scholarly journals Absolute Continuity of Fuzzy Measures and Convergence of Sequence of Measurable Functions

Mathematics ◽  
2020 ◽  
Vol 8 (5) ◽  
pp. 726
Author(s):  
Jun Li
Keyword(s):  
Absolute Continuity ◽  
General Framework ◽  
Type I ◽  
Convergence In Measure ◽  
Fuzzy Measures ◽  
Measurable Functions ◽  
Convergent Sequences

In this note, the convergence of the sum of two convergent sequences of measurable functions is studied by means of two types of absolute continuity of fuzzy measures, i.e., strong absolute continuity of Type I, and Type VI. The discussions of convergence a.e. and convergence in measure are done in the general framework relating to a pair of monotone measures, and general results are shown. The previous related results are generalized.

Lacunary ideal convergence in measure for sequences of fuzzy valued functions

2021 ◽  
Vol 40 (3) ◽  
pp. 5517-5526
Author(s):  
Ömer Kişi
Keyword(s):  
Measure Space ◽  
Finite Measure ◽  
Ideal Convergence ◽  
Convergence In Measure ◽  
Ideal Form ◽  
Measurable Functions ◽  
Finite Measure Space ◽  
Convergence Of Sequences

We investigate the concepts of pointwise and uniform I θ -convergence and type of convergence lying between mentioned convergence methods, that is, equi-ideally lacunary convergence of sequences of fuzzy valued functions and acquire several results. We give the lacunary ideal form of Egorov’s theorem for sequences of fuzzy valued measurable functions defined on a finite measure space ( X , M , μ ) . We also introduce the concept of I θ -convergence in measure for sequences of fuzzy valued functions and proved some significant results.

scholarly journals Lacunary Statistical Convergence in Measure for Double Sequences of Fuzzy Valued Functions

2021 ◽  
Vol 2021 ◽  
pp. 1-12
Author(s):  
Ömer Kişi
Keyword(s):  
Statistical Convergence ◽  
Double Sequence ◽  
Finite Measure ◽  
Measurable Space ◽  
Double Sequences ◽  
Convergence In Measure ◽  
Measurable Functions ◽  
Lacunary Statistical Convergence ◽  
Convergence Of Sequences ◽  
Sequences Of Fuzzy Numbers

Based on the concept of lacunary statistical convergence of sequences of fuzzy numbers, the lacunary statistical convergence, uniformly lacunary statistical convergence, and equi-lacunary statistical convergence of double sequences of fuzzy-valued functions are defined and investigated in this paper. The relationship among lacunary statistical convergence, uniformly lacunary statistical convergence, equi-lacunary statistical convergence of double sequences of fuzzy-valued functions, and their representations of sequences of α -level cuts are discussed. In addition, we obtain the lacunary statistical form of Egorov’s theorem for double sequences of fuzzy-valued measurable functions in a finite measurable space. Finally, the lacunary statistical convergence in measure for double sequences of fuzzy-valued measurable functions is examined, and it is proved that the inner and outer lacunary statistical convergence in measure are equivalent in a finite measure set for a double sequence of fuzzy-valued measurable functions.

scholarly journals ONE-LOOP RENORMALIZATION GROUP EQUATIONS OF THE GENERAL FRAMEWORK WITH TWO HIGGS DOUBLET

1999 ◽  
Vol 14 (05) ◽  
pp. 769-798 ◽  
Author(s):  
G. CVETIČ ◽  
S. S. HWANG ◽  
C. S. KIM
Keyword(s):  
Renormalization Group ◽  
Yukawa Coupling ◽  
General Framework ◽  
Vacuum Expectation ◽  
Finite Energy ◽  
Type I ◽  
Gauge Groups ◽  
Special Cases ◽  
Renormalization Group Equations ◽  
Coupling Parameters

Using a finite energy cutoff method, we derive one-loop renormalization group equations (RGE's) for Yukawa coupling parameters of quarks and for the vacuum expectation values of the Higgs doublets in the general framework of the Standard Model with two Higgs doublets (2HDM "type III"). In the model, the neutral-Higgs-mediated flavor-changing neutral currents are allowed but are assumed to be reasonably suppressed at low energies. The popular "type II" and "type I" models are just special cases of this framework. We then compare our RGE results with those of other authors who derived them for general (semi)simple gauge groups. We find out that our one-loop results disagree with those of Vaughn and Machacek, and agree with those of Jack and Osborn. We identify the mistakes of the former authors. We subsequently present a numerical example for the RGE flow of Yukawa coupling parameters and masses of quarks. The example shows a remarkable persistence of the suppression of the neutral-Higgs-mediated FCNC's as the energy of probes increases, in contrast to the usual expectations and reservations about this model.

