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Mehran  Mazandarani
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Mehran Mazandarani

As the title suggests, in this work, a modern machine learning method called the Q-fractionalism reasoning is introduced. The proposed method is founded upon a synergy of the Q-learning and fractional fuzzy inference systems (FFISs).... more
As the title suggests, in this work, a modern machine learning method called the Q-fractionalism reasoning is introduced. The proposed method is founded upon a synergy of the Q-learning and fractional fuzzy inference systems (FFISs). Unlike other approaches, the Q-fractionalism reasoning not only incorporates the knowledge base to understand how to perform but also explores a reasoning mechanism from the fractional order to justify what it has performed. This method suggests that the agent choose actions aimed at the characterization of reasoning. In fact, the agent deals with states termed as primary and secondary fuzzy states. The primary fuzzy states are unobservable and uncertain, for which the agent chooses actions. However, the projection of primary fuzzy states onto the knowledge base results in secondary fuzzy states, which are observable by the agent, allowing it to detect primary fuzzy states with degrees of detectability. With a practical experiment implemented on a linear switched reluctance motor (LSRM), the results demonstrate that the application of the Q-fractionalism reasoning in the real-time position control of the LSRM leads to a remarkable improvement of about 70% in the accuracy of the control objective compared with a typical fuzzy inference system (FIS) under the same setting.
This paper aims at solving first order linear fuzzy differential equations system by an approach called quasi-level-wise system. Some comparative examples show while some other approaches fail to obtain possible system solutions, the... more
This paper aims at solving first order linear fuzzy differential equations system by an approach called quasi-level-wise system. Some comparative examples show while some other approaches fail to obtain possible system solutions, the proposed approach is able and effective. Moreover, how the linear fuzzy differential equations system may arise in applications is explained and inverted pendulum system is given as an example. Through the example, it is also demonstrated how helpful this fuzzy linear model can be, compared to the crisp linear model.
In this paper, a new definition of fuzzy fractional derivative is presented. The definition does not have the drawbacks of the previous definitions of fuzzy fractional derivatives. This definition does not necessitate that the diameter of... more
In this paper, a new definition of fuzzy fractional derivative is presented. The definition does not have the drawbacks of the previous definitions of fuzzy fractional derivatives. This definition does not necessitate that the diameter of the fuzzy function be monotonic, and it does not refer to derivative of order greater than the one that is considered. Moreover, the fractional derivative of a fuzzy constant is zero based on the definition. Restrictions associated to Caputo-type fuzzy fractional derivatives are expressed. Additionally, generalized Hukuhara difference and generalized difference of perfect type-2 fuzzy numbers are defined. Furthermore, using two examples the advantages of the new definition compared with the others are borne out.
Following type-1 fractional fuzzy inference systems presented recently as the new generation of fuzzy inference systems, interval type-2 fractional fuzzy inference systems (IT2FFISs) as a leap further ahead in the evolution of fuzzy... more
Following type-1 fractional fuzzy inference systems presented recently as the new generation of fuzzy inference systems, interval type-2 fractional fuzzy inference systems (IT2FFISs) as a leap further ahead in the evolution of fuzzy inference systems (FISs) are introduced in this article. The IT2FFISs, which are outlined in this article, add to the armamentarium of FISs some particular concepts such as interval type-2 fractional membership functions, type-2 fractional translation rule, type-2 fracture index, the concept of switching, the entanglement, the degeneracy concept, and so forth. An IT2FFIS exploits not only the tolerance for the uncertainty in the interpretation of the meaning of a word, but also the relevance between the quality and quantity levels of the given information to infer an answer to an inference query. The IT2FFISs make an increase in machine intelligence quotient possible by an increase in the range of FISs order rather than their type. Moreover, the synergy of the concepts coming with various modes of IT2FFISs such as the aggressive mode opens a gate to a space of fuzzy systems outputs which used to be indiscoverable. Furthermore, it is demonstrated that as the type-2 fracture index approaches zero, the space of IT2FFISs outputs contracts and eventually it coincides the space of IT2FISs output when the fracture index is equal to zero. It is also proved that, provided a particular order of the IT2FFIS is taken into account, independent of the problem in question, a typical IT2FIS never leads to results which are more satisfactory than those obtained by the IT2FFIS corresponding to the typical IT2FIS.
