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Öğe The Banach algebras generated by operators with one-point spectrum(2011) Seferoğlu, H.; Şimşek, NecipIn this article, we present some results related to the structure of Banach algebras generated by operators with one-point spectrum. © 2011 Wuhan Institute of Physics and Mathematics.Öğe Banach-saks type and gurarii modulus of convexity of some banach sequence spaces(Hindawi Publishing Corporation, 2014) Hudzik, Henryk; Karakaya, Vatan; Mursaleen, Mohammad; Şimşek, NecipBanach-Saks type is calculated for two types of Banach sequence spaces and Gurarii modulus of convexity is estimated from above for the spaces of one type among them.Öğe Comparative analysis of neural networks in the diagnosis of emerging diseases based on COVID-19(Konuralp Journal of Mathematics, 2021) Kirişci, Murat; Demir, İbrahim; Şimşek, NecipDermatological diseases are frequently encountered in children and adults for various reasons. There are many factors that cause the onset of these diseases and different symptoms are generally seen in each age group. Artificial Neural Networks can provide expert level accuracy in the diagnosis of dermatological findings of patients with COVID-19 disease. Therefore, the use of neural network classification methods can give the best estimation method in dermatology. In this study, the prediction of cutaneous diseases caused by COVID-19 was analyzed by Scaled Conjugate Gradient, Levenberg Marquardt, Bayesian Regularization neural networks. At some points, Bayesian Regularization and Levenberg Marquardt were almost equally effective, but Bayesian Regularization performed better than Levenberg Marquard and called Conjugate Gradient in performance. It is seen that neural network model predictions achieve the highest ac-curacy. For this reason, Artificial Neural Networks are able to classify these diseases as accurately as human experts in an experimental setting.Öğe Decision making method related to Pythagorean Fuzzy Soft Sets with infectious diseases application(King Saud bin Abdulaziz University, 2022) Kirişci, Murat; Şimşek, NecipThis study presents a new algorithm for group decision-making solutions using Pythagorean Fuzzy Soft Matrices (PFSMs) and confident weight is given by experts. Pythagorean Fuzzy Set (PFS) is a generalization of the intuitionistic fuzzy set (IFS). Therefore, in real-life problems for uncertainty, the decision-making mechanism in PFSs outcomes better than IFS decision-making. Pythagorean Fuzzy Soft Set (PFSS) is deriving from the combination of PFS and Soft Set. PFSM is also the matrix representation of PFSSs. Based on the cardinalities of the PFSS, experts have been given a new method that assigns confident weight. Confident weight is given according to the experience and knowledge of each expert. For this process, the choice matrix and the combined choice matrix are created first. PFSMs and choice matrices given for each expert are multiplied and the matrices obtained are summed. Pythagorean distance measurements were used to check the accuracy of the results obtained by applying the algorithm. A medical case was studied to see if the proposed method for group decision-making is feasible. In the section of medical case, infectious diseases that were common before COVID-19 were selected. The newly given algorithm was applied to the opinions of physicians about these diseases. According to the Hamming Distance values, the results of three out of four physicians are the same; In the values obtained with Euclidean distance, it was seen that the opinions of all physicians were the same. It has been revealed that the newly proposed algorithm has increased the reliability of the results from the group decision analysis.Öğe Difference sequence spaces derived by using a generalized weighted mean(2011) Polat H.; Karakaya, Vatan; Şimşek, NecipIn this work, we define new sequence spaces by combining a generalized weighted mean and a difference operator. Afterward, we investigate topological structures, which have completeness, AK-property, and AD-property. Also, we compute the ?-, ?- and ?-duals, and obtain bases for these sequence spaces. Finally, the necessary and sufficient conditions on an infinite matrix belonging to the classes (c(u,?,?):??) and (c(u, ?,?):c) are obtained. © 2011 Elsevier Ltd. All rights reserved.