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Algorithms for solving the optimization problems using fuzzy and intuitionistic fuzzy set

INTERNATIONAL JOURNAL OF SYSTEM ASSURANCE ENGINEERING AND MANAGEMENT 2020年第1期11卷 189-222页

作者： Kumar, P. Senthil Navodaya Inst Technol Dept Humanities & Sci Bijanagera Rd PB 26Navodaya Nagar Raichur 584103 Karnataka India

In this article, the crisp, fuzzy and intuitionistic fuzzy optimization problem is formulated. The basic definitions and notations related to optimization problems are given in the preliminaries section. Algorithms for solving the optimization problems using fuzzy and intuitionistic fuzzy set is presented in this article. Then, with the help of the proposed algorithm the optimal solution of the crisp, fuzzy and intuitionistic fuzzy optimization problems are determined. A new theorem related to type-2 fuzzy/type-2 intuitionistic fuzzy optimization problems is proposed and proved. Some new and concrete results related to type-2 fuzzy/type-2 intuitionistic fuzzy optimization problems are presented. To illustrate the proposed method, some real-life numerical examples are presented. The proposed article provides seven fully worked examples with screenshots of output summaries from the software used in the computations for better understanding. The advantages of the proposed approach as compared to other existing work are also specified. Detail analyses of the comparative study as well the discussion are given. To show the advantages of the proposed approach, superiority analysis is discussed. Comparison analysis and the advantages of the proposed operators are also discussed. Some managerial applications and the advantages of the proposed approach are given. Finally, conclusion and future research directions are also given.

关键词： Fuzzy set Fuzzy number TFN TrFN Intuitionistic fuzzy set Intuitionistic fuzzy number TIFN TrIFN Type-2 FTP Type-2 IFTP Type-2 IFSTP FAP IFAP IFSAP linear programming method Integer programming problem Optimal solution Optimal assignment PSK theorem

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A REVIEW AND DISCUSSION OF SOME methodS FOR SYSTEM IDENTIFICATION AND MODELING

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MEDICAL & BIOLOGICAL ENGINEERING 1968年第3期6卷 231-+页

作者： REID, MH MACKAY, RS Present address: Boston University Medical Center Boston Massachusetts University of California Berkeley California

Mathematically testing the validity of a theoretical model with an observed physical system is an important step in understanding and utilizing such a system. Perhaps even more useful is the generation of computational techniques which use input-output data from physical systems to automatically construct mathematical models which, in some sense, provide the ''best'' descriptions of the real systems. This paper briefly discusses a few of the more recent mathematical techniques available for model generation and testing. A new identification method based upon convex and linear programming is discussed in detail and a number of examples indicating its applicability are given. The linear programming method is basically an approximation to a convex programming problem, the solution of which determines the coefficients of the differential equation describing the observed system data. A number of extensions of the identification method indicate some of its most useful properties. The order of the assumed model differential equation can be larger than that of the unknown system and the identification process will either assign zero values to the superfluous coefficients of the model or pole-zero cancellations will occur in the factored form of the Laplace transform of the model transfer function. ''Best'' lowest order models may be selected automatically. linear constraints among the coefficients of the model differential equation may be used to restrict the allowable ranges of the coefficients. Multiple sets of data for a single system may be used simultaneously in the indentification process. Multiple input-output systems or systems described by difference equations or with transportation lag can also be identified. Coefficients of time varying and/or nonlinear models may be determined. Review on some recent identification methods and a new convex and linear programming method is presented which is particularly applicable to biological and medical experimentation.

关键词： Simplex Algorithm Model Transfer Function Convex programming Problem linear programming method Basic Feasible Solution

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Formulating tightest bounds on causal effects in studies with unmeasured confounders

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STATISTICS IN MEDICINE 2008年第30期27卷 6597-6611页

作者： Kuroki, Manabu Cai, Zhihong Osaka Univ Grad Sch Engn Sci Dept Syst Innovat Osaka 5608531 Japan Kyoto Univ Dept Biostat Grad Sch Publ Hlth Sakyo Ku Kyoto Japan

This paper considers the problem of evaluating the causal effect of ail exposure on ail Outcome in observational studies with both measured and unmeasured confounders between the exposure and the Outcome. Under such a situation, MacLehose et al. (Epidemiology 2005;16:548-555) applied linear programming optimization software to find the minimum and maximum possible Values Of file causal effect for specific numerical data. In this paper, we apply the symbolic Balke-Pearl linear programming method (Probabilistic counterfactuals: semantics, computation, and applications. Ph.D. Thesis, UCLA Cognitive Systems Laboratory, 1995;J. Amer Statist. Assoc. 1997;92:1172-1176) to derive the simple closed-form expressions for the lower and upper bounds on causal effects under various assumptions of monotonicity. These universal bounds enable epidemiologists and medical researchers to assess causal effects from observed data with minimum computational effort, and they further shed light on the accuracy of the assessment. Copyright (C) 2008 John Wiley & Sons, Ltd.