This paper deals with sub-optimal control of a fuzzy linear dynamical system. The aim is to keep the state variables of the fuzzy linear dynamical system close to zero in an optimal manner. In the fuzzy dynamical system, the fuzzy... more
This paper deals with sub-optimal control of a fuzzy linear dynamical system. The aim is to keep the state variables of the fuzzy linear dynamical system close to zero in an optimal manner. In the fuzzy dynamical system, the fuzzy derivative is considered as the granular derivative; and all the coefficients and initial conditions can be uncertain. The criterion for assessing the optimality is regarded as a granular integral whose integrand is a quadratic function of the state variables and control inputs. Using the relative-distance-measure (RDM) fuzzy interval arithmetic and calculus of variations, the optimal control law is presented as the fuzzy state variables feedback. Since the optimal feedback gains are obtained as fuzzy functions, they need to be defuzzified. This will result in the sub-optimal control law. This paper also sheds light on the restrictions imposed by the approaches which are based on fuzzy standard interval arithmetic (FSIA), and use strongly generalized Hukuh...
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In this paper different methods of using fuzzy logic in parallel hybrid vehicles control have been investigated and how to design fuzzy logic controller in these vehicles based on the kind of input, number of inputs, kind and number of... more
In this paper different methods of using fuzzy logic in parallel hybrid vehicles control have been investigated and how to design fuzzy logic controller in these vehicles based on the kind of input, number of inputs, kind and number of output and desired control targets have been explained. Results related to comparison of fuzzy controller against classic controllers with aims of reduction of fuel consumption and environmental pollution are presented. Also, convention fuzzy controllers have been compared with optimized fuzzy controllers and some suggestions for doing other research works in this area have been offered.
ABSTRACT In this note, we show that the proposed approach in [J. Xu, Z. Liao, Z. Hu, A class of linear differential dynamical systems with fuzzy initial condition, Fuzzy Sets Syst. 158 (2007) 2339– 2358] fails to obtain the stable... more
ABSTRACT In this note, we show that the proposed approach in [J. Xu, Z. Liao, Z. Hu, A class of linear differential dynamical systems with fuzzy initial condition, Fuzzy Sets Syst. 158 (2007) 2339– 2358] fails to obtain the stable solutions to the stable linear dynamical systems with fuzzy initial conditions. It will be explained this shortcoming is caused by neglecting to move the stability property of the fuzzy system to the quasi level-wise system. Moreover, to handle this, another approach is proposed similar to the previous one for the stable and unstable systems.
ABSTRACT In this paper, we define a differentiability of the type-2 fuzzy number-valued functions. The definition is based on type-2 Hukuhara difference which is defined in the paper as well. The related theorem of the differentiability... more
ABSTRACT In this paper, we define a differentiability of the type-2 fuzzy number-valued functions. The definition is based on type-2 Hukuhara difference which is defined in the paper as well. The related theorem of the differentiability of the type-2 fuzzy number-valued functions is derived. In addition, a parametric closed form of the perfect triangular quasi type-2 fuzzy numbers is introduced, and finally, the applicability and an approach to solving type-2 fuzzy differential equations are illustrated using some examples and cases.
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ABSTRACT In this paper different methods of using fuzzy logic in parallel hybrid vehicles control have been investigated and how to design fuzzy logic controller in these vehicles based on the kind of input, number of inputs, kind and... more
ABSTRACT In this paper different methods of using fuzzy logic in parallel hybrid vehicles control have been investigated and how to design fuzzy logic controller in these vehicles based on the kind of input, number of inputs, kind and number of output and desired control targets have been explained. Results related to comparison of fuzzy controller against classic controllers with aims of reduction of fuel consumption and environmental pollution are presented. Also, convention fuzzy controllers have been compared with optimized fuzzy controllers and some suggestions for doing other research works in this area have been offered.
