scholarly journals Classification of Complex Fuzzy Numbers and Fuzzy Inner Products

Mathematics ◽  
2020 ◽  
Vol 8 (9) ◽  
pp. 1626
Author(s):  
Jin Hee Yoon ◽  
Taechang Byun ◽  
Ji Eun Lee ◽  
Keun Young Lee
Keyword(s):  
Complex Number ◽  
Fuzzy Number ◽  
Fuzzy Numbers ◽  
Point Of View ◽  
Inner Product ◽  
General Point ◽  
Type I ◽  
Type Ii ◽  
Polar Form ◽  
Schwartz Inequality

The paper is concerned with complex fuzzy numbers and complex fuzzy inner product spaces. In the classical complex number set, a complex number can be expressed using the Cartesian form or polar form. Both expressions are needed because one expression is better than the other depending on the situation. Likewise, the Cartesian form and the polar form can be defined in a complex fuzzy number set. First, the complex fuzzy numbers (CFNs) are categorized into two types, the polar form and the Cartesian form, as type I and type II. The properties of the complex fuzzy number set of those two expressions are discussed, and how the expressions can be used practically is shown through an example. Second, we study the complex fuzzy inner product structure in each category and find the non-existence of an inner product on CFNs of type I. Several properties of the fuzzy inner product space for type II are proposed from the modulus that is newly defined. Specfically, the Cauchy-Schwartz inequality for type II is proven in a compact way, not only the one for fuzzy real numbers. In fact, it was already discussed by Hasanhani et al; however, they proved every case in a very complicated way. In this paper, we prove the Cauchy-Schwartz inequality in a much simpler way from a general point of view. Finally, we introduce a complex fuzzy scalar product for the generalization of a complex fuzzy inner product and propose to study the condition for its existence on CFNs of type I.

A New Point of View for Fuzzy Numbers and Their Defuzzification

2015 ◽  
Vol 23 (06) ◽  
pp. 909-926 ◽  
Author(s):  
Romà Adillon ◽  
Lambert Jorba
Keyword(s):  
Fuzzy Number ◽  
Fuzzy Numbers ◽  
Graphical Representation ◽  
Point Of View ◽  
Geometrical Approach ◽  
Triangular Fuzzy Numbers ◽  
Trapezoidal Fuzzy Numbers

In this paper we develop a new graphical representation of fuzzy numbers, which we then employ to propose a geometrical approach to their defuzzification. The calculations involved in the proposed method and the resultant representation use Moore's semiplane for intervals and therefore are far simpler than those involved in other approaches. We start by representing triangular and trapezoidal fuzzy numbers in Moore's semiplane. Then we extend this work to any fuzzy number. Although this extension has to be undertaken in [Formula: see text], it preserves all the properties we study for trapezoidal and triangular fuzzy numbers in Moore's semiplane.

scholarly journals Parameter Estimation of Type-I and Type-II Hybrid Censored Data from the Log-Logistic Distribution

2016 ◽  
Vol 4 (1) ◽  
pp. 37-44
Author(s):  
Seunggeun Hyun ◽  
Jimin Lee ◽  
Robert Yearout
Keyword(s):  
Censored Data ◽  
Random Variable ◽  
Point Of View ◽  
Logistic Distribution ◽  
Type I ◽  
Type Ii ◽  
Unknown Parameters ◽  
Type Ii Censoring ◽  
Termination Time ◽  
Censoring Scheme

In experiments on product lifetime and reliability testing, there are many practical situations in which researchers terminate the experiment and report the results before all items of the experiment fail because of time or cost consideration. The most common and popular censoring schemes are type-I and type-II censoring. In type-I censoring scheme, the termination time is pre-fixed, but the number of observed failures is a random variable. However, if the mean lifetime of experimental units is somewhat larger than the pre-fixed termination time, then far fewer failures would be observed and this is a significant disadvantage on the efficiency of inferential procedures. In type-II censoring scheme, however, the number of observed failures is pre-fixed, but the experiment time is a random variable. In this case, at least pre-specified number of failure are obtained, but the termination time is clearly a disadvantage from the experimenter’s point of view. To overcome some of the drawbacks in those schemes, the hybrid censoring scheme, which is a mixture of the conventional type-I and type-II censoring schemes, has received much attention in recent years. In this paper, we consider the analysis of type-I and type-II hybrid censored data where the lifetimes of items follow two-parameter log-logistic distribution. We present the maximum likelihood estimators of unknown parameters and asymptotic confidence intervals, and a simulation study is conducted to evaluate the proposed methods.

