful for different operation on hesitant fuzzy sets. The various theorems are proved using the new operators. The study of the proposed new operators has opened a new area of research and applications.

Keywords: vague sets, hesitant fuzzy sets, intuitionistic fuzzy set, fuzzy sets, fuzzy multisets

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Authors: Meiju Chen, Chaoyu Guo, Chia Wei Tang

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The present study's purpose is twofold: first, to construct indicators for learning-oriented school education and, second, to conduct a survey to examine how learning-oriented education has been implemented in junior high schools after the launch of the 12-year compulsory curriculum. For indicator system construction, we compiled relevant literature to develop a preliminary indicator list model and then conducted two rounds of a questionnaire survey to gain comprehensive feedback from experts to finalize our indicator model. In the survey's first round, 12 experts were invited to evaluate the indicators' appropriateness. Based on the experts' consensus, we determined our final indicator list and used it to develop the Fuzzy Delphi questionnaire to finalize the indicator system and each indicator's relative value. For the fact-finding survey, we collected 454 valid samples to examine how the concept of learning-oriented education is adopted and implemented in the junior high school context. We also used this data in our importance-performance analysis to explore the strengths and weaknesses of school education in Taiwan. The results suggest that the indicator system for learning-oriented school education must consist of seven dimensions and 34 indicators. Among the seven dimensions, 'student learning' and 'curriculum planning and implementation' are the most important yet underperforming dimensions that need immediate improvement. We anticipate that the indicator system will be a useful tool for other countries' evaluation of schools' performance in learning-oriented education.

Keywords: learning-oriented education, school education, fuzzy Delphi method, importance-performance analysis

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Authors: Maria Paula Santos, Ana Lucas

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Organizations support their operations and decision making on the data they have at their disposal, so the quality of these data is remarkably important and Data Quality (DQ) is currently a relevant issue, the literature being unanimous in pointing out that poor DQ can result in large costs for organizations. The literature review identified and described 24 Critical Success Factors (CSF) for Data Quality Management (DQM) that were presented to a panel of experts, who ordered them according to their degree of importance, using the Delphi method with the Q-sort technique, based on an online questionnaire. The study shows that the five most important CSF for DQM are: definition of appropriate policies and standards, control of inputs, definition of a strategic plan for DQ, organizational culture focused on quality of the data and obtaining top management commitment and support.

Keywords: critical success factors, data quality, data quality management, Delphi, Q-Sort

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Authors: Oktay Nusratov, Ramin Rzaev, Aydin Goyushov

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Fuzzy inference method based approach to the forming of modular intellectual system of assessment the quality of communication services is proposed. Developed under this approach the basic fuzzy estimation model takes into account the recommendations of the International Telecommunication Union in respect of the operation of packet switching networks based on IP-protocol. To implement the main features and functions of the fuzzy control system of quality telecommunication services it is used multilayer feedforward neural network.

Keywords: quality of communication, IP-telephony, fuzzy set, fuzzy implication, neural network

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Authors: Amirhossein Karamoozian, Desheng Wu, Behzad Abbasnejad

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Building information modelling (BIM) is a new technology to enhance the efficiency of project management in the construction industry. In addition to the potential benefits of this useful technology, there are various risks and obstacles to applying it in construction projects. In this study, a decision making approach is presented for risk assessment in BIM adoption in construction projects. Various risk factors of exerting BIM during different phases of the project lifecycle are identified with the help of Delphi method, experts’ opinions and related literature. Afterward, Shannon’s entropy and Fuzzy TOPSIS (Technique for Order Preference by Similarity to Ideal Situation) are applied to derive priorities of the identified risk factors. Results indicated that lack of knowledge between professional engineers about workflows in BIM and conflict of opinions between different stakeholders are the risk factors with the highest priority.

