Iranian Journal of Fuzzy Systems
https://ijfs.usb.ac.ir/
Iranian Journal of Fuzzy Systemsendaily1Tue, 01 Jun 2021 00:00:00 +0430Tue, 01 Jun 2021 00:00:00 +0430cover IJFS-Vol 18-No 3-June 2021
https://ijfs.usb.ac.ir/article_6090.html
Fuzzy logic and enriched categories
https://ijfs.usb.ac.ir/article_6077.html
We consider a category C enriched over the segment [0,1] whose hom-objects are real numbers from [0,1]. For a suitably defined function $\hat{v}$&nbsp; assigning to each formula $\varphi$ some object of $\C$, the hom-object $\C(\hat{v} (\varphi),\hat{v}(\psi))$ represents the degree of derivability of $\psi$ from $\varphi$. We reformulate completeness result for intuitionistic propositional logic, as well as H\' ajek's completeness results concerning the product, G\" odel and \L ukasiewicz fuzzy logic in the context of enriched category theory.2-set-based extended functions
https://ijfs.usb.ac.ir/article_6078.html
We generalize set-based extended functions, recently introduced by Mesiar et al., into 2-set-based extended functions. In both cases, an efficient reduction of repeated&nbsp; data to be fused is considered which prepares a sound background for big data processing. We discuss and study several types of 2-set-based extended functions, in particular,&nbsp; 2-set-based extended aggregation functions, including t-norms, t-conorms, uninorms, nullnorms and OWA operators.Using a fuzzy expert system as a decision support system to decrease time consumption in the UAST development process: A case study
https://ijfs.usb.ac.ir/article_6079.html
Always the decision of the government to the private sector is faced with the challenges and high level of importance, because these decisions should be taken at the meeting of standards and functional requirements to overcome investors' interests. These decisions include education, and due to the governance nature of education and the governments' strategies in this area, the private sectors who act in it, have been affected by the consequences of different decisions. \\In this paper, our motivation is to propose a system to decide on how to develop applied academic educations at the Applied ScienceEducation Centers (ASEC's) which are supervised by the University of Applied Science and Technology (UAST) in Iran. The method used is theFuzzy Inference System (FIS) to reach this goal. The model performed in this study consists of a two-part FIS for two purposes straight ahead.The first concerns the quantitative development of higher applied education, including the number of Course Request (CR) for each ASEC with 4 inputs and 242 rules. The latter, is related to the qualitative development of higher applied education, including the assessment of the capability and competence of each ASEC for specific CR with the course and student admission background, specialty, committee's and council&rsquo;s opinion, and frequency of course in city or province with 9 inputs, 350 rules, and an output. Each section has its inputs and rules that are determined and used by experts in this domain. \\Our results show that using this method, provides some cost and time savings. This model analyzes in less than 2 minutes, while in practice it could be gain within 1650 person /hours work in different committees that all of them have their costs. Also, results are very close to reality with the advantage that there is no way to apply personal preferences, which largely meets the needs of research.A credibility approach on fuzzy slacks based measure (SBM) DEA model
https://ijfs.usb.ac.ir/article_6080.html
Data Envelopment Analysis (DEA) is a multi-criteria technique based on linear programming to deal with many real-life problems, mostly in nonprofit organizations. The slacks-based measure (SBM) model is one of the DEA model used to assess the relative efficiencies of decision-making units (DMUs). The SBM DEA model directly used input slacks and output slacks to determine the relative efficiency of DMUs. In order to deal with qualitative or uncertain data, a fuzzy SBM DEA model is used to assess the performance of DMUs in this study. The credibility measure approach, transform the fuzzy SBM DEA model into a crisp linear programming model at different credibility levels is used. The results came from the fuzzy DEA model are more rational to the real-world situation than the conventional DEA model. In the end, the data of Indian oil refineries is collected, and the efficiency behavior of the companies obtained by applying the proposed model for its numerical illustration.On the fuzzy solutions of time-fractional problems
https://ijfs.usb.ac.ir/article_6081.html
