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fuzzy variable based fuzzy non-linear programming approach for optimization of complex system reliability

JOURNAL OF INTELLIGENT & fuzzy SYSTEMS 2015年第4期28卷 1899-1908页

作者： Mahapatra, G. S. Mahapatra, B. S. Roy, P. K. Natl Inst Technol Dept Math Pondicherry 609605 Karaikal India Jadavpur Univ Dept Math Kolkata India

All most all systems in the field of science and technology are well complicated by the advent of modernity. Complex system reliability is mainly dependant on the credibility of its components. It is very difficult to evaluate precise value of component's reliability at the beginning stage of reliability evaluation, due to unavailable or inadequate information. In this respect, fuzzy reliability variable can play an important role in complex system reliability evaluation. In this paper, a fuzzy reliability variable based fuzzy non-linear programming problem is formulated to maximize the complex system reliability. Symmetrical trapezoidal fuzzy numbers are used as fuzzy variable for the component's reliability. Since fuzzy variable for optimization is not well defined, we first reduced the problem to an equivalent multi-objective non-linear programming problem. The proposed approach is applied on landing system of Boeing 747D airplane to evaluate the system reliability in fuzzy environment. The proposed approach and the complex system reliability model are well substantiated by providing numerical examples.

关键词： fuzzy variable fuzzy non-linear programming reliability symmetric trapezoidal fuzzy number complex system

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The optimal solution for several different degrees of feasibility for fuzzy linear and non-linear programming problems

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JOURNAL OF INTELLIGENT & fuzzy SYSTEMS 2014年第5期27卷 2611-2622页

作者： Mohtashami, Ali Islamic Azad Univ Qazvin Branch Fac Management & Accounting Dept Ind Management Qazvin Iran

This paper proposes a novel meta-heuristic based algorithm which provides the optimal solution for several different degrees of feasibility for fuzzy linear and nonlinear programming problems. The proposed method has got the ability for solving those problems in which all coefficients of the objective function and constraints are represented by LR fuzzy numbers with linear and/or non-linear membership function. To solve the fuzzy problems, this paper provides a new hybrid genetic algorithm accompanied by a new proposed method of simulating fuzzy coefficients which 1) eliminates the need of applying defuzzification methods and/or expected interval methods, and 2) allows dealing with different types of fuzzy numbers, properly. In order to show the performance of the proposed method, it is compared with "M. Jimenez, M. Arenas, A. Bilbao and M. V. Rodriguez, linear programming with fuzzy parameters: An interactive method resolution, European Journal of Operational Research 177 (2007), 1599-1609.". Computational results reveal that the proposed method is superior to the Jimenez et al. [13] method from the viewpoint of feasibility and optimality.

关键词： Genetic algorithm fuzzy linear programming fuzzy non-linear programming fuzzy number hybrid genetic algorithm (HGA)

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A new concept for fuzzy variable based non-linear programming problem with application on system reliability via genetic algorithm approach

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ANNALS OF OPERATIONS RESEARCH 2016年第2期247卷 853-866页

作者： Mahapatra, G. S. Mahapatra, B. S. Roy, P. K. Natl Inst Technol Puducherry Dept Math Karaikal 609605 India Jadavpur Univ Dept Math Kolkata 700032 India

Fuzziness is the primary and foremost perception of science and technology. This paper, for the first time, introduces a new concept on solution technique for fuzzy variable based non-linear programming problem with both decision variables and restriction being fuzzy in nature. First the problem is transformed in to a multi-objective non-linear programming problem, and then solving it by multiobjective genetic algorithm (MOGA) approach. The proposed procedure is applied on complex system reliability model to evaluate the system reliability in fuzzy environment, using MOGA by implementing new feature as refining operation. Numerical example is presented to illustrate proposed fuzzy system reliability model.