Keywords: risk, BIM, fuzzy TOPSIS, construction projects

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Authors: Liang Zhao, Jili Zhang, Kai Li

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A microcontroller-based fan coil unit (FCU) fuzzy controller is designed and implemented in this paper. The controller employs the concept of duty ratio on the electric valve control, which could make full use of the cooling and dehumidifying capacity of the FCU when the valve is off. The traditional control method and its limitations are analyzed. The hardware and software design processes are introduced in detail. The experimental results show that the proposed method is more energy efficient compared to the traditional controlling strategy. Furthermore, a more comfortable room condition could be achieved by the proposed method. The proposed low-cost FCU fuzzy controller deserves to be widely used in engineering applications.

Keywords: fan coil unit, duty ratio, fuzzy controller, experiment

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Authors: Bessaad Taieb, Benbouali Abderrahmen

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Fuzzy controllers are a powerful tool for controlling complex processes. However, its robustness capacity remains moderately limited because it loses its property for large ranges of parametric variations. In this paper, the proposed control method is designed, based on a fuzzy adaptive controller used as a remedy for this problem. For increase the robustness of the vector control and to maintain the performance of the five-phase asynchronous machine despite the presence of disturbances (variation of rotor resistance, rotor inertia variations, sudden variations in the load etc.), by applying the method of behaviour model control (BMC). The results of simulation show that the fuzzy adaptive control provides best performance and has a more robustness as the fuzzy (FLC) and as a conventional (PI) controller.

Keywords: fuzzy adaptive control, behaviour model control, vector control, five-phase asynchronous machine

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Authors: M. S. Annie Christi

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Transportation Problem (TP) is based on supply and demand of commodities transported from one source to the different destinations. Usual methods for finding solution of TPs are North-West Corner Rule, Least Cost Method Vogel’s Approximation Method etc. The transportation costs tend to vary at each time. We can use fuzzy numbers which would give solution according to this situation. In this study the Best Candidate Method (BCM) is applied. For ranking Centroid Ranking Technique (CRT) and Robust Ranking Technique have been adopted to transform the fuzzy TP and the above methods are applied to EDWARDS Vacuum Company, Crawley, in West Sussex in the United Kingdom. A Comparative study is also given. We see that the transportation cost can be minimized by the application of CRT under BCM.

Keywords: best candidate method, centroid ranking technique, fuzzy transportation problem, robust ranking technique, transportation problem

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Authors: Mandar Ghodekar, Sharad Jadhav, Sangram Jadhav

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Speed control of rotor during startup and under varying load conditions is one of the most difficult tasks of gas turbine operation. In this paper, power plant gas turbine (GE9001E) is considered for this purpose and fuzzy and fuzzy-PI rotor speed controllers are designed. The goal of the presented controllers is to keep the turbine rotor speed within predefined limits during startup condition as well as during operating condition. The fuzzy controller and fuzzy-PI controller are designed using Takagi-Sugeno method and Mamdani method, respectively. In applying the fuzzy-PI control to a gas-turbine plant, the tuning parameters (Kp and Ki) are modified online by fuzzy logic approach. Error and rate of change of error are inputs and change in fuel flow is output for both the controllers. Hence, rotor speed of gas turbine is controlled by modifying the fuel ƒflow. The identified linear ARX model of gas turbine is considered while designing the controllers. For simulations, demand power is taken as disturbance input. It is assumed that inlet guide vane (IGV) position is fixed. In addition, the constraint on the fuel flow is taken into account. The performance of the presented controllers is compared with each other as well as with H∞ robust and MPC controllers for the same operating conditions in simulations.