The main purpose of this paper is to obtain an analytical solution for the time-fractional fuzzy equation. To do this, the time-fractional equation is&nbsp; transformed into an algebraic equation using the fuzzy Laplace and Fourier transforms. The fractional derivatives are described in the Caputo gH-differentiability. In addition, to demonstrate the efficiency of the method some various examples are solved.C-continuous fuzzy posets
https://ijfs.usb.ac.ir/article_6082.html
In this paper, we develop the C-continuity&nbsp;via Scott Q-cotopological spaces, where Q is a commutative and integral quantale.The main results are: (1) The set of all C-compact elements of a completeQ-ordered set is irreducible complete; (2) The Scott Q-cotopology of a Q-ordered set under the fuzzy inclusion order is C-continuous, evenC-prealgebraic; (3) We establish an adjunction between the category of irreducible&nbsp;complete Q-ordered sets and the category of C-prealgebraic complete Q-ordered sets.Construction methods for triangular norms and triangular conorms on appropriate bounded lattices
https://ijfs.usb.ac.ir/article_6083.html
In this study, new methods to construct triangular norms and triangular conorms on appropriate bounded lattices are introduced. Some illustrative examples are given for clarity. Also, the relation between introduced methods and some other approaches is investigated. Finally, it is shown that the introduced construction methods can be generalized by induction to a modified ordinal sum for triangular norms and triangular conorms on appropriate bounded lattices. And some illustrative examples are given.Jensen's inequalities for pseudo-integrals
https://ijfs.usb.ac.ir/article_6084.html
In this paper, we introduce a general$(\oplus,\otimes)$-convex function based on semirings $([a,b],\oplus, \otimes)$ with pseudo-addition $\oplus$ andpseudo-multiplication $\otimes.$ The generalization of the finiteJensen's inequality, as well as pseudo-integral with respect to$(\oplus,\otimes)$-convex functions, is obtained. This also generalizes Jensen's inequalities for Lebesgue integral and the results of Pap and \v{S}trboja \cite{12}. Meanwhile, we also prove Jensen's inequalities for pseudo-integrals on semirings $([a,b], \sup, \otimes)$with respect to nondecreasing functions and present correspondingresults for generalized fuzzy integrals.&nbsp; &nbsp;New results on the migrativity properties for overlap (grouping) functions and uninorms
https://ijfs.usb.ac.ir/article_6085.html
Functional equations involving aggregation functions play an important role in fuzzy sets and fuzzy logic theory. That the migrativity equation as a kind of restricted general associative equation have been proven to be useful in a wide range of fields like decision making, aggregation of information, image processing and so on. In the literature, the already existing results concerning the migrativity equation between overlap (grouping) functions and uninorms are based on the assumption that uninorms belong to one of the most studied classes. In this study we will explore it involving uninorms in a more general setting. To be specific, we investigate the migrativity properties between overlap (grouping) functions and uninorms in the case when uninorms have continuous underlying operators. We will show along the paper that many new solutions to the equation are characterized from this new point of view.Milstein method for solving fuzzy differential equation
https://ijfs.usb.ac.ir/article_6086.html
To solve fuzzy differential equations driven by Liu process, three Milstein schemes are proposed in this work, which are explicit Milstein scheme, semi-implicit Milstein scheme and improved Milstein scheme. Improved Milstein scheme is constructed by correcting the error with semi-implicit method, the error is the difference between the exact solution of fuzzy differential equations and the solution derived from Milstein scheme. These numerical methods are proved to have strong convergence with order two. Accompanying the results above, the concept of mean-stability of numerical schemes for fuzzy differential equations is put forward and analyzed. For a linear test equation, it is showed the mean-stability region of improved Milstein scheme is bigger than explicit Milstein scheme. Finally, the accuracy and effectiveness of these schemes are confirmed through numerical examples.Hyers-Ulam-Rassias stability of quaternion multidimensional fuzzy nonlinear difference equations with impulses
https://ijfs.usb.ac.ir/article_6087.html
