General Fritz Carlson's type inequality for Sugeno integrals.
Graded sets, points and numbers.
The basic tool considered in this paper is the so-called graded set, defined on the analogy of the family of α-cuts of a fuzzy set. It is also considered the corresponding extensions of the concepts of a point and of a real number (again on the analogy of the fuzzy case). These new graded concepts avoid the disadvantages pointed out by Gerla (for the fuzzy points) and by Kaleva and Seikkala (for the convergence of sequences of fuzzy numbers).
Investigation of a Stolarsky type Inequality for Integrals in Pseudo-Analysis
MSC 2010: 03E72, 26E50, 28E10In this paper, we prove a Stolarsky type inequality for pseudo-integrals.
Metrics on vector spaces with -localisation.
Multiplication, distributivity and fuzzy-integral. I
The main purpose is the introduction of an integral which covers most of the recent integrals which use fuzzy measures instead of measures. Before we give our framework for a fuzzy integral we motivate and present in a first part structure- and representation theorems for generalized additions and generalized multiplications which are connected by a strong and a weak distributivity law, respectively.
Multiplication of fuzzy quantities
On a new class of distances between fuzzy numbers.
In the course of the studies on fuzzy regression analysis, we encountered the problem of introducing a distance between fuzzy numbers, which replaces the classical (x - y)2 on the real line. Our proposal is to compute such a function as a suitable weighted mean of the distances between the α-cuts of the fuzzy numbers. The main difficulty is concerned with the definition of the distance between intervals, since the current definitions present some disadvantages which are undesirable in our context....
On an exponential-type fuzzy difference equation.
On Aumann's theorem that the circle does not admit a mean
On granular derivatives and the solution of a granular initial value problem
Perceptions about function changes are represented by rules like “If X is SMALL then Y is QUICKLY INCREASING.” The consequent part of a rule describes a granule of directions of the function change when X is increasing on the fuzzy interval given in the antecedent part of the rule. Each rule defines a granular differential and a rule base defines a granular derivative. A reconstruction of a fuzzy function given by the granular derivative and the initial value given by the rule is similar to Euler’s...
On models of long-term behavior of concrete
Long-term behavior of concrete is modeled by several widely accepted models, such as B3, fib MC 2010, or ACI 209 whose input parameters and output values are not identical to each other. Moreover, the input and, consequently, the output values are uncertain. In this paper, fuzzy input parameters are considered in uncertainty quantification of each model response and, finally, the sets of responses are analyzed by elementary tools of evidence theory. That is, belief and plausibility functions are...
On some isometric spaces of and .
On the existence of a fuzzy integral equation of Urysohn-Volterra type
We present an existence theorem for integral equations of Urysohn-Volterra type involving fuzzy set valued mappings. A fixed point theorem due to Schauder is the main tool in our analysis.
On the Minkowski-Hölder type inequalities for generalized Sugeno integrals with an application
In this paper, we use a new method to obtain the necessary and sufficient condition guaranteeing the validity of the Minkowski-Hölder type inequality for the generalized upper Sugeno integral in the case of functions belonging to a wider class than the comonotone functions. As a by-product, we show that the Minkowski type inequality for seminormed fuzzy integral presented by Daraby and Ghadimi [11] is not true. Next, we study the Minkowski-Hölder inequality for the lower Sugeno integral and the...
Peano type theorem for random fuzzy initial value problem
In this paper we consider the random fuzzy differential equations and show their application by an example. Under suitable conditions the Peano type theorem on existence of solutions is proved. For our purposes, a notion of ε-solution is exploited.
Periodic oscillation of fuzzy Cohen-Grossberg neural networks with distributed delay and variable coefficients.
Pseudo-operations on finite intervals.
Some spaces of double difference sequences of fuzzy numbers
Sum and product of the modified real fuzzy numbers
Symmetry vs. asymmetry.