scholarly journals The Influence of Suprascapular Notch Shape on the Visualization of Structures in the Suprascapular Notch Region: Studies Based on a New Four-Stage Ultrasonographic Protocol

2017 ◽  
Vol 2017 ◽  
pp. 1-7 ◽  
Author(s):  
Hubert Jezierski ◽  
Michał Podgórski ◽  
Ludomir Stefańczyk ◽  
David Kachlik ◽  
Michał Polguj
Keyword(s):  
Color Doppler ◽  
Suprascapular Nerve ◽  
Point Of View ◽  
Transverse Diameter ◽  
Type I ◽  
Type Ii ◽  
Suprascapular Notch ◽  
Type Iii ◽  
Type Iv ◽  
Clinical Point

Evaluation of the morphology of the suprascapular notch region is important from a clinical point of view because it is the most common site of suprascapular nerve compression and injury. A group of 120 patients underwent ultrasound examination of the suprascapular notch region according to our original four-stage “step-by-step” protocol. The notches were classified based on their morphology and measurements like maximal depth (MD) and superior transverse diameter (STD) as follows: type I-MD is longer than STD, type II-MD and STD are equal, type III-STD is longer than MD, and in type IV/V-notches only the bony margin was visualized without depression. Both suprascapular notches were fully visualized in 115 of 120 patients. The type III suprascapular notch was the most prevalent (64.2%), followed by type IV/V (18.7%), type I (11.1%), and type II (6.0%). Color Doppler analysis allowed the suprascapular artery to be recognized in all visualized notches. The suprascapular vein was visible in 176 notches and the suprascapular nerve in 150. Notches containing both suprascapular nerve and vein were significantly wider and shallower than average. As the suprascapular artery is the most easily recognised structure in the area, it may serve as a useful landmark of the suprascapular notch.

Heat-Etching with a Bullivant Type II Simple Freeze-Cleave Device

1970 ◽  
Vol 28 ◽  
pp. 106-107 ◽  
Author(s):  
Ronald S. Weinstein ◽  
N. Scott McNutt
Keyword(s):  
New Zealand ◽  
General Hospital ◽  
Massachusetts General Hospital ◽  
Type I ◽  
Type Ii ◽  
Collaborative Effort ◽  
Temperature And Pressure ◽  
The University

The Type I simple cold block device was described by Bullivant and Ames in 1966 and represented the product of the first successful effort to simplify the equipment required to do sophisticated freeze-cleave techniques. Bullivant, Weinstein and Someda described the Type II device which is a modification of the Type I device and was developed as a collaborative effort at the Massachusetts General Hospital and the University of Auckland, New Zealand. The modifications reduced specimen contamination and provided controlled specimen warming for heat-etching of fracture faces. We have now tested the Mass. General Hospital version of the Type II device (called the “Type II-MGH device”) on a wide variety of biological specimens and have established temperature and pressure curves for routine heat-etching with the device.

Labelling of non-A, non-B hepatitis infected chimpanzee hepatocytes with nuclease-gold conjugates

1984 ◽  
Vol 42 ◽  
pp. 250-251
Author(s):  
G. D. Gagne ◽  
M. F. Miller ◽  
D. A. Peterson
Keyword(s):  
Endoplasmic Reticulum ◽  
Experimental Infection ◽  
Uranyl Acetate ◽  
Type I ◽  
Cellular Injury ◽  
Type Ii ◽  
Tubular Structures ◽  
Type Iii ◽  
Type Iv ◽  
Infected Chimpanzee

Experimental infection of chimpanzees with non-A, non-B hepatitis (NANB) or with delta agent hepatitis results in the appearance of characteristic cytoplasmic alterations in the hepatocytes. These alterations include spongelike inclusions (Type I), attached convoluted membranes (Type II), tubular structures (Type III), and microtubular aggregates (Type IV) (Fig. 1). Type I, II and III structures are, by association, believed to be derived from endoplasmic reticulum and may be morphogenetically related. Type IV structures are generally observed free in the cytoplasm but sometimes in the vicinity of type III structures. It is not known whether these structures are somehow involved in the replication and/or assembly of the putative NANB virus or whether they are simply nonspecific responses to cellular injury. When treated with uranyl acetate, type I, II and III structures stain intensely as if they might contain nucleic acids. If these structures do correspond to intermediates in the replication of a virus, one might expect them to contain DNA or RNA and the present study was undertaken to explore this possibility.

