The resolution of many real-word problems needs calculations and many calculations pass by basic arithmetical operations. This paper shows that in fuzzy mathematics, L-R fuzzy arithmetic, rarely used in the resolution of such problems, plays an important role if it is widened to secant approximations. By the help of a numerical example, the study shows that this arithmetic conducts to the same results than those obtained by the most used and well known alpha-cut and interval arithmetic.
In this study, we examine fuzzy differential equations by using a new and dynamic approach. A novel scheme based on logarithmic mean is discussed in detail and comparison with harmonic mean is also performed with error analysis. Obtained solutions reveal that one gets very accurate and effective results by applying this scheme to solve the fuzzy differential equations.
In this paper, the concept of generalized differentiability and level-wise generalized Hukuhara differentiability are extended for one-dimensional fuzzy-valued convex functions from $${\mathbb{R}}$$ into $$E$$ . In addition, the properties of generalized differentiability and characterization for fuzzy-valued convex functions in terms of generalized differentiability and the fundamental theorem of calculus generalized differential and fuzzy integral are presented in detail. Moreover, the concepts of generalized subgradient and generalized subdifferential in terms of level-wise generalized Hukuhara differentiability are extended for fuzzy-valued convex functions. Finally, by using their properties, the convex fuzzy optimization for the one-dimensional fuzzy-valued convex functions is discussed.
Fuzzy matrices play an important role to model several uncertain systems. In this paper, we define two norms namely ‘sup norm’ and ‘operator norm’ of L-R Hexagonal fuzzy matrix (L-R HFM). We also relate the norm of L-R HFM in the distance d(?̂?LR , ?̂?LR). An analytical concept of power series and invertibility under the norm of L-R HFM have been studied. Some of the relevant properties, theorems based on the norms are investigated.
This paper deals with uncertain parabolic fluid flow problem where the uncertainty occurs due to the initial conditions and parameters involved in the system. Uncertain values are considered as fuzzy and these are handled through a recently developed method. Here the concepts of fuzzy numbers are combined with Finite Difference Method (FDM) and then Fuzzy Finite Difference Method (FFDM) has been proposed. The proposed FFDM has been used to solve the fluid flow problem bounded by two parallel plates. Finally sensitivity of the fuzzy parameters has also been analysed.
In this work, we consider the development of a fuzzy neural network based on probability function for Estimated output of fuzzy regression models with test real input and fuzzy output. The proposed approach is a fuzzification of the outputs and weights of conventional fuzzy neural network based on probability function. The error of the proposed method is based on total square error is minimized by optimization method in order to be able to obtain the optimal weights of the neural network. The advantage of the proposed approach is its simplicity and computation as well as its performance. To compare the performance of the proposed method with the other traditional methods given in the literature several numerical examples are presented.
A revised definition for fuzzy bags is reviewed, developing the concept of bags given by Delgado et al. 2009 from which each bag has two parts, function and summary information. Then, the definitions of fuzzy bag expected value, bag entropy and bag similarity are introduced. By some examples, the new concepts are illustrated.
The purpose of present work is to study some algebraic aspect of fuzzy multiset regular languages. In between, we show the equivalence of multiset regular language and fuzzy multiset regular language. Finally, we introduce the concept of pumping lemma for fuzzy multiset regular languages, which we use to establish a necessary and sufficient condition for a fuzzy multiset language to be non-constant.
In a recent paper, Thomas and Nair have introduced the notions of intuitionistic fuzzy ideal and intuitionistic fuzzy filter on a lattice and some basic properties were proved. In this paper, we characterize these notions in terms of the lattice operations and in terms of their associated crisp sets. We introduce the notions of prime intuitionistic fuzzy ideal and filter as interesting kinds, and then we investigate their various characterizations and different properties.
In processing indecisive or unclear information, the advantages of fuzzy logic and neurocomputing disciplines should be taken into account and combined by fuzzy neural networks. The current research intends to present a fuzzy modeling method using multi-layer fuzzy neural networks for solving a fully fuzzy polynomials system. To clarify the point, it is necessary to inform that a supervised gradient descent-based learning law is employed. The feasibility of the method is examined using computer simulations on a numerical example. The experimental results obtained from the investigation of the proposed method are valid and delivers very good approximation results.
Our purpose is to propose the solution of two person zero-sum continuous differential games in the fuzzy rough environment. This paper uses fuzzy rough sets to measure the dual and multiple uncertainties with high ambiguity and vagueness in continuous differential games. The combination of fuzzy and rough set in continuous differential games represents a new class defined as fuzzy rough continuous differential games. Two person zero-sum fuzzy rough continuous differential games sufficient and necessary conditions are achieved and numerical example is carried out to support the theoretical claims.
In this paper, fuzzy subgroups on direct product of groups over a $t$-norm has been discussed. By using a t-norm T, we characterize some basic properties of $T$-fuzzy direct product of groups and normal $T$-fuzzy direct product of groups. Also we define the concept normal subgroups between $T$-fuzzy direct product of groups and prove some basic properties.
The aim of this work, is to evaluate the value of a fuzzy integral by applying the Newton-Cotes integration rules via a reliable scheme. In order to perform the numerical examples, the CADNA (Control of Accuracy and Debugging for Numerical Applications) library and the CESTAC (Controle et Estimation Stochastique des Arrondis de Calculs) method are applied based on the stochastic arithmetic. By using this method, the optimal number of points in the fuzzy numerical integration rules and the optimal approximate solution are obtained. Also, the accuracy of the fuzzy quadrature rules are discussed. An algorithm is given to illustrate the implementation of the method. In this case, the termination criterion is considered as the Hausdorff distance between two sequential results to be an informatical zero. Two sample fuzzy integrals are evaluated based on the proposed algorithm to show the importance and advantage of using the stochastic arithmetic in place of the floating-point arithmetic.