Öğe Fermatean fuzzy ELECTRE multi-criteria group decision-making and most suitable biomedical material selection(Elsevier B.V., 2022) Kirişci, Murat; Demir, Ibrahim; Şimşek, NecipELECTRE is a family of multi-criteria decision analysis techniques, which has the ability to provide as much as possible precise and suitable set of actions or alternatives to the underlying problem by eliminating the alternatives, which are outranked by others. Group decision-making is an effective process to provide the most appropriate solution to real-world decision-making scenarios by considering and merging the expert opinions of multiple individuals on the problem. The aim of this study is to present an extended version of the ELECTRE I model called the Fermatean fuzzy ELECTRE I method for of multi-criteria group decision-making with Fermatean fuzzy human assessments. The method proposed in this study has the possibility to solve multi-criteria group decision-making problems by using the Fermatean fuzzy decision matrix obtained in Fermatean fuzzy number form in the evaluations made with the available alternatives based on expert opinions. First, the mathematical description of the multi-criteria group decision-making problem with Fermatean fuzzy information has been given. Then, the proposed Fermatean fuzzy ELECTRE I method to deal with the problem has been presented. After the determination of the relative importance degree of experts, the Fermatean fuzzy aggregated averaging operator is employed to merge the individual Fermatean fuzzy decision matrices produced by the experts into the aggregated Fermatean fuzzy decision matrix. Next, for pairwise comparison of available alternatives with respect to considered criteria, the concepts of Fermatean fuzzy strong, midrange, and weak concordance and discordance sets are based on the approach of score function and accuracy function defined for Fermatean fuzzy numbers. Afterward, Fermatean fuzzy concordance and discordance matrices are defined, constructed by concordance and discordance indices. Finally, Fermatean fuzzy effective concordance and discordance matrices are computed to obtain Fermatean fuzzy aggregated outranking matrix, indicating abstract information on dominations of suitable alternatives to the others. The proposed method will be used in material selection in distinct implementations, exclusively in biomedical applications where the prosthesis materials should have similar characteristics to human tissues. Since biomedical materials are used in various parts of the human body for many different purposes, in this study, material selection will be made using the method presented for the femoral component of the hip joint prosthesis for orthopedists and practitioners who will choose biomaterials.Öğe Fixed point theorem for neutrosophic extended metric-like spaces and their application(Yıldız Technical University, 2023) Ishtiaq, Umar; Şimşek, Necip; Javed, Khalil; Ahmed, Khaleel; Uddin, Fahim; Kirişçi, MuratIn this manuscript, our objective is to introduce the notion of neutrosophic extended metric-like spaces. We establish some fixed point theorems in this setting. Neutrosophic extended metric-like spaces metric space uses the idea of continuous triangular norms and continuous triangular conorms in an extended intuitionistic fuzzy metric-like space. Triangular norms are used to generalize with the probability distribution of triangle inequality in metric space conditions. Triangular conorms are known as dual operations of triangular norms. Triangular norms and triangular conorm are very significant for fuzzy operation. The obtained results boost the approaches of existing ones in the literature and are supported by some examples and an application.Öğe Incomplete Fermatean fuzzy preference relations and group decision-making(De Gruyter Open Ltd, 2023) Şimşek, Necip; Kirişci, MuratThere may be cases where experts do not have in-depth knowledge of the problem to be solved in decision-making problems. In such cases, experts may fail to express their views on certain aspects of the problem, resulting in incomplete preferences, in which some preference values are not provided or are missing. In this article, we present a new model for group decision-making (GDM) methods in which experts’ preferences can be expressed as incomplete Fermatean fuzzy preference relations. This model is guided by the additive-consistency property and only uses the preference values the expert provides. An additive consistency definition characterized by a Fermatean fuzzy priority vector has been given. The additive consistency property is also used to measure the level of consistency of the information provided by the experts. The proposed additive consistency definition’s property is presented, as well as a model for obtaining missing judgments in incomplete Fermatean fuzzy preference relations. We present a method for adjusting the inconsistency for Fermatean fuzzy preference relations, a model for obtaining the priority vector, and a method for increasing the consensus degrees of Fermatean fuzzy preference relations. In addition, we present a GDM method in environments with incomplete Fermatean fuzzy preference relations. To show that our method outperforms existing GDM methods in incomplete Fermatean fuzzy preference relations environments, we have provided an example and compared it with some methods. It has been seen that our proposed GDM method is beneficial for GDM in deficient Fermatean fuzzy preference relation environments and produces meaningful results for us.