This article discusses the fuzzy modeling and situational analysis of technological safety of industrial complexes and decision-making for their management in the face of uncertainty and vagueness of the initial information on the basis of the theory of fuzzy sets and fuzzy logic. A formal model for description of fuzzy situations in the form of fuzzy sets and rational decision-making in a vari...

This paper addresses the design of a fuzzy control system with a fuzzy controller and a fuzzy estimator for a fossil fuelled drum boiler-turbine-generator unit on the basis of a dynamic fuzzy model that was developed in our recently published paper. In the design procedure, a dynamics augmentation is introduced and a dynamic fuzzy augmented system is then determined for the nonlinear boiler-tur...

The paper sets forth in detail categorically-algebraic or catalg foundations for the operations of taking the image and preimage of (fuzzy) sets called forward and backward powerset operators. Motivated by an open question of S. E. Rodabaugh, we construct a monad on the category of sets, the algebras of which generate the fixed-basis forward powerset operator of L. A. Zadeh. On the next step, w...

The purpose of this paper is to introduce the concept of L-fuzzybilinear operators. We obtain a decomposition theorem for L-fuzzy bilinearoperators and then prove that a L-fuzzy bilinear operator is the same as apowerset operator for the variable-basis introduced by S.E.Rodabaugh (1991).Finally we discuss the continuity of L-fuzzy bilinear operators.

Using a system of axioms among with a modified definition of boundary on the basis of the intuitionistic fuzzy sets, we formulate an inductive structure for the dimension of fuzzy spaces which has been defined by Coker. This new definition of boundary allows to characterize an intuitionistic fuzzy clopen set as a set with zero boundary. Also, some critical properties and applications are establ...

In this paper, a new definition of bounded fuzzy linear orderhomomorphism on $I$-topological vector spaces is introduced. Thisdefinition differs from the definition of Fang [The continuity offuzzy linear order-homomorphism. J. Fuzzy Math. {bf5}textbf{(4)}(1997), 829--838]. We show that the ``boundedness"and `` boundedness on each layer" of fuzzy linear orderhomomorphisms do not imply each other...

In this paper, we propose the spectral collocation method based on radial basis functions to solve the fractional Bagley-Torvik equation under uncertainty, in the fuzzy Caputo's H-differentiability sense with order ($1< nu < 2$). We define the fuzzy Caputo's H-differentiability sense with order $nu$ ($1< nu < 2$), and employ the collocation RBF method for upper and lower approximate solutions. ...

We present a topological characterization for fuzzy regular languages: we show that there is a bijective correspondence between fuzzy regular languages and the set of all clopen fuzzy subsets with finite image in the induced fuzzy topological space of Stone space (Profinite space), and then we give a representation of closed fuzzy subsets in the induced fuzzy topological space via fuzzy regular...

Ultraprecision turning is a manufacturing process used to generate a high surface roughness in precision components, and its input-output relationships are highly nonlinear. Surface roughness of a turned surface depends on the selection of cutting variables, such as cutting speed, feed and depth of cut. Realizing the fact that fuzzy logic controller (FLC) is a powerful tool for dealing with imp...

Abstract We present a new type of fuzzy controller constructed with the B spline model and its applications in modelling and control Un like the other normalised parameterised set functions for de ning fuzzy sets B spline basis functions do not necessarily span from membership value to but possess the property partition of unity These B spline basis functions are automatically determined after ...