Iranian journal of fuzzy systems
Volume:18 Issue: 2, Mar-Apr 2021

In this paper, we consider the existence of solutions to first-order interval-valued differential equations with length constraints under gH-differentiability. By using the fixed point theory of compact maps on metric spaces, we provide some sufficient conditions for the existence of solutions. At the end of this paper, we show some examples to illustrate our results.

The Farlie-Gumble-Morgenstren (FGM) family  and  archimedean family are the most popular parametric families of copulas.  In the present paper, we propose an extension of archimedean copulas with concave multiplicative generators in the style of FGM family. In particular, our method allows the modelling of higher positive dependence than the other FGM extensions in the literature. The construction and characteristics of the proposed model along with some examples of parametric subfamilies are provided. A numerical study is used to illustrate the methodology.

Fuzzy random partial differential equations (PDEs) present a connection between random dynamical systems with nonstatistical inexactness data. These blended models could be efficiently used in modeling dynamical systems working in vagueness and ambiguity environments such as fuzzy random adaptive control, fuzzy random financial prediction, fuzzy random biological modeling, etc. In this article, we study Goursat problem for fuzzy random wave equations in the framework of generalized complete metric spaces in the sense of Luxemburg. We consider equations under generalized Hukuhara differentiability. The force functions are constrained by generalized Lipschitz conditions, that makes the range of PDEs types wider than using unbounded and locally Lipschitz conditions. The existence, uniqueness and boundedness of fuzzy solutions are investigated by employing Picard successive approximation method and Luxemburg fixed point theorem. Some illustrated examples are given to demonstrate for theoretical results.

This paper proposed an extension for the classical partial univariate regression model with non-fuzzy inputs and triangular fuzzy output. For this purpose, the popular non-parametric estimator and  the conventional arithmetic operations of triangular fuzzy numbers were combined to construct a fuzzy univariate regression model. Then, a hybrid algorithm was developed to estimate the bandwidth  and fuzzy regression coefficient. Some common goodness-of-fit criteria were also used to examine the performance of the proposed method. The effectiveness of the proposed method was then illustrated through two numerical examples including a simulation study. The proposed method was also compared with several common fuzzy linear regression models with exact inputs and fuzzy outputs. Compared to the available fuzzy linear regressions models, the numerical results clearly indicated that the proposed fuzzy regression model is capable of exhibiting more accurate performances.

This article aimed to investigate the problem of global dissipativity of Fuzzy Bidirectional Associative Memory  Neural Networks (FBAMNNs- for short) with proportional delays. Via Lyapunov Functionals (LFs- for short) and Linear Matrix Inequality (LMI- for short) approach, we obtained new sufficient conditions to guarantee the global dissipativity and global exponential dissipativity of the proposed model. In addition, two different types of activation functions are considered, including general bounded and Lipschitz-type activation functions. Moreover, the globally attractive and globally exponentially attractive sets are presented. Lastly, two numerical examples are given to illustrate the effectiveness of the developed results.

Due to the large use of fuzzy numbers, the ranking of these numbers is very important.In this paper, we propose a new method for ranking generalized fuzzy numbers with different left and right heights.The proposed method, at first obtains the centers of gravity of fuzzy numbers and left and right side crisp numbers; then by computing left and right areas associated with them, ranks the fuzzy numbers. The proposed method can overcome the flaws and defects of some ranking methods, and the provided examples are evidence of this. Finally this method is applied to the fuzzy risk analysis problem.

Multiple twin support vector machine (MTSVM) which evaluates all the training data into a ``one-versus-rest'' structure is a multi-class classification algorithm. It has extensive applications in the multi-class classification problems. Like twin support vector machine (TSVM), MTSVM treats all sample points equally because it lacks the ability to judge the importance of different sample points. In order to improve the classification performance of MTSVM, a new method of adding interval-valued fuzzy membership degree to sample points is proposed. In this way, a novel interval-valued fuzzy multiple twin support vector machine (IVF-MTSVM) is established in this paper. Previous methods of adding fuzzy membership degree to sample points are totally based on their importance to the class, while the method in this paper emphasizes the importance of sample points to the classification model, and takes into account the importance to the class to some extent. This is a new perspective to establish fuzzy membership degree to sample points in support vector machines since it is different from the previous methods in thinking. Then the solution to IVF-MTSVM is derived. Experiments on UCI datasets show that this new method has certain advantages over other multi-class twin support vector machine methods in ``one-versus-rest'' structure and other fuzzy multiple twin support vector machine established by some previous methods. Finally, Friedman test and Benferroni-Dunn test are used to verify the statistical significance of this new method.

