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1. Fixed point result in controlled fuzzy metric spaces with application to dynamic market equilibrium

Creator:
Tiwari, Rakesh, Rakočević, Vladimir, and Rajput, Shraddha
Format:
bez média and svazek
Type:
model:article and TEXT
Subject:
fixed point, fuzzy metric spaces, controlled fuzzy metric spaces, fuzzy Θf-contractive mapping, and dynamic market equilibrium
Language:
English
Description:
In this paper, we introduce Θf-type controlled fuzzy metric spaces and establish some fixed point results in this spaces. We provide suitable examples to validate our result. We also employ an application to substantiate the utility of our established result for finding the unique solution of an integral equation emerging in the dynamic market equilibrium aspects to economics.
Rights:
http://creativecommons.org/licenses/by-nc-sa/4.0/ and policy:public

2. Two-stage stochastic programming for engineering problems

Creator:
Popela, Pavel, Novotný, Jan, Roupec, Jan, Hrabec, Dušan, and Olstad, Asmund
Format:
bez média and svazek
Type:
model:article and TEXT
Subject:
two-stage stochastic programming, modelling, scenarios, decomposition, and algorithms
Language:
English
Description:
The purpose of the paper is to present existing and discuss modified optimization models and solution techniques which are suitable for engineering decision-making problems containing random elements with emphasis on two decision stages. The developed aproach is called two-stage stochastic programming and the paper links motivation, applicability, theoretical remarks, transformations, input data generation techniques, and selected decomposition algorithms for generalized class of engineering problems. The considered techniques have been found applicable by the experience of the authors in various areas of engineering problems. They have been applied to engineering design problems involving constraints based on differential equations to achieve reliable solutions. They have served for technological process control e.g. in melting, casting, and sustainable energy production. They have been used for industrial production technologies involving related logistics, as e.g. fixed interval scheduling under uncertainty. The paper originally introduces several recent improvements in the linked parts and it focuses on the unified two-stage stochastic programming approach to engineering problems in general. It utilizes authentic experience and ideas obtained in certain application areas and advises their fruitful utilization for other cases. The paper follows the paper published in 2000 which deals with the applicability of static stochastic programs to engineering design problems. Therefore, it refers to the basic concepts and notation introduced there and reviews only the principal ideas in the beginning. Then. it focuses on motivation of recourse concepts and two decision stages from engineering point of view. The principal models are introduced and selected theoretical features are reviewed. They are also accompanied by the discussion about difficulties caused by real-world cases. Scenario-based approach is detailed as the important one for the solution of engineering problems, discussion in data input generation is added together with model transformation remarks. Robust algorithms suitable for engineering problems involving nonlinearities and integer variable are selected and scenario-based decomposition is preferred. An original experience with using heuristics is shared. Several postprocessing remarks are added at the end of the paper, which is followed by an extensive literature review. and Obsahuje seznam literatury
Rights:
http://creativecommons.org/licenses/by-nc-sa/4.0/ and policy:public