Comparative surface and ultrastructural views of methylotrophic bacteria by TEM, STEM, SE, and freeze-etch electron microscopy.

1987 ◽  
Vol 45 ◽  
pp. 792-793
Author(s):  
T.A. Fassel ◽  
M.J. Schaller ◽  
M.E. Lidstrom ◽  
C.C. Remsen
Keyword(s):  
Cytoplasmic Membrane ◽  
Structural Features ◽  
Methylotrophic Bacteria ◽  
Type I ◽  
Type Ii ◽  
Membrane Complex ◽  
Oxidation Of Methane ◽  
Methane Oxidizing Bacteria ◽  
Wall Structures ◽  
Methylomonas Albus

Methylotrophic bacteria play an Important role in the environment in the oxidation of methane and methanol. Extensive intracytoplasmic membranes (ICM) have been associated with the oxidation processes in methylotrophs and chemolithotrophic bacteria. Classification on the basis of ICM arrangement distinguishes 2 types of methylotrophs. Bundles or vesicular stacks of ICM located away from the cytoplasmic membrane and extending into the cytoplasm are present in Type I methylotrophs. In Type II methylotrophs, the ICM form pairs of peripheral membranes located parallel to the cytoplasmic membrane. Complex cell wall structures of tightly packed cup-shaped subunits have been described in strains of marine and freshwater phototrophic sulfur bacteria and several strains of methane oxidizing bacteria. We examined the ultrastructure of the methylotrophs with particular view of the ICM and surface structural features, between representatives of the Type I Methylomonas albus (BG8), and Type II Methylosinus trichosporium (OB-36).

OPTICAL STUDIES OF TYPE I AND TYPE II RECOMBINATION IN GaAs-AlAs QUANTUM WELLS

1987 ◽  
Vol 48 (C5) ◽  
pp. C5-525-C5-528 ◽  
Author(s):  
K. J. MOORE ◽  
P. DAWSON ◽  
C. T. FOXON
Keyword(s):  
Quantum Wells ◽  
Type I ◽  
Type Ii ◽  
Optical Studies

An old friend is better than two new ones? Approaches to market research in the context of digital transformation for the antitrust laws enforcement

2020 ◽  
pp. 37-55 ◽  
Author(s):  
A. E. Shastitko ◽  
O. A. Markova
Keyword(s):  
Business Models ◽  
Rapid Development ◽  
Digital Transformation ◽  
Market Definition ◽  
Type I ◽  
Type Ii ◽  
Digital Platforms ◽  
Advantages And Disadvantages ◽  
Pass Through ◽  
Type Ii Errors

Digital transformation has led to changes in business models of traditional players in the existing markets. What is more, new entrants and new markets appeared, in particular platforms and multisided markets. The emergence and rapid development of platforms are caused primarily by the existence of so called indirect network externalities. Regarding to this, a question arises of whether the existing instruments of competition law enforcement and market analysis are still relevant when analyzing markets with digital platforms? This paper aims at discussing advantages and disadvantages of using various tools to define markets with platforms. In particular, we define the features of the SSNIP test when being applyed to markets with platforms. Furthermore, we analyze adjustment in tests for platform market definition in terms of possible type I and type II errors. All in all, it turns out that to reduce the likelihood of type I and type II errors while applying market definition technique to markets with platforms one should consider the type of platform analyzed: transaction platforms without pass-through and non-transaction matching platforms should be tackled as players in a multisided market, whereas non-transaction platforms should be analyzed as players in several interrelated markets. However, if the platform is allowed to adjust prices, there emerges additional challenge that the regulator and companies may manipulate the results of SSNIP test by applying different models of competition.

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