scholarly journals Multiplicative form of the Lagrangian

2016 ◽  
Vol 189 (3) ◽  
pp. 1693-1711 ◽  
Author(s):  
K. Surawuttinack ◽  
S. Yoo-Kong ◽  
M. Tanasittikosol
Keyword(s):  
Multiplicative Form

A Multi-MOORA decision making method based on muirhead mean operators and complex spherical fuzzy uncertain linguistic setting

2021 ◽  
pp. 1-26
Author(s):  
Fen Wang ◽  
Zeeshan Ali ◽  
Tahir Mahmood ◽  
Shouzhen Zeng
Keyword(s):  
Decision Making ◽  
General Structure ◽  
Aggregation Operators ◽  
Ratio Analysis ◽  
Multi Objective Optimization ◽  
Linguistic Terms ◽  
Modifiable Factors ◽  
Multi Attribute Decision Making ◽  
Multiplicative Form ◽  
Actual Life

The Muirhead mean (MM) operators offer a flexible arrangement with its modifiable factors because of Muirhead’s general structure. On the other hand, MM aggregation operators perform a significant role in conveying the magnitude level of options and characteristics. In this manuscript, the complex spherical fuzzy uncertain linguistic set (CSFULS), covering the grade of truth, abstinence, falsity, and their uncertain linguistic terms is proposed to accomplish with awkward and intricate data in actual life dilemmas. Furthermore, by using the MM aggregation operators with the CSFULS, the complex spherical fuzzy uncertain linguistic MM (CSFULMM), complex spherical fuzzy uncertain linguistic weighted MM (CSFULWMM), complex spherical fuzzy uncertain linguistic dual MM (CSFULDMM), complex spherical fuzzy uncertain linguistic dual weighted MM (CSFULDWMM) operators, and their important results are also elaborated with the help of some remarkable cases. Additionally, multi-attribute decision-making (MADM) based on the Multi-MOORA (Multi-Objective Optimization Based on a Ratio Analysis plus full multiplicative form), and proposed operators are developed. To determine the rationality and reliability of the elaborated approach, some numerical examples are illustrated. Finally, the supremacy and comparative analysis of the elaborated approaches with the help of graphical expressions are also developed.

scholarly journals HOW TO INVEST IN BELGIAN SHARES BY MULTIMOORA OPTIMIZATION

2013 ◽  
Vol 14 (5) ◽  
pp. 940-956 ◽  
Author(s):  
Willem K. M. Brauers ◽  
Romualdas Ginevičius
Keyword(s):  
Reference Point ◽  
Point Theory ◽  
Multiple Objectives ◽  
Ratio Analysis ◽  
Multi Objective Optimization ◽  
Dimensionless Numbers ◽  
Multi Objective ◽  
Multiplicative Form ◽  
Objective Reference ◽  
Alternative Solutions

Different multiple objectives expressed in different units make optimization difficult. Therefore, the internal mechanical solution of a Ratio System, producing dimensionless numbers, is preferred to weights, which are most of the time used to compare the different units. In addition, the ratio system creates the opportunity to use a second approach: a non-subjective Reference Point Theory. Therefore, the Reference Point Theory uses the ratios found in the ratio system as co-ordinates for the alternative solutions, which are then compared to a Maximal Objective Reference Point. The two approaches form a control on each other. This overall theory is called MOORA (Multi-Objective Optimization by Ratio Analysis). The results are still more convincing if a Full Multiplicative Form is added, three methods assembled under the name of MULTIMOORA. At that moment, the control by three different approaches forms a guaranty for a solution being as non-subjective as possible. As to calculate the sum of three obtained ranks is not allowed, a theory of Ordinal Dominance is developed in order to remain in the ordinal sphere.

scholarly journals LITHUANIAN CASE STUDY OF MASONRY BUILDINGS FROM THE SOVIET PERIOD

2012 ◽  
Vol 18 (3) ◽  
pp. 444-456 ◽  
Author(s):  
Willem Karel M. Brauers ◽  
Modestas Kracka ◽  
Edmundas Kazimieras Zavadskas
Keyword(s):  
Reference Point ◽  
Building Envelope ◽  
Soviet Period ◽  
Masonry Buildings ◽  
Building Insulation ◽  
Effective Selection ◽  
Multiplicative Form ◽  
Save Energy ◽  
Selection Of

