Related papers: Fuzzification of Fractal Calculus
The theory of fractional calculus has developed in a number of directions over the years, including: the formulation of multiple different definitions of fractional differintegration; the extension of various properties of standard calculus…
In the context of fuzzy logic, ordinal sums provide a method for constructing new functions from existing functions, which can be triangular norms, triangular conorms, fuzzy negations, copulas, overlaps, uninorms, fuzzy implications, among…
This paper introduced a way of fractal to solve the problem of taking count of the integer partitions, furthermore, using the method in this paper some recurrence equations concerning the integer partitions can be deduced, including the…
We set the main concepts for multiplicative fractional calculus. We define Caputo, Riemann and Letnikov multiplicative fractional derivatives and multiplicative fractional integrals and study some of their properties. Finally, the…
Since categories are graphs with additional "structure", one should start from fuzzy graphs in order to define a theory of fuzzy categories. Thus is makes sense to introduce categories whose morphisms are associated with a plausibility…
Complex systems (CS) are ubiquitous in nature. It is argued that fractional order (FO) calculus is more suitable to describe fractal systems. Motivated by the fractal space time theory some fractional generalizations of Scrodinger and…
We re-examine a practical aspect of combinatorial fuzzy problems of various types, including search, counting, optimization, and decision problems. We are focused only on those fuzzy problems that take series of fuzzy input objects and…
Systems of fuzzy relation equations and inequalities in which an unknown fuzzy relation is on the one side of the equation or inequality are linear systems. They are the most studied ones, and a vast literature on linear systems focuses on…
The aim of this work is to introduce the main concepts of Fractional Calculus, followed by one of its application to classical electrodynamics, illustrating how non-locality can be interpreted naturally in a fractional scenario. In…
Fracterms are introduced as a proxy for fractions. A precise definition of fracterms is formulated and on that basis reasonably precise definitions of various classes of fracterms are given. In the context of the meadow of rational numbers…
A new fuzzy optimization framework that extends FCM causality is proposed. This model utilizes the dynamics to map data into metrics and create a framework that examines logical implication and hierarchy of concepts using a multiplex.…
Fuzzy sets are the cornerstone of a non-additive uncertainty theory, namely possibility theory, and of a versatile tool for both linguistic and numerical modeling. Numerous works now combine fuzzy concepts with other scientific disciplines…
The measure of distance between two fuzzy sets is a fundamental tool within fuzzy set theory, however, distance measures currently within the literature use a crisp value to represent the distance between fuzzy sets. A real valued distance…
This study reexamines diffusive representations for fractional integrals with the goal of pioneering new variants of such representations. These variants aim to offer highly efficient numerical algorithms for the approximate computation of…
A complex fuzzy Lie algebra is a fuzzy Lie algebra whose membership function takes values in the unit circle in the complex plane. In this paper, we deine the complex fuzzy Lie subalgebras and complex fuzzy ideals of Lie algebras. Then, we…
Interval calculus is a relatively new branch of mathematics. Initially understood as a set of tools to assess the quality of numerical calculations (rigorous control of rounding errors), it became a discipline in its own rights today.…
Fractals such as the Cantor set can be equipped with intrinsic arithmetic operations (addition, subtraction, multiplication, division) that map the fractal into itself. The arithmetics allows one to define calculus and algebra intrinsic to…
A fractional Hamiltonian formalism is introduced for the recent combined fractional calculus of variations. The Hamilton-Jacobi partial differential equation is generalized to be applicable for systems containing combined Caputo fractional…
Fractional analysis is applied to describe classical dynamical systems. Fractional derivative can be defined as a fractional power of derivative. The infinitesimal generators {H, .} and L=G(q,p) \partial_q+F(q,p) \partial_p, which are used…
A few of the algebraic and topological properties of int. fuzzy continuity and int. fuzzy uniform continuity are investigated. Also, the concept of int. fuzzy uniform convergence is introduced thereafter a few result on int. fuzzy uniform…