http://ieeexplore.ieee.org/iel5/5/31196/01451889.pdf

Random differential equations in science and engineering

/pdf/elementary-numerical-analysis-c3jwdaojjj.pdf

Elementary Numerical Analysis

Fractional calculus for interval-valued functions

A survey on fuzzy fractional differential and optimal control nonlocal evolution equations

Greenhouse climate control is complicated procedure since the number of variables involved on it and which are dependent on each other. This paper presents a contribution to integrate greenhouse inside climate key's parameters, leading to promote a comfortable micro-climate for the plants growth while saving energy and water resources. A smart fuzzy logic based control system was introduced and improved through specific measure to the temperature and humidity correlation. As well, the system control was enhanced with wireless data monitoring platform for data routing and logging, which provides real time data access. The proposed control system was experimentally validated. The efficiency of the system was evaluated showing important energy and water saving.

Smart greenhouse fuzzy logic based control system enhanced with wireless data monitoring.

http://profdoc.um.ac.ir/articles/a/1029540.pdf

Modified fractional Euler method for solving Fuzzy Fractional Initial Value Problem

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 (FDEs) 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 FDEs more conveniently than 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 modeling 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.

Granular Differentiability of Fuzzy-Number-Valued Functions

Type-2 fuzzy fractional derivatives

Differentiability of type-2 fuzzy number-valued functions

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 Hukuhara and generalized Hukuhara differentiability concepts for obtaining the optimal control law. The granular eigenvalues notion is also defined. Using an RLC circuit mathematical model, it is shown that, due to their unnatural behavior in the modeling phenomenon, the FSIA-based approaches may obtain some eigenvalues sets that might be different from the inherent eigenvalues set of the fuzzy dynamical system. This is, however, not the case with the approach proposed in this study. The notions of granular controllability and granular stabilizability of the fuzzy linear dynamical system are also presented in this paper. Moreover, a sub-optimal control for regulating a Boeing 747 in longitudinal direction with uncertain initial conditions and parameters is gained. In addition, an uncertain suspension system of one of the four wheels of a bus is regulated using the sub-optimal control introduced in this paper.

Mehran Mazandarani

Papers

Modified fractional Euler method for solving Fuzzy Fractional Initial Value Problem

Granular Differentiability of Fuzzy-Number-Valued Functions

Type-2 fuzzy fractional derivatives

Differentiability of type-2 fuzzy number-valued functions

Sub-optimal control of fuzzy linear dynamical systems under granular differentiability concept.