Keywords: gas turbine, fuzzy controller, fuzzy PI controller, power plant

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Authors: T. Pathinathan, M. Peter

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Fuzzy graphs incorporate concepts from graph theory with fuzzy principles. In this paper, we make a study on the properties of fuzzy graphs which are non-cyclic and are of two-dimensional in structure. In particular, this paper presents 2D structure or the structure of double layer for a non-cyclic fuzzy graph whose underlying crisp graph is non-cyclic. In any graph structure, introducing 2D structure may lead to an inherent cycle. We propose relevant conditions for 2D structured non-cyclic fuzzy graphs. These conditions are extended even to fuzzy graphs of the 3D structure. General theoretical properties that are studied for any fuzzy graph are verified to 2D structured or double layered fuzzy graphs. Concepts like Order, Degree, Strong and Size for a fuzzy graph are studied for 2D structured or double layered non-cyclic fuzzy graphs. Using different types of fuzzy graphs, the proposed concepts relating to 2D structured fuzzy graphs are verified.

Keywords: double layered fuzzy graph, double layered non–cyclic fuzzy graph, order, degree and size

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Authors: Younis Jabarzadeh, Rahim Sarvari, Negar Ahmadi Alghalandis

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Entrepreneurship at both individual and organizational level is one of the most driving forces in economic development and leads to growth and competition, job generation and social development. Especially in developing countries, the role of entrepreneurship in economic and social prosperity is more emphasized. But the effect of global economic development on the environment is undeniable, especially in negative ways, and there is a need to rethink current business models and the way entrepreneurs act to introduce new businesses to address and embed environmental issues in order to achieve sustainable development. In this paper, green or sustainable entrepreneurship is addressed in Iran to identify challenges and barriers entrepreneurs in the economic and social sectors face in developing green business solutions. Sustainable or green entrepreneurship has been gaining interest among scholars in recent years and addressing its challenges and barriers need much more attention to fill the gap in the literature and facilitate the way those entrepreneurs are pursuing. This research comprised of two main phases: qualitative and quantitative. At qualitative phase, after a thorough literature review, fuzzy Delphi method is utilized to verify those challenges and barriers by gathering a panel of experts and surveying them. In this phase, several other contextually related factors were added to the list of identified barriers and challenges mentioned in the literature. Then, at the quantitative phase, Interpretive Structural Modeling is applied to construct a network of interactions among those barriers identified at the previous phase. Again, a panel of subject matter experts comprised of academic and industry experts was surveyed. The results of this study can be used by policymakers in both the public and industry sector, to introduce more systematic solutions to eliminate those barriers and help entrepreneurs overcome challenges of sustainable entrepreneurship. It also contributes to the literature as the first research in this type which deals with the barriers of sustainable entrepreneurship and explores their interaction.

Keywords: green entrepreneurship, barriers, fuzzy Delphi method, interpretive structural modeling

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Authors: Syed Talib Abbas Raza, Tahseen Ahmed Jilani, Saleem Abdullah

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This paper presents interval-valued intuitionistic fuzzy soft sets based TOPSIS method for group decision making. The interval-valued intuitionistic fuzzy soft set is a mutation of an interval-valued intuitionistic fuzzy set and soft set. In group decision making problems IVIFSS makes the process much more algebraically elegant. We have used weighted arithmetic averaging operator for aggregating the information and define a new Hybrid Score Function as metric tool for comparison between interval-valued intuitionistic fuzzy values. In an illustrative example we have applied the developed method to a criminological problem. We have developed a group decision making model for integrating the imprecise and hesitant evaluations of multiple law enforcement agencies working on target killing cases in the country.

Keywords: group decision making, interval-valued intuitionistic fuzzy soft set, TOPSIS, score function, criminology

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Authors: Sukhveer Singh, Sandeep Singh

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A bi-objective fuzzy transportation problem with the objectives to minimize the total fuzzy cost and fuzzy time of transportation without according priorities to them is considered. To the best of our knowledge, there is no method in the literature to find efficient solutions of the bi-objective transportation problem under uncertainty. In this paper, a bi-objective transportation problem in an uncertain environment has been formulated. An algorithm has been proposed to find efficient solutions of the bi-objective transportation problem under uncertainty. The proposed algorithm avoids the degeneracy and gives the optimal solution faster than other existing algorithms for the given uncertain transportation problem.

