scholarly journals A characterization theorem for levelwise statistical convergence

Filomat ◽  
2011 ◽  
Vol 25 (1) ◽  
pp. 133-143 ◽  
Author(s):  
Salih Aytar
Keyword(s):  
Cauchy Sequence ◽  
Statistical Convergence ◽  
Fuzzy Numbers ◽  
Characterization Theorem ◽  
Bounded Sequence ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Statistical Cluster ◽  
Necessary And Sufficient ◽  
Cluster Points

In the present paper, we prove a characterization theorem which gives a necessary and sufficient condition for a sequence of fuzzy numbers to be levelwise statistically convergent in the space of fuzzy numbers. As an application of this theorem we utilize the idea of statistical equi-continuity in order to obtain a condition which guarantees the set of levelwise statistical cluster points of a statistically bounded sequence to be nonempty and a levelwise statistically Cauchy sequence to be levelwise statistically convergent.

New Classes of Statistically Pre-Cauchy Triple Sequences of Fuzzy Numbers Defined by Orlicz Function

2018 ◽  
Vol 85 (3-4) ◽  
pp. 411
Author(s):  
Sangita Saha ◽  
Santanu Roy
Keyword(s):  
Cauchy Sequence ◽  
Fuzzy Numbers ◽  
Orlicz Function ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Real Numbers ◽  
Fuzzy Real Numbers ◽  
Sequences Of Fuzzy Numbers ◽  
Necessary And Sufficient

In this article, the concept of statistically pre-Cauchy sequence of fuzzy real numbers having multiplicity greater than two defined by Orlicz function is introduced. A characterization of the class of bounded statistically pre-Cauchy triple sequences of fuzzy numbers with the help of Orlicz function is presented. Then a necessary and suffcient condition for a bounded triple sequence of fuzzy real numbers to be statistically pre-Cauchy is proved. Also a necessary and sufficient condition for a bounded triple sequence of fuzzy real numbers to be statistically convergent is derived. Further, a characterization of the class of bounded statistically convergent triple sequences of fuzzy numbers is presented and linked with Cesaro summability.

scholarly journals Convexity Invariance of Fuzzy Sets under the Extension Principles

2012 ◽  
Vol 2012 ◽  
pp. 1-13 ◽  
Author(s):  
Dong Qiu ◽  
Weiquan Zhang
Keyword(s):  
Fuzzy Sets ◽  
Fuzzy Numbers ◽  
Sufficient Conditions ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Arithmetic Operations ◽  
Extension Principles ◽  
Necessary And Sufficient

We discuss the convexity invariance of fuzzy sets under the extension principles. Particularly, we give a necessary and sufficient condition for a mapping to be an inverse *-convex transformation, and also obtain some sufficient conditions for a mapping to be an *-convex transformation. Two applications are given to illustrate the obtained results. Finally, we give some applications of the main results to the hyperstructure convexity invariance of type 2 fuzzy sets under hyperalgebra operations, and to the convexity invariance of fuzzy numbers under basic arithmetic operations.

Geometric aspects of CR-warped product submanifolds of T-manifolds

2017 ◽  
Vol 10 (04) ◽  
pp. 1750067
Author(s):  
Akram Ali ◽  
Wan Ainun Mior Othman
Keyword(s):  
Warped Product ◽  
Characterization Theorem ◽  
Second Fundamental Form ◽  
Warping Function ◽  
Sufficient Condition ◽  
Warped Products ◽  
Necessary And Sufficient Condition ◽  
Space Forms ◽  
The Second Fundamental Form ◽  
Necessary And Sufficient

In this paper, we study CR-warped product submanifolds of [Formula: see text]-manifolds. We prove that the CR-warped product submanifolds with invariant fiber are trivial warped products and provide a characterization theorem of CR-warped products with anti-invariant fiber of [Formula: see text]-manifolds. Moreover, we develop an inequality of CR-warped product submanifolds for the second fundamental form in terms of warping function and the equality cases are considered. Also, we find a necessary and sufficient condition for compact oriented CR-warped products turning into CR-products of [Formula: see text]-space forms.

scholarly journals The Algorithm of Fully Fuzzy Cognitive Map Models

2019 ◽  
Vol 4 (6) ◽  
pp. 145-154 ◽  
Author(s):  
Erastus O. Ogunti ◽  
Oluwasegun A. Somefun ◽  
Benedict T. Terkura ◽  
Gideon E. Enoch
Keyword(s):  
Cognitive Mapping ◽  
Fuzzy Numbers ◽  
Cognitive Map ◽  
Fuzzy Cognitive Map ◽  
Fuzzy Arithmetic ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Arithmetic Operations ◽  
Dynamic Activity ◽  
Necessary And Sufficient