Recently, Fang and Hu introduced the definition of semi-t-operators on bounded lattices. In this study, we propose several construction methods to obtain such a semi-t-operator from a given semi-t-conorm and semi-t-norm on bounded lattices. Furthermore, we discuss the presence of idempotent semi-t-operators on bounded lattices, and show several different methods for construction of idempotent semi-t-operators on bounded lattices with additional constraints.

In this paper, a new separated design of adaptive observer-based fault estimator (FE) and fault-tolerant control (FTC) is introduced for nonlinear systems along with sensor and actuator faults in the presence of external disturbance and parametric modeling uncertainty by T-S fuzzy modeling, which can easily challenge integrated design strategies. Firstly, a new fuzzy adaptive FE estimates actuator/sensor faults, and the system states simultaneously and also can automatically estimate and compensates bi-directional uncertainties between FE function and control system. Secondly, a fuzzy state feedback FTC controller is designed based on these estimations. Then the proposed separated FE/FTC design presented which is solved by linear matrix inequality via $H_infty$ optimization. Finally, a tutorial example of an inverted pendulum on a cart demonstrates the validity and effectiveness of the proposed design.

This paper presents a suitable solution procedure to solve the fully rough multi-objective multi-level linear fractional programming (FRMMFP) problem. First, an extension of interval method is presented to deal with roughness of the stated problem. Then, an iterative technique is proposed for linearization of fractional objectives. Finally, a modification of fuzzy approach is provided in the environment of the fully rough to solve the linear model. An example is provided for understanding the solution procedure of the proposed method.

This paper deals with the synchronization problem of bidirectional associative memory (BAM) Cohen-Grossberg fuzzy cellular neural networks (CGFCNNs) with discrete time-varying and unbounded distributed delays. Some sufficient conditions are obtained to guarantee the robust synchronizationof BAM CGFCNNs with discrete time-varying and unbounded distributed delays subjected to parametric uncertainty by using Lyapunov-Krasovskii (LK) functional and Linear matrix inequality (LMI) approach.Sufficient criteria ensure that the error dynamics of considered system is globally asymptotically stable. Finally, numerical examples with simulations are given to show the efficacy of the derived results.

This note is the continuation of the paper entitled ``Fuzzy universal algebras on $L$-sets"(IJFS, Volume 16, Number 4, (2019), pp. 175--187) and it focuses on $mathcal{Q}$-valued (universal) algebras on $mathcal{Q}$-typed sets. When $mathcal{Q}$ is an involutive quantaloid, some basic related notions in $mathcal{Q}$-valued algebra such as subalgebra, quotient algebra, homomorphism, congruence, direct product and variety etc are given and the properties of them are studied. When $mathcal{Q}$ is still a symmetric quantaloid, the $mathcal{Q}$-valued algebra is lifted to $mathcal{Q}$-valued power algebra, and the power isomorphism theorem is given.  As a special case of $mathcal{Q}$-valued algebra, the fuzzy universal algebra on $L$-set is presented naturally when $L$ is a commutative and divisible quantale.

The reliability of a warm standby series-parallel system without adequate samples is studied based on the uncertainty theory. It is assumed that the lifetimes of system elements follow independent uncertainty distributions with uncertain parameters. Three different switch models, including absolutely reliable mode, discrete mode and continuous mode, are developed for the warm standby series-parallel system. Besides, the cold standby series-parallel system is discussed as a special case. The reliability function and mean time to failure of each developed model are analyzed. A numerical example for the system with different switches is implemented to illustrate the application and efficiency of the proposed models.