Keywords: uncertain transportation problem, efficient solution, ranking function, fuzzy transportation problem

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Authors: Abder-Rahman Ali, Adélaïde Albouy-Kissi, Manuel Grand-Brochier, Viviane Ladan-Marcus, Christine Hoeffl, Claude Marcus, Antoine Vacavant, Jean-Yves Boire

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In this paper, we present a new segmentation approach for focal liver lesions in contrast enhanced ultrasound imaging. This approach, based on a two-cluster Fuzzy C-Means methodology, considers type-II fuzzy sets to handle uncertainty due to the image modality (presence of speckle noise, low contrast, etc.), and to calculate the optimum inter-cluster threshold. Fine boundaries are detected by a local recursive merging of ambiguous pixels. The method has been tested on a representative database. Compared to both Otsu and type-I Fuzzy C-Means techniques, the proposed method significantly reduces the segmentation errors.

Keywords: defuzzification, fuzzy clustering, image segmentation, type-II fuzzy sets

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Authors: Antonios Paraskevas, Michael Madas

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For a university to maintain its international competitiveness in education, it is essential to recruit qualitative academic staff as it constitutes its most valuable asset. This selection demonstrates a significant role in achieving strategic objectives, particularly by emphasizing a firm commitment to exceptional student experience and innovative teaching and learning practices of high quality. In this vein, the appropriate selection of academic staff establishes a very important factor of competitiveness, efficiency and reputation of an academic institute. Within this framework, our work demonstrates a comprehensive methodological concept that emphasizes on the multi-criteria nature of the problem and on how decision makers could utilize our approach in order to proceed to the appropriate judgment. The conceptual framework introduced in this paper is built upon a hybrid neutrosophic method based on the Neutrosophic Analytical Hierarchy Process (N-AHP), which uses the theory of neutrosophy sets and is considered suitable in terms of significant degree of ambiguity and indeterminacy observed in decision-making process. To this end, our framework extends the N-AHP by incorporating the Neutrosophic Delphi Method (N-DM). By applying the N-DM, we can take into consideration the importance of each decision-maker and their preferences per evaluation criterion. To the best of our knowledge, the proposed model is the first which applies Neutrosophic Delphi Method in the selection of academic staff. As a case study, it was decided to use our method to a real problem of academic personnel selection, having as main goal to enhance the algorithm proposed in previous scholars’ work, and thus taking care of the inherit ineffectiveness which becomes apparent in traditional multi-criteria decision-making methods when dealing with situations alike. As a further result, we prove that our method demonstrates greater applicability and reliability when compared to other decision models.

Keywords: analytical hierarchy process, delphi method, multi-criteria decision maiking method, neutrosophic set theory, personnel recruitment

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Authors: Antonios Paraskevas, Michael Madas

Abstract:

For a university to maintain its international competitiveness in education, it is essential to recruit qualitative academic staff as it constitutes its most valuable asset. This selection demonstrates a significant role in achieving strategic objectives, particularly by emphasizing a firm commitment to the exceptional student experience and innovative teaching and learning practices of high quality. In this vein, the appropriate selection of academic staff establishes a very important factor of competitiveness, efficiency and reputation of an academic institute. Within this framework, our work demonstrates a comprehensive methodological concept that emphasizes the multi-criteria nature of the problem and how decision-makers could utilize our approach in order to proceed to the appropriate judgment. The conceptual framework introduced in this paper is built upon a hybrid neutrosophic method based on the Neutrosophic Analytical Hierarchy Process (N-AHP), which uses the theory of neutrosophy sets and is considered suitable in terms of a significant degree of ambiguity and indeterminacy observed in the decision-making process. To this end, our framework extends the N-AHP by incorporating the Neutrosophic Delphi Method (N-DM). By applying the N-DM, we can take into consideration the importance of each decision-maker and their preferences per evaluation criterion. To the best of our knowledge, the proposed model is the first which applies the Neutrosophic Delphi Method in the selection of academic staff. As a case study, it was decided to use our method for a real problem of academic personnel selection, having as the main goal to enhance the algorithm proposed in previous scholars’ work, and thus taking care of the inherent ineffectiveness which becomes apparent in traditional multi-criteria decision-making methods when dealing with situations alike. As a further result, we prove that our method demonstrates greater applicability and reliability when compared to other decision models.