Exhaustivity and absolute continuity of fuzzy measures

1998 ◽  
Vol 96 (2) ◽  
pp. 231-238 ◽  
Author(s):  
Qingshan Jiang ◽  
Hisakichi Suzuki ◽  
Zhenyuan Wang ◽  
George J. Klir
Keyword(s):  
Absolute Continuity ◽  
Fuzzy Measures

scholarly journals A Multi-Valued Choquet Integral with Respect to a Multisubmeasure

2015 ◽  
Vol 61 (1) ◽  
pp. 129-152 ◽  
Author(s):  
Floarea-Nicoleta Sofian-Boca
Keyword(s):  
Convex Sets ◽  
Choquet Integral ◽  
Order Relation ◽  
Convergence Theorems ◽  
Fuzzy Measures ◽  
Measurable Functions

Abstract Jang, Kim and Kwon introduced a multi-valued Choquet integral for multifunctions with respect to real fuzzy measures and Zhang, Guo and Liu established for this kind of integral some convergence theorems. The aim of this paper is to present another type of set-valued Choquet integral, called by us the Aumann-Choquet integral, for non-negative measurable functions with respect to multisubmeasures taking values in the class of all non-empty,compact and convex sets of ℝ+ on which we use the order relation considered by Guo and Zhang. For this kind of integral, we study some important properties and we prove that if we add some supplementary properties to the multisubmeasure then they are also preserved by the set-valued function defined as Aumann-Choquet integral.

p-convergence in measure of a sequence of measurable functions and corresponding minimal elements of c0

Positivity ◽  
2008 ◽  
Vol 13 (1) ◽  
pp. 243-253 ◽  
Author(s):  
Nikolaos Papanastassiou ◽  
Christos Papachristodoulos
Keyword(s):  
Minimal Elements ◽  
Convergence In Measure ◽  
Measurable Functions

scholarly journals Fuzzy Measures Defined by Fuzzy Integral and their Absolute Continuity

1996 ◽  
Vol 203 (1) ◽  
pp. 150-165 ◽  
Author(s):  
Zhenyuan Wang ◽  
George J. Klir ◽  
Wei Wang
Keyword(s):  
Absolute Continuity ◽  
Fuzzy Integral ◽  
Fuzzy Measures

scholarly journals Spaces of measurable functions

2013 ◽  
Vol 11 (7) ◽  
Author(s):  
Piotr Niemiec
Keyword(s):  
Hilbert Space ◽  
Measure Space ◽  
Finite Measure ◽  
Metrizable Space ◽  
Equivalence Classes ◽  
Convergence In Measure ◽  
Measurable Functions ◽  
Almost Everywhere ◽  
Finite Measure Space ◽  
Completely Metrizable

AbstractFor a metrizable space X and a finite measure space (Ω, $\mathfrak{M}$, µ), the space M µ(X) of all equivalence classes (under the relation of equality almost everywhere mod µ) of $\mathfrak{M}$-measurable functions from Ω to X, whose images are separable, equipped with the topology of convergence in measure, and some of its subspaces are studied. In particular, it is shown that M µ(X) is homeomorphic to a Hilbert space provided µ is (nonzero) nonatomic and X is completely metrizable and has more than one point.

scholarly journals Quantifying the effects of anagenetic and cladogenetic evolution

2014 ◽  
Author(s):  
Krzysztof Bartoszek
Keyword(s):  
Generating Functions ◽  
Evolutionary Biology ◽  
General Framework ◽  
Common Ancestor ◽  
Recent Common Ancestor ◽  
Phenotypic Change ◽  
Type I ◽  
Ongoing Debate ◽  
Most Recent Common Ancestor ◽  
Types Of Change

An ongoing debate in evolutionary biology is whether phenotypic change occurs predominantly around the time of speciation or whether it instead accumulates gradually over time. In this work I propose a general framework incorporating both types of change, quantify the effects of speciational change via the correlation between species and attribute the proportion of change to each type. I discuss results of parameter estimation of Hominoid body size in this light. I derive mathematical formulae related to this problem, the probability generating functions of the number of speciation events along a randomly drawn lineage and from the most recent common ancestor of two randomly chosen tip species for a conditioned Yule tree. Additionally I obtain in closed form the variance of the distance from the root to the most recent common ancestor of two randomly chosen tip species.

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