Following type-1 fractional fuzzy inference systems presented recently as the new generation of fuzzy inference systems, interval type-2 fractional fuzzy inference systems (IT2FFISs) as a leap further ahead in the evolution of fuzzy... more
Following type-1 fractional fuzzy inference systems presented recently as the new generation of fuzzy inference systems, interval type-2 fractional fuzzy inference systems (IT2FFISs) as a leap further ahead in the evolution of fuzzy inference systems (FISs) are introduced in this article. The IT2FFISs, which are outlined in this article, add to the armamentarium of FISs some particular concepts such as interval type-2 fractional membership functions, type-2 fractional translation rule, type-2 fracture index, the concept of switching, the entanglement, the degeneracy concept, and so forth. An IT2FFIS exploits not only the tolerance for the uncertainty in the interpretation of the meaning of a word, but also the relevance between the quality and quantity levels of the given information to infer an answer to an inference query. The IT2FFISs make an increase in machine intelligence quotient possible by an increase in the range of FISs order rather than their type. Moreover, the synergy of the concepts coming with various modes of IT2FFISs such as the aggressive mode opens a gate to a space of fuzzy systems outputs which used to be indiscoverable. Furthermore, it is demonstrated that as the type-2 fracture index approaches zero, the space of IT2FFISs outputs contracts and eventually it coincides the space of IT2FISs output when the fracture index is equal to zero. It is also proved that, provided a particular order of the IT2FFIS is taken into account, independent of the problem in question, a typical IT2FIS never leads to results which are more satisfactory than those obtained by the IT2FFIS corresponding to the typical IT2FIS.
The tutorial includes 7 sections and introduces briefly the new generation of fuzzy inference systems that is called fractional fuzzy inference systems, FFISs for short. Also, some explanations about the implementation of FFISs in Matlab... more
The tutorial includes 7 sections and introduces briefly the new generation of fuzzy inference systems that is called fractional fuzzy inference systems, FFISs for short. Also, some explanations about the implementation of FFISs in Matlab software have been provided.
ABSTRACT In this paper, we introduce two definitions of the differentiability of type-2 fuzzy number-valued functions of fractional order. The definitions are in the sense of Riemann–Liouville and Caputo derivative of order... more
ABSTRACT In this paper, we introduce two definitions of the differentiability of type-2 fuzzy number-valued functions of fractional order. The definitions are in the sense of Riemann–Liouville and Caputo derivative of order 0<beta<1, and based on type-2 Hukuhara difference and H2 differentiability. The existence and uniqueness of the solutions of type-2 fuzzy fractional differential equations (T2FFDEs) under Caputo type-2 fuzzy fractional derivative and the definition of Laplace transform of type-2 fuzzy number-valued functions are also given. Moreover, the approximate solution to T2FFDE by a Predictor-Evaluate–Corrector-Evaluate (PECE) method is presented. Finally, the approximate solutions of two examples of linear and nonlinear T2FFDEs are obtained using the PECE method, and some cases of T2FFDEs applications in some sciences are presented.
Since the term ''Fuzzy differential equations'' (FDEs) emerged in the literature in 1978, prevailing research effort has been dedicated not only to the development of the concepts concerning the topic, but also to its potential... more
Since the term ''Fuzzy differential equations'' (FDEs) emerged in the literature in 1978, prevailing research effort has been dedicated not only to the development of the concepts concerning the topic, but also to its potential applications. This paper presents a chronological survey on fuzzy differential equations of integer and fractional orders. Attention is concentrated on the FDEs in which a definition of fuzzy derivative of a fuzzy number-valued function has been taken into account. The chronological rationale behind considering FDEs under each concept of fuzzy derivative is highlighted. The pros and cons of each approach dealing with FDEs are also discussed. Moreover, some of the proposed FDEs applications and methods for solving them are investigated. Finally, some of the future perspectives and challenges of fuzzy differential equations are discussed based on our personal view point.