Keywords: multi-criteria decision making methods, analytical hierarchy process, delphi method, personnel recruitment, neutrosophic set theory

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Authors: M. Doumi, A. Miloudi, A. G. Aissaoui, K. Tahir, C. Belfedal, S. Tahir

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The studies on the photovoltaic system are extensively increasing because of a large, secure, essentially exhaustible and broadly available resource as a future energy supply. However, the output power induced in the photovoltaic modules is influenced by an intensity of solar cell radiation, temperature of the solar cells and so on. Therefore, to maximize the efficiency of the photovoltaic system, it is necessary to track the maximum power point of the PV array, for this Maximum Power Point Tracking (MPPT) technique is used. Some MPPT techniques are available in that perturbation and observation (P&O) and Fuzzy logic controller (FLC). The fuzzy control method has been compared with perturb and observe (P&O) method as one of the most widely conventional method used in this area. Both techniques have been analyzed and simulated. MPPT using fuzzy logic shows superior performance and more reliable control with respect to the P&O technique for this application.

Keywords: photovoltaic system, MPPT, perturb and observe, fuzzy logic

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Authors: Elda Maraj, Shkelqim Kuka

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Coronary heart disease causes many deaths in the world. Unfortunately, this problem will continue to increase in the future. In this paper, a fuzzy logic model to predict coronary heart disease is presented. This model has been developed with seven input variables and one output variable that was implemented for 30 patients in Albania. Here fuzzy logic toolbox of MATLAB is used. Fuzzy model inputs are considered as cholesterol, blood pressure, physical activity, age, BMI, smoking, and diabetes, whereas the output is the disease classification. The fuzzy sets and membership functions are chosen in an appropriate manner. Centroid method is used for defuzzification. The database is taken from University Hospital Center "Mother Teresa" in Tirana, Albania.

Keywords: coronary heart disease, fuzzy logic toolbox, membership function, prediction model

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Authors: Roland Lachmayer, Mahtab Afsari

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Research is the cornerstone for advancement of human communities. So that it is one of the indexes for evaluating advancement of countries. Research projects are usually cost and time-consuming and do not end in result in short term. Project scheduling is one of the integral parts of project management. The present article offers a new method by using C# and Matlab software to solve Fuzzy GERT networks for Exclusive-OR kind of nodes to schedule the network. In this article we concentrate on flowcharts that we used in Matlab to show how we apply Matlab to schedule Exclusive-OR nodes.

Keywords: research projects, fuzzy GERT, fuzzy CPM, CPM, α-cuts, scheduling

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Authors: Liang-Hsuan Chen, Sheng-Shing Nien

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This study aims to develop approaches to formulate intuitionistic fuzzy regression (IFR) models for many decision-making applications in the fuzzy environments using intuitionistic fuzzy observations. Intuitionistic fuzzy numbers (IFNs) are used to characterize the fuzzy input and output variables in the IFR formulation processes. A mathematical programming problem (MPP) is built up to optimally determine the IFR parameters. Each parameter in the MPP is defined as a couple of alternative numerical variables with opposite signs, and an intuitionistic fuzzy error term is added to the MPP to characterize the uncertainty of the model. The IFR model is formulated based on the distance measure to minimize the total distance errors between estimated and observed intuitionistic fuzzy responses in the MPP resolution processes. The proposed approaches are simple/efficient in the formulation/resolution processes, in which the sign of parameters can be determined so that the problem to predetermine the sign of parameters is avoided. Furthermore, the proposed approach has the advantage that the spread of the predicted IFN response will not be over-increased, since the parameters in the established IFR model are crisp. The performance of the obtained models is evaluated and compared with the existing approaches.

