Iranian Journal of Fuzzy Systems
https://ijfs.usb.ac.ir/
Iranian Journal of Fuzzy Systemsendaily1Thu, 01 Apr 2021 00:00:00 +0430Thu, 01 Apr 2021 00:00:00 +0430cover vol.18-no.2-April 2021
https://ijfs.usb.ac.ir/article_5910.html
On the existence of solutions to interval-valued differential equations with length constraints
https://ijfs.usb.ac.ir/article_5909.html
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.FGM generated archimedean copulas with concave multiplicative generators
https://ijfs.usb.ac.ir/article_5911.html
The Farlie-Gumble-Morgenstren (FGM) family&nbsp; and&nbsp; archimedean family are the most popular parametric families of copulas.&nbsp; 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.On Goursat problem for fuzzy random partial differential equations under generalized Lipschitz conditions
https://ijfs.usb.ac.ir/article_5912.html
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.Parameter estimation in fuzzy partial univariate linear regression model with non-fuzzy inputs and triangular fuzzy outputs
https://ijfs.usb.ac.ir/article_5913.html
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&nbsp; 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&nbsp; 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.Global dissipativity of fuzzy bidirectional associative memory neural networks with proportional delays
https://ijfs.usb.ac.ir/article_5914.html
This article aimed to investigate the problem of global dissipativity of Fuzzy Bidirectional Associative Memory&nbsp; 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.A novel method for ranking generalized fuzzy numbers with two different heights and its application in fuzzy risk analysis
https://ijfs.usb.ac.ir/article_5915.html
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.A novel interval-valued fuzzy multiple twin support vector machine
https://ijfs.usb.ac.ir/article_5916.html
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.Semi-t-operators and idempotent semi-t-operators on bounded lattices
https://ijfs.usb.ac.ir/article_5918.html
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.A new separated fault estimator and fault-tolerant control design strategy for uncertain nonlinear systems using T-S fuzzy modeling
https://ijfs.usb.ac.ir/article_5919.html
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.Building fuzzy approach with linearization technique for fully rough multi-objective multi-level linear fractional programming problem
https://ijfs.usb.ac.ir/article_5920.html
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.Synchronization of BAM Cohen--Grossberg FCNNs with mixed time delays
https://ijfs.usb.ac.ir/article_5921.html
This paper deals with the synchronization problem of bidirectional associative memory (BAM)&nbsp;Cohen-Grossberg fuzzy cellular neural networks (CGFCNNs) with discrete time-varying and unbounded&nbsp;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&nbsp;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&nbsp;stable. Finally, numerical examples with simulations are given to show the&nbsp;efficacy of the derived results.Note on " Fuzzy universal algebras on L-sets"
https://ijfs.usb.ac.ir/article_5922.html
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.&nbsp; 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.Reliability analysis of a warm standby series-parallel system with different switches and bi-uncertain lifetimes
https://ijfs.usb.ac.ir/article_5923.html
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.Persian-translation vol.18-no.2-April 2021
https://ijfs.usb.ac.ir/article_5924.html
(1908-5384) 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_5657.html
Always the decision of the government to the private sector 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.&nbsp;In this paper, our motivation is to propose the system to decide on how to develop applied academic educations at the Applied ScienceEducation Centers (ASEC's) which supervised by the University of Applied Science and Technology (UAST) in Iran. The method used is theFuzzy Inference System (FIS) to obtain 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 with4 inputs and 242 rules. The latter, related to the qualitative development of higher applied education, including the assessment of the capabilityand 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 determinedand used by experts in this domain.&nbsp;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.(2009-6152) 2-set-based extended functions
https://ijfs.usb.ac.ir/article_5816.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.(2004-5800) Fuzzy logic and enriched categories
https://ijfs.usb.ac.ir/article_5817.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.(1909-5443) A credibility approach on fuzzy slacks based measure (SBM) DEA model
https://ijfs.usb.ac.ir/article_5835.html
Data Envelopment Analysis (DEA) is a multi-criteria technique based on linear programming to deal with many real-life&nbsp;problems, mostly in nonprofit organizations. The slacks-based measure (SBM) model is one of the DEA model used to&nbsp;assess the relative efficiencies of decision-making units (DMUs). The SBM DEA model directly used input slacks and&nbsp;output slacks to determine the relative efficiency of DMUs. In order to deal with qualitative or uncertain data, a fuzzySBM DEA model is used to assess the performance of DMUs in this study. The credibility measure approach, transform&nbsp;the fuzzy SBM DEA model into a crisp linear programming model at different credibility levels is used. The resultscame from the fuzzy DEA model are more rational to the real-world situation than the conventional DEA model. In&nbsp;the end, the data of Indian oil refineries is collected, and the efficiency behavior of the companies obtained by applyingthe proposed model for its numerical illustration.(2001-5666) C-continuous fuzzy posets
https://ijfs.usb.ac.ir/article_5836.html
In this paper, we develop the C-continuity via Scott Q-cotopological spaces, where Q is a commutative and integral&nbsp;quantale. The main results are: (1) The set of all C-compact elements of a complete Q-ordered set is irreduciblecomplete; (2) The Scott Q-cotopology of a Q-ordered set under the fuzzy inclusion order is C-continuous, even C-prealgebraic; (3) We establish an adjunction between the category of irreducible complete Q-ordered sets and thecategory of C-prealgebraic complete Q-ordered sets.(2006-5969) Construction methods for triangular norms and triangular conorms on appropriate bounded lattices
https://ijfs.usb.ac.ir/article_5856.html
In this study, new methods to construct triangular norms and triangular conorms on appropriate bounded lattices are&nbsp;introduced. Some illustrative examples are given for clarity. Also, the relation between introduced methods and someother approaches is investigated. Finally, it is shown that the introduced construction methods can be generalized by&nbsp;induction to a modified ordinal sum for triangular norms and triangular conorms on appropriate bounded lattices. Andsome illustrative examples are given.(1912-5608) Jensen's inequalities for pseudo-integrals
https://ijfs.usb.ac.ir/article_5893.html
In this paper, we introduce a general&nbsp;$(\oplus,\otimes)$-convex function based on semirings $([a,b],&nbsp;\oplus, \otimes)$ 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 $([a,b], \sup, \otimes)$&nbsp;with respect to nondecreasing functions and present corresponding&nbsp;results for generalized fuzzy integrals.(2004-5828) On the fuzzy solutions of time-fractional problems
https://ijfs.usb.ac.ir/article_5935.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.