In this paper, we consider the Hyers-Ulam-Rassias stability of theimpulsive fuzzy nonlinear difference equations in the multidimensional fuzzy quaternion space.Some sufficient conditions of the Hyers-Ulam-Rassias stability are established for the quaternion multidimensional fuzzy nonlinear difference equations with impulses and several examples are demonstrated to show the feasibility of our obtained results.A bilateral fuzzy support vector machine hybridizing the Gaussian mixture model
https://ijfs.usb.ac.ir/article_6088.html
The fuzzy support vector machine is one of the most exceptional methods to deal with uncertainty in the classification problem. The membership function is a proper way to model uncertainty. The goal of the membership function is to distinguish the different points in terms of their importance. The ordinary design of the membership function relies on the distance of the observations to the class center. However, the class center is affected by the presence of outliers.&nbsp; To prevent this effect, we utilized an unsupervised learning method called the Gaussian mixture model in the structure of the membership function. The proposed membership function is presented in two different categories distance-based and Bayes-based. Unlike the classical membership function, the contribution of outliers in the training phase decreased by diminishing their degree of importance.&nbsp; Hybridizing the classic fuzzy support vector machine classifier with the Gaussian mixture model will enhance the classification accuracy and also will prevent overfitting problems. The superiority of the proposed methods assessed by the synthetic and benchmarking dataset. The statistical significance is assessed by using the non-parametric Friedman and post-hoc Nemenyi tests.Improved fuzzy clustering algorithm using adaptive particle swarm optimization for nonlinear system modeling and identification
https://ijfs.usb.ac.ir/article_6089.html
In this paper, an improved Type2-PCM clustering algorithm based on improved adaptive particle swarm optimization called Type2-PCM-IAPSO is proposed. Firstly, a new clustering algorithm called Type2-PCM is proposed. The Type2-PCM algorithm can solve the problems encountered by fuzzy c-means algorithm (FCM), Gustafson-Kessel algorithm (G-K), possibilistic c-means algorithm (PCM) and NPCM (sensitivity to noise or aberrant points and local minimal sensitivity). . . etc. Secondly, we combined our Type2-PCM algorithm with the improved adaptive particle swarm optimization algorithm (IAPSO) to ensure proper convergence to a local minimum of the objective function. The effectiveness of the two proposed algorithms Type2-PCM and Type2-PCM-IAPSO was tested on a system described by a different equation, Box-Jenkins gas furnace, dryer system and the convection system. The validation tests used showed good performance of these algorithms. However, their average square error test (MSE) shows a better behaviour of the Type2-PCM-IAPSO algorithm compared to the FCM, G-K, PCM, FCM-PSO, Type2-PCM-PSO, RKPFCM and RKPFCM-PSO algorithms.translations IJFS-Vol 18-No 3-June 2021
https://ijfs.usb.ac.ir/article_6091.html
(2002-5724) Disturbance estimator based dynamic compensator design for fractional order fuzzy control systems
https://ijfs.usb.ac.ir/article_5988.html
The robust stabilization problem for singular fractional order time delay T-S fuzzy systems with nonlinearities and unknown external disturbances is addressed in this paper. An equivalent-input-disturbance (EID) estimator is used to estimate the impact of external disturbances and nonlinearities on the system output. Based on this EID approach, a dynamic compensator is designed to solve the stabilization problem of the considered system. Moreover, by considering a relevant Lyapunov-Krasovskii functional candidate and by using Lyapunov technique, the stability conditions in terms of LMIs are acquired for the considered closed-loop system. At last, to validate the effectiveness of the proposed result, two numerical examples are provided.(2004-5799) An interactive fuzzy programming approach for a new multi-objective multi-product oil pipeline scheduling problem
https://ijfs.usb.ac.ir/article_5989.html