Keywords: fuzzy sets, intuitionistic fuzzy number, intuitionistic fuzzy regression, mathematical programming method

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Authors: Georgios Charizanos, Haydar Demirhan, Duygu Icen

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Two of the most impactful issues in classical logistic regression are class imbalance and complete separation. These can result in model predictions heavily leaning towards the imbalanced class on the binary response variable or over-fitting issues. Fuzzy methodology offers key solutions for handling these problems. However, most studies propose the transformation of the binary responses into a continuous format limited within [0,1]. This is called the possibilistic approach within fuzzy logistic regression. Following this approach is more aligned with straightforward regression since a logit-link function is not utilized, and fuzzy probabilities are not generated. In contrast, we propose a method of fuzzifying binary response variables that allows for the use of the logit-link function; hence, a probabilistic fuzzy logistic regression model with the Monte Carlo method. The fuzzy probabilities are then classified by selecting a fuzzy threshold. Different combinations of fuzzy and crisp input, output, and coefficients are explored, aiming to understand which of these perform better under different conditions of imbalance and separation. We conduct numerical experiments using both synthetic and real datasets to demonstrate the performance of the fuzzy logistic regression framework against seven crisp machine learning methods. The proposed framework shows better performance irrespective of the degree of imbalance and presence of separation in the data, while the considered machine learning methods are significantly impacted.

Keywords: fuzzy logistic regression, fuzzy, logistic, machine learning

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Authors: Abdelati El Allaoui, Said Melliani, Lalla Saadia Chadli

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The objective of this paper is to study the existence and uniqueness of Mild solutions for a complex fuzzy evolution equation with nonlocal conditions that accommodates the notion of fuzzy sets defined by complex-valued membership functions. We first propose definition of complex fuzzy strongly continuous semigroups. We then give existence and uniqueness result relevant to the complex fuzzy evolution equation.

Keywords: Complex fuzzy evolution equations, nonlocal conditions, mild solution, complex fuzzy semigroups

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Authors: Jolly Puri, Shiv Prasad Yadav

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Multi-component data envelopment analysis (MC-DEA) is a popular technique for measuring aggregate performance of the decision making units (DMUs) along with their components. However, the conventional MC-DEA is limited to crisp input and output data which may not always be available in exact form. In real life problems, data may be imprecise or fuzzy. Therefore, in this paper, we propose (i) a fuzzy MC-DEA (FMC-DEA) model in which shared and undesirable fuzzy resources are incorporated, (ii) the proposed FMC-DEA model is transformed into a pair of crisp models using cut approach, (iii) fuzzy aggregate performance of a DMU and fuzzy efficiencies of components are defined to be fuzzy numbers, and (iv) a numerical example is illustrated to validate the proposed approach.

Keywords: multi-component DEA, fuzzy multi-component DEA, fuzzy resources, decision making units (DMUs)

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Authors: Pui Hong Chung, Cyrus Leung, Jun Li, Kin On Kwok, Ek Yeoh