Precision in the real world is covered by imprecision and arithmetic operations serve as the foundations of computation. Since the introduction of Fuzzy Cognitive mapping, the dynamic model used to establish the fuzzy cognitive map, used conventional arithmetic operations on asymmetric fuzzy sets.Therefore, for a cognitive map, to be completely fuzzy, it should incorporate the use of fuzzy arithmetic and fuzzy numbers in describing the concept nodes and the cause-effect lines defining its structure. It then can be stated that the necessary and sufficient condition for a cognitive map to be fully fuzzy is that its dynamic activity or operation, be achieved only through fuzzy mathematics.This paper presents an introductory analysis into the peculiar design of the fully fuzzy structure of the cognitive map.

A Proposed Framework Emphasizing Auditor Reliability over Auditor Independence

2003 ◽  
Vol 17 (3) ◽  
pp. 257-266 ◽  
Author(s):  
Mark H. Taylor ◽  
F. Todd DeZoort ◽  
Edward Munn ◽  
Martha Wetterhall Thomas
Keyword(s):  
Public Interest ◽  
Auditor Independence ◽  
Public Confidence ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Accounting Profession ◽  
The Public ◽  
Necessary And Sufficient

This paper introduces an auditor reliability framework that repositions the role of auditor independence in the accounting profession. The framework is motivated in part by widespread confusion about independence and the auditing profession's continuing problems with managing independence and inspiring public confidence. We use philosophical, theoretical, and professional arguments to argue that the public interest will be best served by reprioritizing professional and ethical objectives to establish reliability in fact and appearance as the cornerstone of the profession, rather than relationship-based independence in fact and appearance. This revised framework requires three foundation elements to control subjectivity in auditors' judgments and decisions: independence, integrity, and expertise. Each element is a necessary but not sufficient condition for maximizing objectivity. Objectivity, in turn, is a necessary and sufficient condition for achieving and maintaining reliability in fact and appearance.

The Power of Public Positions

2018 ◽  
Author(s):  
Thomas Sinclair
Keyword(s):  
Detailed Analysis ◽  
Political Authority ◽  
The State ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
State Institutions ◽  
State Of Nature ◽  
Necessary And Sufficient

The Kantian account of political authority holds that the state is a necessary and sufficient condition of our freedom. We cannot be free outside the state, Kantians argue, because any attempt to have the “acquired rights” necessary for our freedom implicates us in objectionable relations of dependence on private judgment. Only in the state can this problem be overcome. But it is not clear how mere institutions could make the necessary difference, and contemporary Kantians have not offered compelling explanations. A detailed analysis is presented of the problems Kantians identify with the state of nature and the objections they face in claiming that the state overcomes them. A response is sketched on behalf of Kantians. The key idea is that under state institutions, a person can make claims of acquired right without presupposing that she is by nature exceptional in her capacity to bind others.

scholarly journals Lorentz Boosts and Wigner Rotations: Self-Adjoint Complexified Quaternions

Physics ◽  
2021 ◽  
Vol 3 (2) ◽  
pp. 352-366
Author(s):  
Thomas Berry ◽  
Matt Visser
Keyword(s):  
Point Of View ◽  
Sufficient Condition ◽  
Use Of Self ◽  
Necessary And Sufficient Condition ◽  
Wigner Rotation ◽  
Inertial Frames ◽  
Explicit Formulae ◽  
Specific Implementation ◽  
Necessary And Sufficient ◽  
Lorentz Boosts

In this paper, Lorentz boosts and Wigner rotations are considered from a (complexified) quaternionic point of view. It is demonstrated that, for a suitably defined self-adjoint complex quaternionic 4-velocity, pure Lorentz boosts can be phrased in terms of the quaternion square root of the relative 4-velocity connecting the two inertial frames. Straightforward computations then lead to quite explicit and relatively simple algebraic formulae for the composition of 4-velocities and the Wigner angle. The Wigner rotation is subsequently related to the generic non-associativity of the composition of three 4-velocities, and a necessary and sufficient condition is developed for the associativity to hold. Finally, the authors relate the composition of 4-velocities to a specific implementation of the Baker–Campbell–Hausdorff theorem. As compared to ordinary 4×4 Lorentz transformations, the use of self-adjoint complexified quaternions leads, from a computational view, to storage savings and more rapid computations, and from a pedagogical view to to relatively simple and explicit formulae.

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