In this paper, a new fuzzy multi-objective multi-product pipeline scheduling problem is introduced. The systemconsists of a single refinery, a unique distribution center, and a multi-product pipeline. Restrictions such as batchsizing, discharging rate, forbidden sequences, batch volumetric, etc. are considered. Due to the uncertain nature of real-world problems, some parameters of the system are considered as fuzzy values. Tardiness and earliness penalties are considered with a time dependent non-linear function. The basic aim of this scheduling problem is to achieve the optimal sequence for pumping batches of oil products to maximize the financial benefit and simultaneously sacrifice the customers with on-time delivery as a multi-objective problem. To tackle this problem, a two-stage methodology is proposed. In the first stage, the fuzzy formulation is converted to its equivalent crisp form by a credibility-based chance-constrained programming approach. In the second stage, the multi-objective crisp formulation is solved by some well-known approaches in the literature. Some test problems are generated and solved by the proposed approaches and the obtained Pareto-optimal solutions are analyzed and compared using some distance-based comparison metrics.(1912-5628) F-transforms determined by implicators
https://ijfs.usb.ac.ir/article_6012.html
This work aims to study F-transforms based on general implicators and to investigate their basic properties. Interestingly, we show that some of the properties of&nbsp; F-transforms fail to hold in the case of implicators, such as $S$- and QL-implicators. Further, we establish an equivalence between L-fuzzy transformation systems and $F$-transforms.(2002-5720) On the symmetric quintuple implicational method of fuzzy reasoning
https://ijfs.usb.ac.ir/article_6025.html
A novel fuzzy reasoning method called the SQI (symmetric quintuple implicational) method&nbsp;is put forward, which is a generalization of the QIP (quintuple implication principle) method. First of all, the symmetric quintuple implicational principles are presented, which are distinct from the ones of the QIP method. Then unified optimal solutions of the SQI method are obtained for FMP (fuzzy modus ponens) and FMT (fuzzy modus tollens), meanwhile corresponding reversible properties are verified. Furthermore, focusing on the case of multiple rules, optimal solutions of the SQI method are achieved, which involves two general approaches, i.e., FITA (first-infer-then-aggregate) and FATI (first-aggregate-then-infer). Equivalence relation of continuity and interpolation is analyzed for both FITA and FATI under the environment of the SQI method. Finally, one computing example arising in the field of affective computing is given for the SQI method with FATI. It is found that the SQI method preserves the same properties as the QIP method.(2004-5794) A multi-attribute assessment of fuzzy regression models
https://ijfs.usb.ac.ir/article_6026.html
Most of the fuzzy regression approaches proposed in the literature adopted a single objective function in the generation of fuzzy regression models.These approaches mostly being criticized by their weak performances analysis and their sensitivity to outliers.Therefore, this paper develops a new multi-objective two-stage optimization and decision technique for fuzzy regression modeling problems in order to handle both of the criticisms.To handle the outlier problems, in the first stage, dynamic robust to outlier objective functions is considered in the estimation problem.The estimation problem is solved by running an algorithm which generates a set of fuzzy regression models.Then, in the next stage, we design a decision schema by employing Multi-Attribute Decision Making (MADM) problem.Here, the VIKOR method is employed as a proper means to provide a design to rank the generated fuzzy regression models by the first stage to introduce the most desirable model.We include simulation numerical results and a real-world house price problem in order to highlight the advantages of the proposed method in a comparison study.The results demonstrate the effectiveness of the proposed multi-objective optimization method to handle outlier detection problem while the prediction accuracy of the model is improved(2007-6020) A consistency-driven approach to construction of Z-number-valued pairwise comparison matrices
https://ijfs.usb.ac.ir/article_6028.html
The notion of consistency is used to estimate the quality of preference knowledge and its stability for reliable evaluation of decision alternatives. It is well-known that a set of strict consistency conditions are used to keep the rationality of preference intensities between compared elements. These requirements are not achievable in the real situations when decision maker has limited rationality and partially reliable preferences. In this study, we propose an approach to deriving consistency-driven preference degrees for such kind of situations. A preference degree is described by a Z-number to reflect imprecision and partial reliability of preference knowledge. An optimization problem with Z-number valued variables is used to formulate design of consistent preferences. A real-world decision making problem is considered to illustrate application of the proposed method and conduct comparison with an existing technique.(2004-5835) On the properties of the fuzzy weighted average of fuzzy numbers with normalized fuzzy weights
