On decompositions of continuity via idealization

We have introduced α-I-open, semi-I-open and β-I-open sets via idealization and using these sets obtained new decompositions of continuity. This revised version was published online in June 2006 with corrections to the Cover Date.     

On decompositions of continuity and some weaker forms of continuity via idealization

Summary We give decompositions of continuity and some weaker forms of continuity via idealization using the concepts of <InlineEquation ID=IE"1"><EquationSource Format="TEX"><![CDATA[<InlineEquation ID=IE"2"><EquationSource Format="TEX"><![CDATA[<InlineEquation ID=IE"3"><EquationSource Format="TEX"><![CDATA[<InlineEquation ID=IE"4"><EquationSource Format="TEX"><![CDATA[<InlineEquation ID=IE"5"><EquationSource Format="TEX"><![CDATA[<InlineEquation ID=IE"6"><EquationSource Format="TEX"><![CDATA[<InlineEquation ID=IE"7"><EquationSource Format="TEX"><![CDATA[<InlineEquation ID=IE"8"><EquationSource Format="TEX"><![CDATA[$]]></EquationSource></InlineEquation>]]></EquationSource></InlineEquation>]]></EquationSource></InlineEquation>]]></EquationSource></InlineEquation>]]></EquationSource></InlineEquation>]]></EquationSource></InlineEquation>]]></EquationSource></InlineEquation>]]></EquationSource></InlineEquation>\mathcal{A_{I}}$-sets, $\alpha \mathcal{A_{I}}$-sets, $B_{1I}$-sets, $B_{2I}$-sets, $B_{3I}$-sets, $\alpha C_{I}$-sets and $WLC_{I}$-sets.     

Some new sets and decompositions of A I-R-continuity, α-I-continuity, continuity via idealization

The concepts of I-R closed set, A _I-R-set, α _I M ₁-set, α _I M ₂-set, α _I N ₁-set, α _I N ₂-set, α _I N ₃-set, α _I N ₄-set and α _I N ₅-set are introduced via idealization. New decompositions of some weaker forms of continuity are obtained by using these sets.     

Construction of quotient BCI(BCK)-algebra via a fuzzy ideal

The present paper gives a new construction of a quotient BCI(BCK)-algebraX/μ by a fuzzy ideal μ inX and establishes the Fuzzy Homomorphism Fundamental Theorem. We show that if μ is a fuzzy ideal (closed fuzzy ideal) ofX, thenX/μ is a commutative (resp. positive implicative, implicative) BCK (BCI)-algebra if and only if μ is a fuzzy commutative (resp positive implicative, implicative) ideal ofX. Moreover we prove that a fuzzy ideal of a BCI-algebra is closed if and only if it is a fuzzy subalgebra ofX. We show that if the period of every element in a BCI-algebraX is finite, then any fuzzy ideal ofX is closed. Especially, in a well (resp, finite, associative, quasi-associative, simple) BCI-algebra, any fuzzy ideal must be closed.     

A decomposition of continuity in ideal topological spaces

We introduce the notions of w-I-continuous and w*-I-continuous functions in ideal topological spaces and investigate some of their properties. Additionally, we obtain a decomposition of continuous functions.     

Comparing and ranking fuzzy numbers using ideal solutions

This paper presents a new approach for comparing and ranking fuzzy numbers in a simple manner in decision making under uncertainty. The concept of ideal solutions is sensibly used, and a distance-based similarity measure between fuzzy numbers is appropriately adopted for effectively determining the overall performance of each fuzzy number in comparing and ranking fuzzy numbers. As a result, all the available information characterizing a fuzzy number is fully utilized, and both the absolute position and the relative position of fuzzy numbers are adequately considered, resulted in consistent rankings being produced in comparing and ranking fuzzy numbers. The approach is computationally simple and its underlying concepts are logically sound and comprehensible. A comparative study is conducted on the benchmark cases in the literature that shows the proposed approach compares favorably with other approaches examined.     

Ranking fuzzy numbers based on ideal solution

In this paper, we consider the factor of the decision maker’s risk preference, and define the left and right deviation degree respectively. Besides, we propose a new formula of the fuzzy degree. Then we get the multiattribute matrix of fuzzy numbers. We rank fuzzy numbers with the help of an ideal solution. Some numerical examples are displayed to illustrate the validity and advantages of the proposed ranking method.     

A decomposition of continuity via ideals

A new class of sets in ideal topological spaces is introduced and using these sets, a decomposition of continuity is given.      

A class of strong forms of fuzzy complete continuity

The aim of this paper is devoted to make use of operations on I^X of a fuzzy topological space X to unify and generalize classes of strong forms of fuzzy complete continuity. Furthermore, we add more types of strong forms of fuzzy completely continuous functions by choosing special operations. A comparison between these types of functions is of interest. Preservations of some fuzzy aspects under these functions are studied.     

Growth properties of Fourier transforms via moduli of continuity

We obtain new inequalities for the Fourier transform, both on Euclidean space, and on non-compact, rank one symmetric spaces. In both cases these are expressed as a gauge on the size of the transform in terms of a suitable integral modulus of continuity of the function. In all settings, the results present a natural corollary: a quantitative form of the Riemann-Lebesgue lemma. A prototype is given in one-dimensional Fourier analysis.     

On the restudy of fuzzy complex analysis: Part II. The continuity and differentiation of fuzzy complex functions

We consider functions mapping complex numbers into fuzzy complex numbers or mapping fuzzy complex numbers into complex numbers. We study the continuity and differentiation of such functions.     

Approximating the ideal free distribution via reaction-diffusion-advection equations

We consider reaction-diffusion-advection models for spatially distributed populations that have a tendency to disperse up the gradient of fitness, where fitness is defined as a logistic local population growth rate. We show that in temporally constant but spatially varying environments such populations have equilibrium distributions that can approximate those that would be predicted by a version of the ideal free distribution incorporating population dynamics. The modeling approach shows that a dispersal mechanism based on local information about the environment and population density can approximate the ideal free distribution. The analysis suggests that such a dispersal mechanism may sometimes be advantageous because it allows populations to approximately track resource availability. The models are quasilinear parabolic equations with nonlinear boundary conditions.     

Ophthalmological prognosis via fuzzy subsets

This paper examines the possibility of handling treatment effects as a fuzzy relational problem with particular reference to ophthalmology. An ophthalmological evaluation is considered to consist of two major stages. Firstly, an explanation of a patient's eye-health state in terms of known disease labels is formulated through diagnosis. Secondly, the effectiveness of a therapeutic strategy designed to restore a patient's normal eye-health, is then predicted via prognosis. The paper considers the latter aspect in the sense of assessing the effects of medical intervention by comparing pre- and post-therapeutic fuzzy subsets.     

Cardinality of fuzzy sets via bags

We discuss the concept of a bag. We then investigate the use of these structures for the representation of cardinality of a fuzzy set.