This paper presents a new machinery of compositional rule of inference called fractional fuzzy inference system (FFIS). An FFIS is a fuzzy inference system (FIS) in which consequent parts of a rule base consist of a new type of membership... more
This paper presents a new machinery of compositional rule of inference called fractional fuzzy inference system (FFIS). An FFIS is a fuzzy inference system (FIS) in which consequent parts of a rule base consist of a new type of membership functions called fractional membership functions. Fractional membership functions are characterized using fractional indices. There are two types of fractional indices. Each type can be either constant or dynamic. An FFIS intelligently considers not only the truth degrees of information included in membership functions, but also the volume of the information in the process of making a conclusion. In other words, the volume of information extracted from a membership function depends on the truth degree of information. Concretely, the higher the truth degree, the larger the volume of information that is involved in the process of making a conclusion. It is shown that typical FISs, e.g. Mamdani’s or Larsen’s FISs, are special cases of FFISs. Specifically, as the fractional indices approach one, the FFIS approaches a typical FIS. In addition, using two theorems proved in this paper, it is demonstrated that, independent of the problem in question, a typical FIS never leads to results which are more satisfactory than those obtained by the FFIS corresponding to the typical FIS provided that a particular set of fractional indices is taken into account. Put another way, it seems sound to expect that applying FFIS always leads to more satisfactory results than applying its corresponding FIS. It is also shown that FFIS grants a special dynamic to FIS which can be also customized according to a new concept called reaction trajectories map (RTM). Particularly, the RTM enables decision makers to select an FFIS more suitable for their purpose. Some more concepts such as the left and right orders of an FFIS and the fracture index are also introduced in this paper.
This paper is devoted to make a framework for studying a class of uncertain differential equations called Z-differential equations. In order to achieve the purpose, we first introduce four basic operations on Z +-numbers based on... more
This paper is devoted to make a framework for studying a class of uncertain differential equations called Z-differential equations. In order to achieve the purpose, we first introduce four basic operations on Z +-numbers based on semi-granular function. Then, the limit and continuity concepts of a Z-number-valued function are given, under a definition of a metric on the space of Z +-numbers. Moreover, the concepts of Z-differentiability, Z-integral, and Z-Laplace transform of a Z-number-valued function are introduced. In addition, by giving some theories proved in this paper, a basis for calculus-Z-calculus-is established. We further give theories based on which existence and uniqueness of Z-differential equations are investigated. A conceptual unity between Z-differential equations and Z +-numbers is also shown. The conceptual unity demonstrates that a Z-differential equation may be expressed as a bimodal differential equation combining a fuzzy differential equation and a random differential equation. Moreover, the concept of a bimodal cut called (s, µ)-cut is introduced and its relation to other new concepts such as acceptable time and acceptable information area is explained. Using an example, the application of Z-differential equations in medicine is clarified. It is demonstrated that Z-differential equations outperform fuzzy differential equations in making a decision under uncertainty.
In this paper, using the concept of horizontal membership functions, a new definition of fuzzy derivative called granular derivative is proposed based on granular difference. Moreover, a new definition of fuzzy integral called granular... more
In this paper, using the concept of horizontal membership functions, a new definition of fuzzy derivative called granular derivative is proposed based on granular difference. Moreover, a new definition of fuzzy integral called granular integral is defined, and its relation with the granular derivative is given. A new definition of a metric - granular metric - on the space of type-1 fuzzy numbers, and a concept of continuous fuzzy functions are also presented. Restrictions associated to previous approaches - Hukuhara differentiability, strongly generalized Hukuhara differentiability, generalized Hukuhara differentiability, generalized differentiability, Zadeh’s extension principle, and fuzzy differential inclusions - dealing with fuzzy differential equations are expressed. It is shown that the proposed approach does not have the drawbacks of the previous approaches. It is also demonstrated how this approach enables researchers to solve fuzzy differential equations more conveniently than the ever before. Moreover, we showed that this approach does not necessitate that the diameter of the fuzzy function be monotonic. It is also proved that the result of each of the four basic operations on fuzzy numbers introduced based on the proposed approach leads to a fuzzy number. Moreover, the condition for the existence of the granular derivative of a fuzzy function is provided by a theorem. Additionally, by two examples, it is shown that the existence of the granular derivative of a fuzzy function does not imply the existence of the generalized Hukuhara differentiability of the fuzzy function, and vice versa. The terms doubling property and unnatural behavior in modelling (UBM) phenomenon are also introduced. Furthermore, using some examples the paper proceeds to elaborate on the efficiency and effectiveness of the proposed approach. Moreover, as an application of the proposed approach, the response of Boeing 747 to impulsive elevator input is obtained in the presence of uncertain initial conditions and parameters.