Öğe Lacunary statistical convergence of sequences of functions in intuitionistic fuzzy normed space(2014) Karakaya, Vatan; Şimşek, Necip; Gürsoy, Faik; Ertürk, MüzeyyenIn this paper we study lacunary statistical convergence of sequences of functions in intuitionistic fuzzy normed spaces. We define concept of lacunary statistical pointwise convergence and lacunary statistical uniform convergence in intuitionistic fuzzy normed spaces and we give some basic properties of these concepts. © 2014 - IOS Press and the authors. All rights reserved.Öğe Measure of noncompactness of matrix operators on some difference sequence spaces of weighted means(2011) Mursaleen, Mohammad; Karakaya, Vatan; Polat, Harun; Şimşek, NecipFor a sequence x=(xk), we denote the difference sequence by ?x=(xk-xk-1). Let u=(uk)k=0? and v=(vk)k=0? be the sequences of real numbers such that uk?0, vk?0 for all k?N. The difference sequence spaces of weighted means ?(u,v,?) are defined as ?(u,v,?)=x=(xk):W(x)??, where ?= c,c0 and ?? and the matrix W=(wnk) is defined by wnk=un(vk-vk+1);(k<n) ,unvn;(k=n),0;(k>n). In this paper, we establish some identities or estimates for the operator norms and the Hausdorff measures of noncompactness of certain matrix operators on ?(u,v,?). Further, we characterize some classes of compact operators on these spaces by using the Hausdorff measure of noncompactness. © 2011 Elsevier Ltd. All rights reserved.Öğe Neutrosophic metric spaces(Springer, 2020) Kirişçi, Murat; Şimşek, NecipNeutrosophy consists of neutrosophic logic, probability, and sets. Actually, the neutrosophic set is a generalisation of classical sets, fuzzy set, intuitionistic fuzzy set, etc. A neutrosophic set is a mathematical notion serving issues containing inconsistent, indeterminate, and imprecise data. The notion of intuitionistic fuzzy metric space is useful in modelling some phenomena where it is necessary to study the relationship between two probability functions. In this paper, the definition of new metric space with neutrosophic numbers is given. Neutrosophic metric space uses the idea of continuous triangular norms and continuous triangular conorms in intuitionistic fuzzy metric space. Triangular norms are used to generalize with the probability distribution of triangle inequality in metric space conditions. Triangular conorms are known as dual operations of triangular norms. Triangular norms and triangular conorm are very significant for fuzzy operations. Neutrosophic metric space was defined with continuous triangular norms and continuous triangular conorms. Several topological and structural properties neutrosophic metric space have been investigated. The analogues of Baire Category Theorem and Uniform Convergence Theorem are given for Neutrosophic metric spaces.Öğe Neutrosophic normed spaces and statistical convergence(Springer, 2020) Kirişçi, Murat; Şimşek, NecipWe define the neutrosophic normed space and the statistical convergence in neutrosophic normed space. We give the statistically Cauchy sequence in neutrosophic normed space and present the statistically completeness in connection with a neutrosophic normed space.Öğe New matrix domain derived by the matrix product(University of Nis, 2016) Karakaya, Vatan; Şimşek, Necip; Doğan, KadriIn this work, we define new sequence spaces by using the matrix obtained by product of factorable matrix and generalized difference matrix of order m. Afterward, we investigate topological structure which are completeness, AK-property, AD-property. Also, we compute the ?-, ?- and ? - duals, and obtain bases for these sequence spaces. Finally we give necessary and sufficient conditions on matrix transformation between these new sequence spaces and c, ??. © 2016, University of Nis. All rights reserved.Öğe A new risk assessment method for autonomous vehicle driving systems: fermatean fuzzy ahp approach(İstanbul Ticaret Üniversitesi, 2023) Şimşek, Necip; Kirişçi, MuratThe autonomous vehicle driving systems' decision-making processes are distinct from those of the users, enabling them to supervise and control the operations of automobiles in both anticipated and unforeseen situations. Although utilizing this technology has several benefits, including fewer accidents brought on by human error and more effective energy usage, it is also clear that there are significant risks associated. Therefore, it will be useful to design a risk assessment application for these systems given the risks connected with autonomous vehicles and/or driving systems that must be assessed and addressed. This article presents a multicriteria decision-making strategy to evaluate the risk probabilities of autonomous vehicle driving systems by combining the AHP technique with interval-valued Fermatean fuzzy sets. Intervalvalued Fuzzy Fermat presents six options for autonomous driving systems for vehicles, which have been evaluated in the application based on six main criteria and fifteen sub-criteria criteria. The findings of this study have demonstrated that the threat posed by cyberattacks is being addressed and given priority to improve the success of the introduction of autonomous vehicle driving systems.