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Introduction: Studies for TB control in intermediate tuberculosis burden countries (IBCs) comprise a relatively small proportion in TB control literature, as compared to the effort put in high and low burden counterparts. It currently lacks of consensus in the optimal weapons and strategies we can use to combat TB in IBCs; guidelines of TB control are inadequate and thus posing a great obstacle in eliminating TB in these countries. To fill-in the research and services gap, we need to summarize the findings of the effort in this regard and to seek consensus in terms of policy making for TB control, we have devised a series of scoping and Delphi studies for these purposes. Method: The scoping and Delphi studies are conducted in parallel to feed information for each other. Before the Delphi iterations, we have invited three local experts in TB control in Hong Kong to participate in the pre-assessment round of the Delphi study to comments on the validity, relevance, and clarity of the Delphi questionnaire. Result: Two scoping studies, regarding LTBI control in health care workers in IBCs and TB control in elderly of IBCs respectively, have been conducted. The result of these two studies is used as the foundation for developing the Delphi questionnaire, which tapped on seven areas of question, namely: characteristics of IBCs, adequacy of research and services in LTBI control in IBCs, importance and feasibility of interventions for TB control and prevention in hospital, screening and treatment of LTBI in community, reasons of refusal to/ default from LTBI treatment, medical adherence of LTBI treatment, and importance and feasibility of interventions for TB control and prevention in elderly in IBCs. The local experts also commented on the two scoping studies conducted, thus act as the sixth phase of expert consultation in Arksey and O’Malley framework of scoping studies, to either nourish the scope and strategies used in these studies or to supplement ideas for further scoping or systematic review studies. In the subsequent stage, an international expert panel, comprised of 15 to 20 experts from IBCs in Western Pacific Region, will be recruited to join the two-round anonymous Delphi iterations. Four categories of TB control experts, namely clinicians, policy makers, microbiologists/ laboratory personnel, and public health clinicians will be our target groups. A consensus level of 80% is used to determine the achievement of consensus on particular issues. Key messages: 1. Scoping review and Delphi method are useful to identify gaps and then achieve consensus in research. 2. Lots of resources are put in the high burden countries now. However, the usually neglected intermediate-burden countries with TB is an indispensable part for achieving the ambitious WHO End TB 2035 target.

Keywords: dephi questionnaire, tuberculosis, WHO, latent TB infection

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Authors: O. Poleshchuk, E. Komarov

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This paper presents a regression model for interval type-2 fuzzy sets based on the least squares estimation technique. Unknown coefficients are assumed to be triangular fuzzy numbers. The basic idea is to determine aggregation intervals for type-1 fuzzy sets, membership functions of whose are low membership function and upper membership function of interval type-2 fuzzy set. These aggregation intervals were called weighted intervals. Low and upper membership functions of input and output interval type-2 fuzzy sets for developed regression models are considered as piecewise linear functions.

Keywords: interval type-2 fuzzy sets, fuzzy regression, weighted interval

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Authors: Chen T. Chen, Hui L. Cheng

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Due to the different knowledge, experience and expertise of experts, they usually provide the different opinions in the group decision-making process. Therefore, it is an important issue to reach the group consensus of opinions of experts in group multiple-criteria decision-making (GMCDM) process. Because the subjective opinions of experts always are fuzziness and uncertainties, it is difficult to use crisp values to describe the real opinions of experts or decision-makers. It is reasonable for experts to use the linguistic variables to express their opinions. The hesitant fuzzy set are extended from the concept of fuzzy sets. Experts use the hesitant fuzzy sets can be flexible to describe their subjective opinions. In order to aggregate the hesitant fuzzy linguistic variables of all experts effectively, an adjustment method based on distance function will be presented in this paper. Based on the opinions adjustment method, this paper will present an effective approach to adjust the hesitant fuzzy linguistic variables of all experts to reach the group consensus. Then, a new hesitant linguistic GMCDM method will be presented based on the group consensus of hesitant fuzzy linguistic variables. Finally, an example will be implemented to illustrate the computational process to enhance the practical value of the proposed model.