This paper presents the process of effective selection of building elements for renovation important for energy saving in buildings. A large part of energy is lost in non-effective buildings. Therefore, in renovation of buildings, it is important to select effective structural improvements. Building insulation could not only save energy but also time, money and materials, which means that different objectives expressed in different units have to be fulfilled. Although different methods exist for the application of Multi Objective Optimisation, MULTIMOORA, which is composed of three sub-methods – Ratio System, Reference Point Method that uses ratios from the ratio system, and the Full Multiplicative Form – was preferred. Consequently, different solutions for building envelope renovation were ranked by MULTIMOORA as applied for masonry buildings from the Soviet period.

scholarly journals Rényi Entropy Power Inequalities via Normal Transport and Rotation

Entropy ◽  
2018 ◽  
Vol 20 (9) ◽  
pp. 641 ◽  
Author(s):  
Olivier Rioul
Keyword(s):  
Shannon’S Entropy ◽  
Renyi Entropy ◽  
Rényi Entropy ◽  
Shannon's Entropy ◽  
Change Of Variable ◽  
Power Inequality ◽  
Multiplicative Form ◽  
Normal Transport ◽  
Comprehensive Framework

Following a recent proof of Shannon’s entropy power inequality (EPI), a comprehensive framework for deriving various EPIs for the Rényi entropy is presented that uses transport arguments from normal densities and a change of variable by rotation. Simple arguments are given to recover the previously known Rényi EPIs and derive new ones, by unifying a multiplicative form with constant c and a modification with exponent α of previous works. In particular, for log-concave densities, we obtain a simple transportation proof of a sharp varentropy bound.

Fuzzy Logical Approach to Perception of Dot Numerosity

1989 ◽  
Vol 69 (3-2) ◽  
pp. 1319-1329
Author(s):  
Toshiyuki Yamashita
Keyword(s):  
Human Perception ◽  
Logical Approach ◽  
Multiplicative Form ◽  
Logic System ◽  
Fuzzy Logical

The present study utilized a fuzzy logical approach for understanding human perception or judgments of dot numerosity. In Exp. 1 subjects were required to view dot patterns and to judge the truthfulness of the single and combined statements which asserted that the number of dots was large. The results indicated that (a) the rules based on the minimum and maximum truthfulness of the component statements best approximate subjective conjunction and disjunction about dot numerosity, when subjects kept the operations of the standard logic system in mind. (b) When the subjects based their judgments on perceptive impression, their judgments were best fitted by the multiplicative form.

scholarly journals Induced encystment improves resistance to preservation and storage of Acanthamoeba castellanii

Parasitology ◽  
2008 ◽  
Vol 135 (12) ◽  
pp. 1401-1405 ◽  
Author(s):  
S. J. CAMPBELL ◽  
P. R. INGRAM ◽  
C. W. ROBERTS ◽  
F. L. HENRIQUEZ
Keyword(s):  
Adverse Effects ◽  
Dimethyl Sulfoxide ◽  
Room Temperature ◽  
Acanthamoeba Castellanii ◽  
Storage Conditions ◽  
Multiplicative Form ◽  
Efficient Recovery ◽  
And Storage

SUMMARYSeveral conditions that allow the preservation, storage and rapid, efficient recovery of viable Acanthamoeba castellanii organisms were investigated. The viability of trophozoites (as determined by time to confluence) significantly declined over a period of 12 months when stored at −70°C using dimethyl sulfoxide (DMSO; 5 or 10%) as cryopreservant. As A. castellanii are naturally capable of encystment, studies were undertaken to determine whether induced encystment might improve the viability of organisms under a number of storage conditions. A. castellanii cysts stored in the presence of Mg2+ at 4°C remained viable over the study period, although time to confluence was increased from approximately 8 days to approximately 24 days over the 12-month period. Storage of cysts at −70°C with DMSO (5 or 10%) or 40% glycerol, but not 80% glycerol as cryopreservants increased their viability over the 12-month study period compared with those stored at room temperature. Continued presence of Mg2+ in medium during storage had no adverse effects and generally improved recovery of viable organisms. The present study demonstrates that A. castellanii can be stored as a non-multiplicative form inexpensively, without a need for cryopreservation, for at least 12 months, but viability is increased by storage at −70°C.

scholarly journals Asymptotic Expansion in Multiplicative Form in the Central Limit Theorem in the Case of Gamma Distribution