Öğe A novel kernel principal component analysis with application disaster preparedness of hospital: interval-valued Fermatean fuzzy set approach(Springer, 2023) Kirişci, Murat; Şimşek, Necipn an interval-valued Fermatean fuzzy environment, a group decision-making issue relating to data on the disaster preparedness of hospitals is presented in this presentation. Interval-valued Fermatean fuzzy sets have the benefit of being able to accurately reflect the assessment data provided by decision-makers through both qualitative and quantitative elements for the examination of “disaster preparedness of hospitals” challenges. The conventional decision-making techniques will falter, nevertheless, if the dimension and nonlinear connection of the choice data keep expanding. To lower the dimensionality for nonlinear characteristics, we build the interval-valued Fermatean fuzzy linguistic kernel principal component analysis model. In the last part of the study, an illustrative example is given about the method proposed and the assessment of the disaster preparedness of the university hospital according to the hospital management cycle and the detection of its deficiencies. After making a comparison analysis and expressing the advantages of the method, we explained the theoretical, managerial, and political implications of the evaluations to be made with the method we recommend in all hospitals, based on the illustrative example given.Öğe The novel VIKOR methods for generalized Pythagorean fuzzy soft sets and its application to children of early childhood in COVID-19 quarantine(Springer, 2021) Kirişçi, Murat; Demir, İbrahim; Şimşek, Necip; Topaç, Nihat; Bardak, MusaIn this work, the new VIKOR methods are established using the generalized Pythagorean fuzzy soft sets (GPFSSs). For GPFSSs, the distance measures such as Hamming, Euclidean, and generalized are given. Further, the basic characteristics of these distance measures are examined. Fuzzy and soft sets are strong instruments for uncertainty. This strongness has been demonstrated by the GPFSS combining Pythagorean fuzzy sets and soft sets and applied to imprecise and ambiguous information. In this context, new remoteness index-based methods have been proposed, which are dissimilar from available VIKOR methods. The displaced and fixed ideals positive and negative Pythagorean fuzzy values (PFV) were defined. Thus, based on this definition, displaced positive ideal remoteness indices, negative ideal remoteness indices, and fixed positive ideal, negative ideal remoteness indices were discussed. Two different weights are used here: weights based on OF preference information and precise weights calculated with the expectation score function. The VIKOR method given here provides a different way from canonical VIKOR methods: rank candidate alternatives and determining a compromise solution based on different preference structures. The processes principles of the newly defined GPFSSs VIKOR methods are given by four algorithms. An example of these algorithms is given with the behavioral development and cognitive development of the children of Early Childhood children in the COVID-19 quarantine.Öğe ON BEHAVIOUR OF DARBO FIXED POINT THEOREM UNDER FUNCTION SEQUENCES(Yokohama Publ, 2019) Karakaya, Vatan; Sekman, Derya; Şimşek, NecipA lot of work has been done on fixed point studies using function classes. In this work, the existence of fixed point is investigated by taking function sequences instead of function classes. This idea has been applied to the Darbo fixed point theorem and obtained some results. Also, the study was supported by an interesting example held the conditions of function sequences.Öğe On fine spectra and subspectrum (approximate point, defect and compression) of operator with periodic coefficients(Yokohama Publications, 2017) Karakaya, Vatan; Dzh. Manafov, Manaf; Şimşek, NecipThe main purpose of this work is to determine of fine spectra and subspectra such as approximate point spectrum, defect spectrum and compression spectrum of the difference operator with periodic coefficients over the sequence spaces ?1.. © 2017.Öğe On geometrical properties of some Banach spaces(2013) Şimşek, Necip; Savaş, Ekrem; Karakaya, VatanIn this work, we prove that modular spaces V ?(?; p) defined in [26] have the k-nearly uniform convexity(k - NUC property) when they are endowed with the Luxemburg norm. We also prove that these spaces have the uniform Opial property with the Luxemburg norm. The above investigated geometric properties will enable us to obtain some fixed point results inmodular spaces. © 2013 NSP. Natural Sciences Publishing Cor.Öğe On ideal convergence of sequences of functions in intuitionistic fuzzy normed spaces(2014) Karakaya, Vatan; Şimşek, Necip; Ertürk, Müzeyyen; Gürsoy, FaikIn this work, our purpose is to introduce I-convergence of sequences of functions in intuitionistic fuzzy normed space by combining the I-convergence, the sequences of functions and the intuitionistic fuzzy normed spaces, and to investigate relations among concepts such as I-convergence, statistical convergence and the usual convergence of sequences of functions in intuitionistic fuzzy normed space. © 2014 NSP Natural Sciences Publishing Cor.