关键词： causal risk difference linear programming method monotonic assumption potential response model

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linear programming APPLICATION FOR IRRIGATION NETWORK MANAGEMENT-IMPLEMENTATION IN THE IRRIGATION NETWORK REGION OF PINIOS (CENTRAL GREECE)

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IRRIGATION AND DRAINAGE 2016年第4期65卷 514-521页

作者： Sakellariou-Makrantonaki, M. Tzimopoulos, C. Giouvanis, V. Univ Thessaly Sch Agr Sci Dept Agr Crop Prod & Rural Environm Fytokou Str Nea Ionia 38446 Volos Greece Fac Engn Sch Rural & Surveying Engn Dept Transportat & Hydraul Engn Thessaloniki Greece

The purpose of this study is to find the optimal economical organization of agricultural production, by minimizing the use of available water resources. This purpose can be achieved by combining operational research and hydrology for the development of the appropriate methodology. For the study, the area of the Local Organization for Land Reclamation (LOLR) of Pinios was chosen, as this is a representative part of the plain of Thessaly and the findings could contribute to the total gross value of production in the region (central Greece). The method of linear programming was used for the optimization of agricultural production. The first results obtained within the predefined constraints led us to crop restructuring, while economic profit was increased by 41.7% and water saving reached 4.2%. Copyright (C) 2016 John Wiley & Sons, Ltd.

关键词： irrigation network management linear programming method optimum scenario

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linear and quadratic programs for the conductivity reconstruction of subsurface

Linear and quadratic programs for the conductivity reconstru...

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IEEE International Geoscience and Remote Sensing Symposium

作者： Hidalgo, H Gómez-Treviño, E CICESE Ensenada 22860 Baja California Mexico

ISBN: (纸本)0780387422

An approach for constructing vertical sections of the electrical conductivity of the earth on the basis of surface measurements is presented. Electromagnetic measurements are effected every few meters across strike using pairs of horizontal and vertical coils, with the separation between Source and receiver varying in order to sample different depths. The data provides information about the vertical and horizontal distribution of electrical conductivity of a section of the earth. The recovering of the true conductivity distribution frorn the measurements is a nonlinear inverse problem that allows some useful linear approximations, which we exploit here using linear programming techniques. A regularization approach is considered using, epsilon-insensitive functions for both, the fitness to the data and the penalizing function. This representation enforces a model structure of blocks immersed in a homogeneous basement, a useful model in many practical instances.

关键词： terrestrial electricity geographic information systems linear programming quadratic programming inverse problems geophysical techniques approximation theory linear programming method quadratic program subsurface conductivity reconstruction vertical section construction Earth electrical conductivity surface measurement electromagnetic measurement information data vertical distribution horizontal distribution conductivity distribution nonlinear inverse problem linear approximation regularization method epsiv-insensitive function data fitness penalizing function block model structure homogeneous basement

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Modelling DGM(1,1) under the criterion of the minimization of mean absolute percentage error

Modelling DGM(1,1) under the criterion of the minimization o...

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2nd International Symposium on Knowledge Acquisition and Modeling

作者： Wu, Lifeng Wang, Yinao Wenzhou Univ Coll Math & Informat Sci Wenzhou Peoples R China

ISBN: (纸本)9780769538884

In this paper, we present linear programming method in order to estimate the parameters of the DGM(1,1) model under the criterion of the minimization of mean absolute percentage error (MAPE) (some authors called average relative error). A published article is chosen for practical tests of this method, the results show that this method can obviously improve the simulation accuracy.

关键词： DGM model GM(1,1) model Mathematical Modelling linear programming method mean absolute percentage error

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Modelling GM(1,1) under the criterion of the minimization of mean absolute percentage error

Modelling GM(1,1) under the criterion of the minimization of...