https://ijfs.usb.ac.ir/article_6037.html
Weighted average with normalized weights is a widely used aggregation operator that takes into account the varying degrees of importance of the numbers in a data set. It possesses some important properties, like monotonicity, continuity, additivity, etc., that play an important role in practical applications. The inputs of the aggregation as well as the normalized weights are usually not known precisely. In such a case, their values can be expressed by fuzzy numbers, and the fuzzy weighted average of fuzzy numbers with normalized fuzzy weights needs to be employed in the model. The aim of the paper is to reveal whether and in which way the properties of the weighted average operator can be observed also for its fuzzy extension. It is shown that it possesses three conditions characteristic for aggregation operators -- identity, monotonicity and boundary conditions, and besides that, also compensation, idempotency, stability for linear transformation, 1-lipschitzianity, and continuity. Furthermore, it is proved that it preserves strict monotonicity in case of positive fuzzy weights, and symmetry in case of equal fuzzy weights, although it does not coincide with the fuzzy arithmetic mean operator in such a case. One of the most valuable result of the study is the fact that in contrast to the crisp weighted average operator, it is not additive. The importance of the obtained results is discussed and illustrated by several illustrative examples.(2010-6234) On matrix games with 2-tuple intuitionistic fuzzy linguistic payoffs
https://ijfs.usb.ac.ir/article_6056.html
In real-world decision-making problems, experts often prefer to express their views, regarding problem parameters, in a natural language rather than precise numerical form. Linguistic representation models have been widely used to solve many decision-making problems with qualitative information. Game theory has been found successful applications in a wide range of areas. This paper presents an extensive study of matrix games with qualitative payoffs. The work uses 2-tuple intuitionistic fuzzy linguistic values (2-TIFLVs) to represent the payoffs of the matrix game. We develop the mathematical formulation and concepts of the solutions for matrix games with payoffs represented by 2-TIFLVs. Paper also shows that matrix games with payoffs of 2-TIFLVs have solutions that can be obtained by transforming the matrix game in a pair of linear/nonlinear programming problems. Finally, a real-life numerical is given to illustrate the developed method.(2008-6070) Preference implication-based approach to ranking fuzzy numbers
https://ijfs.usb.ac.ir/article_6058.html
Dombi and&nbsp; Baczynski presented a new approach to the problem of implication operation by introducing the preference implication, which has very advantageous properties. In this paper, it is presented how the preference implication is connected with soft inequalities and with sigmoid functions. Utilizing this connection the preference implication-based preference measure for two fuzzy numbers is introduced and its key properties, including the reciprocity, are described. Then, the exact expression for computing the new preference measure for trapezoidal fuzzy numbers is presented. Here, using the new preference measure, two crisp relations over trapezoidal fuzzy numbers are introduced. It is shown that one of them is a strict (but not a total) order relation, and the other one is an equivalence relation. The strict order relation can be used to rank comparable fuzzy numbers, while the equivalence relation, which we call the indifference relation, expresses that the order of some fuzzy numbers is indifferent. These two crisp relations can be used to rank a collection of trapezoidal fuzzy numbers. Lastly, the proposed ranking method is compared with some well-known existing fuzzy number ranking methods.(2007-6045) Developing a fuzzy programming model for improving outpatient appointment scheduling
https://ijfs.usb.ac.ir/article_6068.html
