An adaptive neuro fuzzy inference system based on interval Gaussian type-2 fuzzy sets in the antecedent part and Gaussian type-1 fuzzy sets as coefficients of linear combination of input variables in the consequent part is presented in this paper. The capability of the proposed method (we named ANFIS2) for function approximation and dynamical system identification is remarkable. The structure o...

The theoretical background for abstract formalization of the vague phenomenon of complex systems is the fuzzy set theory. In the paper, vague data is defined as specialized fuzzy sets fuzzy numbers and a fuzzy linear regression model is described as a fuzzy function with fuzzy numbers as vague regression parameters. To identify the fuzzy coefficients of the model, the genetic algorithm is used....

Fuzzy random variables possess several interpretations. Historically, they were proposed either as a tool for handling linguistic label information in statistics or to represent uncertainty about classical random variables. Accordingly, there are two different approaches to the definition of the variance of a fuzzy random variable. In the first one, the variance of the fuzzy random variable is ...

Firstly, in this paper, we apply the Fuzzy Restricted Variation Method to achieve an analytical and approximate unsymmetrical fuzzy solution for Fully Fuzzy Quadratic Equation. In this application, after finding the real root of 1-cut of $tilde{A}tilde{X}^{2}+tilde{B}tilde{X}+tilde{C}=tilde{D}$, initial guess is always chosen with possible unknown parameters that leads to highly accurate soluti...

The information systems with incomplete attribute values and fuzzy decisions commonly exist in practical problems. On the base of the notion of variable precision rough set model for incomplete information system and the rough set model for incomplete and fuzzy decision information system, the variable rough set model for incomplete and fuzzy decision information system is constructed, which is...

To address the hesitancy, inconsistency and uncertainty of decision makers’ cognitions, linguistic interval hesitant fuzzy sets (LIHFSs) are efficient tools. This paper focuses on studying the application of LIHFSs. To do this, two correlation coefficients of LIHFSs are defined, which needn't consider the length of elements in LIHFSs or the arrangement of their possible interval values. To addr...

According to the current literature, there are two different approaches to the definition of the variance of a fuzzy random variable. In the first one, the variance is defined as a fuzzy interval, offering a gradual description of our incomplete knowledge about the variance of an underlying, imprecisely observed, classical random variable. In the second case, the variance of the fuzzy random va...