2019 ◽  
pp. 12-23
Author(s):  
Vitaly Sobolev
Keyword(s):  
Asymptotic Expansion ◽  
Central Limit Theorem ◽  
Limit Theorem ◽  
Central Limit ◽  
Gamma Distribution ◽  
Asymptotic Expansions ◽  
Approximation Accuracy ◽  
The Central Limit Theorem ◽  
Multiplicative Form ◽  
T Distribution

Study of estimation of accuracy of approximations in the Central limit theorem (CLT) is one of the known problems in probability theory. The main result here is the estimate of the theorem of Berry — Esseen. Its low accuracy is well known. So this theorem guarantees accuracy of approximation 103 in the CLT only if the number of summands in the normed sum is greater than 160 000. Therefore, increasing the accuracy of the approximations in the CLT is an actual task. In particular, for this purpose are used asymptotic expansions in the Central limit theorem. As a rule, asymptotic expansions have additive form. Although it is possible to construct expansions in the multiplicative form. So V.M. Kalinin in [3] received the multiplicative form of the asymptotic expansions. However, he constructed asymptotic expansions for probability distributions (multinomial, Poisson, Student’s t-distribution). So very naturally the question arises: how to build multiplicative expansions in CLT? Secondly, what are the forms of decompositions in CLT in terms of accuracy approximations are better: additive or multiplicative? This paper proposes new asymptotic expansions in the central limit theorem which permit us to approximate distributions of normalized sums of independent gamma random variables with explicit estimates of the approximation accuracy and comparing them with expansions in terms of Chebyshev — Hermite polynomials. New asymptotic expansions is presented in the following theorem. Comparing multiplicative asymptotic expansion from theorem 1 with the additive asymptotic expansion from [5], we obtain that multiplicative asymptotic expansion of the density of normalized the sums in the case of gamma distribution give a much greater accuracy numerical calculations are compared with asymptotic additive expansion provided a much smaller number of calculations. The author would like to thank Vladimir Senatov for setting the task and paying attention to this work.

scholarly journals Assessment of the application feasibility of the genetic algorithm for airports operations optimization based on the collaborative decision-making principles

2019 ◽  
Vol 22 (5) ◽  
pp. 85-93
Author(s):  
G. M. Lebedev ◽  
V. B. Malygin
Keyword(s):  
Genetic Algorithm ◽  
Decision Making ◽  
Traffic Control ◽  
Traffic Management ◽  
Air Traffic ◽  
Aviation Industry ◽  
Collaborative Decision Making ◽  
Original Product ◽  
Multiplicative Form ◽  
Collaborative Decision

The article proposes a formalization methodology of the basic characteristics of the production processes of the aviation industry major components, such as airlines, airports and air traffic control authorities. This technique is not exhaustive, but it is quite suitable as the basis for the formation of the initial data for decision-making optimization under the conditions of airport operations performance and air traffic management, based on the principles of work coordination of the airports operational units. It is proposed to use a genetic algorithm as a tool for optimizing collaborative decision-making, which allows for a smaller number of iterations in real time to obtain a suboptimal solution that meets the requirements of the process participants. The mathematical model in multiplicative form is presented in making an assessment of the application feasibility of the genetic algorithm, taking into account the interests of three stakeholders. Planning the use of aircraft for the airport flight schedule based on the formalized data of the airline fleet, the capabilities of the base airport apron, as well as the restrictions of permanent and temporary nature is accepted as the original product. The article demonstrates the potential advantage of the genetic algorithm, the point of which is that within each step of a suboptimal choice of priorities instead of brute-force options limited but effective direct search of a reduced number of those options that have been chosen as the "elite" by using multiplicative form is carried out.

scholarly journals Rényi Entropy Power Inequalities via Normal Transport and Rotation

2018 ◽  
Author(s):  
Olivier Rioul
Keyword(s):  
Shannon’S Entropy ◽  
Shannon's Entropy ◽  
Change Of Variable ◽  
Power Inequality ◽  
Multiplicative Form ◽  
Normal Transport ◽  
Comprehensive Framework

Following a recent proof of Shannon's entropy power inequality (EPI), a comprehensive framework for deriving various EPIs for the Rényi entropy is presented that uses transport arguments from normal densities and a change of variable by rotation. Simple arguments are given to recover the previously known Rényi EPIs and derive new ones, by unifying a multiplicative form with constant c and a modification with exponent α of previous works. In particular, for log-concave densities, we obtain a simple transportation proof of a sharp varentropy bound.

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