Appointment scheduling for outpatient services is a challenge in the healthcare sector. For addressing this challenge, most studies assumed that patients&rsquo; unpunctuality and the duration of service have constant values or a specific probability distribution function. Consequently, there is a research gap to consider the uncertainty of both patients&rsquo; unpunctuality and the duration of service in terms of fuzzy sets. Therefore, this research aims to consider fuzzy values for both unpunctuality and duration of service have to improve an outpatient appointment scheduling (the time interval between two patients) in a referral clinic with the objective of reducing the total weight of waiting time, idle time, and overtime. Four different fuzzy linear programming models and 36 scenarios have been developed based on the show, no-show of patients, single-book, and double-book by using GAMS software. These four models are as follows: (1) probability of no-show equal to zero, (2) probability of no-show equal to 20\%, (3) probability of no-show equal to zero and with double-book factor, and (4) probability of no-show equal to 20\% and with double-book factor. The results of the first, second, third, and fourth models, respectively, present the scenarios considering 10, 5, 15, and 15 minutes for the time interval between two patients that have the minimum total weight of patient waiting times, physician idle times, and physician overtime. By considering these findings, the investigated referral clinic can improve its appointment system&rsquo;s performance. Moreover, other similar clinics can apply the proposed model for improving their appointment systems' performance.(2008-6107) Continuous probability-interval valued fuzzy preference relations and its application in group decision making
https://ijfs.usb.ac.ir/article_6069.html
Probabilistic hesitant fuzzy set represents the occurrence probabilities of elements.The probabilistic hesitant fuzzy preference relations can more effectively express the&nbsp;hesitant preference information of decision makers.But in the existing research, all of them are based on discrete probability distribution.In order to give decision maker more evaluation space,continuous probability distribution is necessary to be considered.Therefore, in this paper, the continuous probability-interval valued fuzzy setis defined and its probability is represented by a probability density function.A method of converting probabilistic hesitant fuzzy set into continuous probability-interval valued fuzzy set&nbsp;is developed to transform discrete data into continuous data.Then, the continuous probability-interval valued fuzzy preference relations is presented.In order to consider the consistency of continuous probability-interval valued fuzzy preference relations, the multiplication consistent expected preference relations is proposed.The individual consistency index and group consensus index are also presented to determine the consistency level.And then, an algorithm is introduced for checking and improving the individual consistency level and&nbsp;group consensus level.Finally, a numerical example is shown to the effectiveness of proposed algorithm,the comparative analysis is given with the existing methods toshow the superiority of this algorithm.(2008-6142) Sensitivity and strong sensitivity on induced dynamical systems
https://ijfs.usb.ac.ir/article_6074.html
Given a metric space $X$, we consider the family of all normal upper semicontinuous fuzzy sets on $X$, denoted by $\mathcal{F}(X)$, and a discrete dynamical system $(X,f)$. In this paper, we study when $(\mathcal{F}(X), \widehat{f})$ is (strongly) sensitive, where $\widehat{f}$ is the Zadeh's extension of $f$ and $\mathcal{F}(X)$ is equipped with different metrics: The uniform metric, the Skorokhod metric, the sendograph metric and the endograph metric. We prove that the sensitivity in the induced dynamical system $(\mathcal{K}(X),\overline{f})$ is equivalent to the sensitivity in $ \widehat{f} :\mathcal{F}(X)\to \mathcal{F}(X) $ with respect to the uniform metric, the Skorokhod metric and the sendograph metric. We also show that the following conditions are equivalent:\item {\rm a)} $(X,f)$ is strongly sensitive;\item {\rm b)} $(\mathcal{F}(X), \widehat{f})$ is strongly sensitive, where $\mathcal{F}(X)$ is equipped with the uniform metric;\item {\rm c)} $(\mathcal{F}(X), \widehat{f})$ is strongly sensitive, where $\mathcal{F}(X)$ is equipped with the Skorokhod metric;\item {\rm d)} $(\mathcal{F}(X), \widehat{f})$ is strongly sensitive, where $\mathcal{F}(X)$ is equipped with the sendograph metric.(2003-5785) Approximating credibilistic constraints by robust counterparts of uncertain linear inequality
https://ijfs.usb.ac.ir/article_6075.html