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International Conference on Advanced Materials and Engineering Materials (ICAMEM 2011)

作者： Chen, Haijun Lou, Xijuan Jie, Liu Handan Coll Dept Math Handan 056005 HeBei Peoples R China

ISBN: (纸本)9783037853559

In this paper, we present two methods to estimate the parameters of the GM (1,1)model under. The criterion of the minimization of mean absolute percentage error (MAPE) (some authors called Average relative error). A linear programming method is used to optimize the whiting value of grey derivative of GM(1,1),four published articles are chosen for practical tests of this method, the results show that this method can obviously improve the simulation accuracy. Another method is that the problem of estimation parameters of GM(1,1) model is transformed into the minimax optimization problem, then use the library function fminimax in MATLAB to solve the minimax optimization problem, the same four published articles are chosen for practical tests of this modelling method, as shown in these results, this method can obtain the local optimal parameters, yield the lower MAPE than the existing method. But it is sensitive for the initial approximation and requires a good initial approximation, the results of compared with different initial approximations show that the parameters which are obtained by the former method is the better initial approximation.

关键词： Grey system GM(1,1) model Simulation accuracy linear programming method Mini-max optimization problem Mean absolute percentage error

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Optimized Decision Making for Power Grid Safety Correction Based on Sub-regional Load Control 4

Optimized Decision Making for Power Grid Safety Correction B...

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IEEE 4th Information Technology and Mechatronics Engineering Conference (ITOEC)

作者： Wang, Yi Shan, Xin Zha, Guoqiang ARI Grp Corp State Grid Elect Power Res Inst Nanjing 210003 Jiangsu Peoples R China ARI Technol Co Ltd Nanjing 211106 Jiangsu Peoples R China Tate Key Lab Smart Grid Protect & Control Nanjing 211106 Jiangsu Peoples R China

ISBN: (纸本)9781538653739

In the case of large-scale power loss fault in the operation of UHV AC-DC hybrid power grid, it is impossible to adjust the grid correction control problem by the unit output adjustment. Fully utilize the adjustable capacity of the load control to achieve safety correction control to meet the load control aid decision-making requirements of existing dispatching system. According to the characteristics of the dispatching system in accordance with the sub-regional load as the target of unified implementation of load control, this paper proposes a safety correction optimized aid decision-making calculation method based on sub-regional load control, with the sub-regional load as the control object and the minimum sub-regional load as the target. Consider the system power flow constraint, the sub-regional controllable load constraint and the key monitoring section safety constraints, the continuous power flow method and the line planning method are combined to solve the problem. The proposed method has the characteristics of simple model, easy solution and good convergence. It shows the effectiveness of the proposed method in the actual power grid.(1)

关键词： Sub-regional load control safety correction aid decision making continuous power flow method linear programming method

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New lower and upper bounds on Armstrong codes 17

New lower and upper bounds on Armstrong codes

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17th International Workshop on Algebraic and Combinatorial Coding Theory (ACCT)

作者： Alexandrova, Todorka Boyvalenkov, Peter Sali, Attila Bulgarian Acad Sci Inst Math & Informat Sofia Bulgaria Budapest Univ Technol & Econ Alfred Renyi Inst Math Budapest Hungary Budapest Univ Technol & Econ Dept Comp Sci Budapest Hungary

ISBN: (纸本)9781665402873

An Armstrong(q, k, n) code is a q-ary code of length n of minimum distance n - k + 1 such that for every (k - 1)-subset of coordinates there exists a pair of codewords that agree exactly there. Let f (q, k) denote the largest n such that an Armstrong(q, k, n) code exists. Upper and lower bounds on f (q, k) were given earlier in general, and in the case when k > k(0)(q). In the present paper we propose a new construction to provide Armstrong((p +1)/2, 2l, p) for a prime p and give an upper bound in the case of fixed k and large enough q. Both results imply improvements on corresponding general known bounds for large enough q.

关键词： Armstrong code linear programming method Krawtchouk polynomials

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The Hierarchical Control with Stability and Production Level Control of Cement NSP Kilns

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IFAC Proceedings Volumes 1987年第8期20卷 117-122页

作者： S. Hagimura T. Saito Y. Yagihara T. Kominami Research and Development Division Chichibu Cement Co. Ltd. Kumagaya Saitama Japan 360 Chichibu Branch Office System Sougoh Co. Ltd. 794-6 Omiya Chichibu Saitama Japan 368

The ceaent industry process has a characteristic of broad frequency domain (from a minute to a few days). First we identified multi-dimensional AR model in high frequency domain and realized stability controls by state-space aethod. As the result, we have gotten satisfactory results of control. The other hand, we can't say certainly that normal setpoints provided by staffs and operators of the field are optimal. Then we identified a process of low frequency domain and simulated a optimal control by AR model and linear programming method. According to realizing this control, we can get dynamic optimum setpoints.

关键词： Cement industry stability state-space method optimal control linear programming method

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