Keywords: group multi-criteria decision-making, linguistic variables, hesitant fuzzy linguistic variables, distance function, group consensus

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Authors: Ismail Karaca, Ridvan Saracoglu, Omer Soner

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Fuzzy Logic, an advanced method to support decision-making, is used by various scientists in many disciplines. Fuzzy programming is a product of fuzzy logic, fuzzy rules, and implication. In marine science, fuzzy programming for ships is dramatically increasing together with autonomous ship studies. In this paper, a program to support the decision-making process for ship navigation has been designed. The program is produced in fuzzy logic and rules, by taking the marine accidents and expert opinions into account. After the program was designed, the program was tested by 46 ship accidents reported by the Transportation Safety Investigation Center of Turkey. Wind speed, sea condition, visibility, day/night ratio have been used as input data. They have been converted into a risk factor within the Fuzzy Logic Designer application and fuzzy rules set by marine experts. Finally, the expert's meteorological risk factor for each accident is compared with the program's risk factor, and the error rate was calculated. The main objective of this study is to improve the navigational safety of ships, by using the advance decision support model. According to the study result, fuzzy programming is a robust model that supports safe navigation.

Keywords: calculation of risk factor, fuzzy logic, fuzzy programming for ship, safety navigation of ships

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Authors: Shahabeddin Sotudian, M. H. Fazel Zarandi, I. B. Turksen

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Hepatitis is one of the most common and dangerous diseases that affects humankind, and exposes millions of people to serious health risks every year. Diagnosis of Hepatitis has always been a challenge for physicians. This paper presents an effective method for diagnosis of hepatitis based on interval Type-II fuzzy. This proposed system includes three steps: pre-processing (feature selection), Type-I and Type-II fuzzy classification, and system evaluation. KNN-FD feature selection is used as the preprocessing step in order to exclude irrelevant features and to improve classification performance and efficiency in generating the classification model. In the fuzzy classification step, an “indirect approach” is used for fuzzy system modeling by implementing the exponential compactness and separation index for determining the number of rules in the fuzzy clustering approach. Therefore, we first proposed a Type-I fuzzy system that had an accuracy of approximately 90.9%. In the proposed system, the process of diagnosis faces vagueness and uncertainty in the final decision. Thus, the imprecise knowledge was managed by using interval Type-II fuzzy logic. The results that were obtained show that interval Type-II fuzzy has the ability to diagnose hepatitis with an average accuracy of 93.94%. The classification accuracy obtained is the highest one reached thus far. The aforementioned rate of accuracy demonstrates that the Type-II fuzzy system has a better performance in comparison to Type-I and indicates a higher capability of Type-II fuzzy system for modeling uncertainty.

Keywords: hepatitis disease, medical diagnosis, type-I fuzzy logic, type-II fuzzy logic, feature selection

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Authors: Nastaran Hajiheydari, Mohammad Soltani Delgosha

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Vendor (supplier) selection is a group decision-making (GDM) process, in which, based on some predetermined criteria, the experts’ preferences are provided in order to rank and choose the most desirable suppliers. In the real business environment, our attitudes or our choices would be made in an uncertain and indecisive situation could not be expressed in a crisp framework. Intuitionistic fuzzy sets (IFSs) could handle such situations in the best way. VIKOR method was developed to solve multi-criteria decision-making (MCDM) problems. This method, which is used to determine the compromised feasible solution with respect to the conflicting criteria, introduces a multi-criteria ranking index based on the particular measure of 'closeness' to the 'ideal solution'. Until now, there has been a little investigation of VIKOR with IFS, therefore we extended the intuitionistic fuzzy (IF) VIKOR to solve vendor selection problem under IF GDM environment. The present study intends to develop an IF VIKOR method in a GDM situation. Therefore, a model is presented to calculate the criterion weights based on entropy measure. Then, the interval-valued intuitionistic fuzzy weighted geometric (IFWG) operator utilized to obtain the total decision matrix. In the next stage, an approach based on the positive idle intuitionistic fuzzy number (PIIFN) and negative idle intuitionistic fuzzy number (NIIFN) was developed. Finally, the application of the proposed method to solve a vendor selection problem illustrated.

Keywords: group decision making, intuitionistic fuzzy set, intuitionistic fuzzy entropy measure, vendor selection, VIKOR

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