Research Interests:
In this note, it is shown that some obtained results in Solaymani Fard and Ghal-Eh (2011) are not true.
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In this note, we show that the proposed approach in [J. Xu, Z. Liao, Z. Hu, A class of linear differential dynamical systems with fuzzy initial condition, Fuzzy Sets Syst. 158 (2007) 2339– 2358] fails to obtain the stable solutions to the... more
In this note, we show that the proposed approach in [J. Xu, Z. Liao, Z. Hu, A class of linear differential dynamical systems with fuzzy initial condition, Fuzzy Sets Syst. 158 (2007) 2339– 2358] fails to obtain the stable solutions to the stable linear dynamical systems with fuzzy initial conditions. It will be explained this shortcoming is caused by neglecting to move the stability property of the fuzzy system to the quasi level-wise system. Moreover, to handle this, another approach is proposed similar to the previous one for the stable and unstable systems.
In this paper, we introduce two definitions of the differentiability of type-2 fuzzy number-valued functions of fractional order. The definitions are in the sense of Riemann–Liouville and Caputo derivative of order 0<beta<1, and based on... more
In this paper, we introduce two definitions of the differentiability of type-2 fuzzy number-valued functions of fractional order. The definitions are in the sense of Riemann–Liouville and Caputo derivative of order 0<beta<1, and based on type-2 Hukuhara difference and H2 differentiability.
The existence and uniqueness of the solutions of type-2 fuzzy fractional differential equations (T2FFDEs) under Caputo type-2 fuzzy fractional derivative and the definition of Laplace transform of type-2 fuzzy number-valued functions are also given.
Moreover, the approximate solution to T2FFDE by a Predictor-Evaluate–Corrector-Evaluate (PECE) method is presented. Finally, the approximate solutions of two examples of linear and nonlinear T2FFDEs are obtained using the PECE method, and some cases of T2FFDEs applications in some sciences are presented.
In this paper, we define a differentiability of the type-2 fuzzy number-valued functions. The definition is based on type-2 Hukuhara difference which is defined in the paper as well. The related theorem of the differentiability of the... more
In this paper, we define a differentiability of the type-2 fuzzy number-valued functions. The definition is based on type-2 Hukuhara difference which is defined in the paper as well. The related theorem of the differentiability of the type-2 fuzzy number-valued functions is derived. In addition, a parametric closed form of the perfect triangular quasi type-2 fuzzy numbers is introduced, and finally, the applicability and an approach to solving type-2 fuzzy differential equations are illustrated using some examples and cases.
In this paper, the solution to Fuzzy Fractional Initial Value Problem [FFIVP] under Caputo-type fuzzy fractional derivatives by a modified fractional Euler method is presented. The Caputo-type fuzzy fractional derivatives are defined... more
In this paper, the solution to Fuzzy Fractional Initial Value Problem [FFIVP] under Caputo-type fuzzy fractional derivatives by a modified fractional Euler method is presented. The Caputo-type fuzzy fractional derivatives are defined based on Hukuhara difference and strongly generalized fuzzy differentiability. The modified fractional Euler method based on a generalized Taylor’s formula and a modified trapezoidal rule is used for solving initial value problem under fuzzy fractional differential equation of order β∈(0,1). Solving two examples of linear and nonlinear FFIVP illustrates the method.
One of the contributions of the fractional fuzzy inference systems, the new branch of fuzzy systems.
Are you working on fuzzy systems or interested in them? If so, you can join the WhatsApp group of the Fuzzy Systems Community. In this group, we share our experiences and information about almost everything, not only focusing on fuzzy... more
Are you working on fuzzy systems or interested in them?

If so, you can join the WhatsApp group of the Fuzzy Systems Community. In this group, we share our experiences and information about almost everything, not only focusing on fuzzy systems but also on journals, reviewers, editors, available positions, and opportunities. We discuss and share our experiences freely and, indeed, FRANKLY!
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