This paper studies a class of credibilistic optimization (CO) problems, in which a convex&nbsp; objective is minimized subject to ambiguous credibilistic constraints. The considered CO problem is usually computational intractable. Our purpose in this paper is to&nbsp; discuss the robust counterpart approximations of ambiguous credibilistic constraints. Under mild assumptions, the closed property about the feasible region of credibilistic constraint is discussed. Using the obtained results, this paper deals with the robust counterpart approximations of credibilistic constraints under two types of ambiguity sets of possibility distributions. The first type is exponential function-based ambiguity set of possibility distribution, while the second type of ambiguity set is a particular case of the first one, and it is based on range and expectation information of fuzzy variables. The developed approximation techniques are capable to utilize the knowledge of ambiguity sets of possibility distributions when building distribution uncertainty-immunized solutions. As a result, the obtained safe approximations of ambiguous credibilistic&nbsp; constraints are computationally tractable convex/linear constraints.&nbsp; To apply the proposed approximation approach, a portfolio optimization problem is addressed, in which the investor is to find a portfolio to maximize the value-at-risk of his total return under the support and expectation information of uncertain returns. We use two types of robust counterpart approximations to credibilistic constraints.&nbsp; The computational results support our arguments.(2008-6074) Multidimensional interval type 2 epistemic fuzzy arithmetic
https://ijfs.usb.ac.ir/article_6076.html
The article presents a new, multidimensional arithmetic of type 2 fuzzy numbers (M-IT2-F arithmetic) in which the result is a multidimensional fuzzy set. This arithmetic increases the accuracy of calculations and the scope of problems solved in relation to the currently used interval type 2 standard fuzzy arithmetic (IT2-SF arithmetic). The proposed M-IT2-F arithmetic has mathematical properties that IT2-SF arithmetic does not have. Thanks to these properties, it provides accurate calculation results that are not over- or under-estimated in terms of uncertainty. The paper contains comparisons of both types of arithmetic in application to two problems. Fuzzy arithmetic is not a finished work and is in a phase of continuous improvement and development. M-IT2-F arithmetic is a higher form of M-IT2 (non-fuzzy) arithmetic.(1909-5488) A fuzzy generalized predictive controller to optimal drug dosage therapy of mathematical modeling of HIV
https://ijfs.usb.ac.ir/article_6094.html
This paper proposes a fuzzy-GPC based on a mathematical model of human immunodeficiency virus (HIV) to determine the drug dosage and control the progression of the illness. For this purpose, a Takagi-Sugeno (TS) fuzzy model is generated to identify the nonlinear behavior of HIV. The parameters of HIV are estimated by the least square error (LSE) estimation method. Moreover, three scenarios are proposed to control HIV. In scenario 1, according to TS fuzzy model, generalized Predictive Control (GPC) is designed for a daily base drug therapy. Scenario 2 and 3 are more practical. In scenario 2, since the biological behavior of patients are different, the variation in the patients biology is taken into account by generating data according to a group of patients with varying parameters in their mathematical model. In senario3, since daily diagnosis of patient&rsquo;s health is costly, it is assumed that a patient information is available every month, and drug dosage is determined each month. As a result of which, the sample time of the measurement increases to 30 make it a multi-rate system. The result shows that the TS fuzzy models&nbsp; the mathematical model of HIV very well, and in all scenarios, the proposed controller has a good performance and the number of healthy cells are controlled in acceptable amount.(2010-6230) Robust stabilization of uncertain rectangular singular fractional order T-S fuzzy systems with the fractional order $0
https://ijfs.usb.ac.ir/article_6096.html
This paper presents a novel method to investigate the robust stabilization problem of uncertain rectangular singular fractional order Takagi-Sugeno (T-S) fuzzy systems with the fractional order $0&lt;\alpha&lt;1$. Firstly, the uncertain rectangular singular fractional order T-S fuzzy system is transformed into an augmented uncertain square singular fractional order T-S fuzzy system by designing a new T-S fuzzy dynamic compensator. Secondly, a sufficient condition in the form of linear matrix inequalities (LMI) is obtained for the robust stabilization of the uncertain rectangular singular fractional order T-S fuzzy system. Finally, a numerical example is given to verify the effectiveness of the results proposed.