关键词： fuzzy variable fuzzy non-linear programming Reliability Complex system Genetic algorithm Triangular fuzzy number

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Energy Purchasing Strategy On The Brazilian Regulated Electricity Market: A fuzzy Model

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IEEE LATIN AMERICA TRANSACTIONS 2016年第2期14卷 737-745页

作者： Unsihuay, C. Perondi, G. Univ Fed Parana UFPR Dept Engn Eletr Curitiba Parana Brazil Companhia Paranaense Energia COPEL Curitiba Parana Brazil

Brazilian regulatory model of electricity imposes that distribution companies should acquire all your energy market related to captive customers on, regulated auctions, and distributed generation, whose energy is traded with public calls. An energy market forecast is designed by the utilities and this forecast has to be a 100% covered with contracts agreed from regulated trades. The challenge of utilities is to forecast their own energy market five years in advance, which brings to the process a high level of uncertainty. This paper presents a methodology for planning the purchase of electricity by distribution agents in the Brazilian regulated contracting environment (ACR). The contracting strategy covers a horizon of 5 years, with monthly discretization and the goal is to minimize the total cost of energy procurement strategy. The proposed model considers the current regulatory Brazilian Laws of energy contracting by distribution companies, i.e. energy purchases from auctions in the regulated environment, distributed generation - GD, Compensation Mechanism Surplus and Deficit - MCSD and short-term market. The uncertainties of future electric consumption are modeled following a fuzzy approach. Thus, the formulation if proposed model is a fuzzy non-linear programming problem. Results show the importance of the short-term modeling and the consideration of MCSD and GD in the Energy Purchase Strategy on the Brazilian Regulated Electricity Market.

关键词： Energy purchasing strategy distribution companies Brazilian electricity market fuzzy non-linear programming short-term market

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Deriving Weights from Group fuzzy Pairwise Comparison Judgement Matrices

Deriving Weights from Group Fuzzy Pairwise Comparison Judgem...

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World Conference on Information Systems and Technologies (WorldCIST)

作者： Almulhim, Tarifa S. Mikhailov, Ludmil Xu, Dong-Ling Univ Manchester Manchester Business Sch Manchester M15 6PB Lancs England

ISBN: (纸本)9783642369810

Several Multi-Criteria Decision Making (MCDM) methods involve pairwise comparisons to obtain the preferences of decision makers (DMs). This paper proposes a fuzzy group prioritization method for deriving group priorities/weights from fuzzy pairwise comparison matrices. The proposed method considers the different importance weights of multiple DMs by extending the fuzzy Preferences programming Method (FPP). The elements of the group pairwise comparison matrices are presented as fuzzy numbers rather than exact numerical values in order to model the uncertainty and imprecision in the DMs' judgments. Unlike the known fuzzy prioritization techniques, the proposed method is able to derive crisp weights from incomplete and fuzzy set of comparison judgments and doesn't require additional aggregation procedures. A prototype of a decision tool is developed to assist DMs to use the proposed method for solving fuzzy group prioritization problems. A detailed numerical example is used to illustrate the proposed approach.

关键词： fuzzy non-linear programming fuzzy Preferences programming Method Multiple Criteria Decision-Making Triangular fuzzy Number

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Solution of single and multi-objective fixed reorder quantity system by general fuzzy programming technique

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INTERNATIONAL JOURNAL OF MANAGEMENT SCIENCE AND ENGINEERING MANAGEMENT 2010年第5期5卷 323-333页

作者： Banerjee, S. Roy, T. K. Bengal Engn & Sci Univ Dept Math Howrah 711103 W Bengal India

This paper considers a multi item single period inventory problem with floor space constraint where the demand of the items follows probability distributions. Two different stochastic models are discussed where the demand follows Uniform distribution and Exponential distribution respectively. Firstly the fixed reorder quantity system with backorder and secondly fixed reorder quantity system with lost sales are discussed. Then consideration is adopted as a multi objective stochastic inventory model where average annual cost of the first item as well as the same of the second item are minimized simultaneously and is also formulated in fuzzy environment introducing fuzziness in the objectives. In this paper the concept of General fuzzy non-linear programming Technique is applied to solve a multi objective single period stochastic inventory problem with floor space constraint. The solution is illustrated by numerical example and the results of different models are compared.

关键词： general fuzzy non-linear programming fuzzy optimization fuzzy non-linear programming stochastic inventory model membership function

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Multi-item stochastic and fuzzy-stochastic inventory models under two restrictions

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COMPUTERS & OPERATIONS RESEARCH 2004年第11期31卷 1793-1806页

作者： Das, K Roy, TK Maiti, M Vidyasagar Univ Dept Appl Math Oceanol & Comp Programming Midnapore 721102 India Deemed Univ BE Coll Dept Math Howrah India

Multi-item stochastic and fuzzy-stochastic inventory models are formulated under total budgetary and space constraints. Here, the inventory costs are directly proportional to the respective quantities, unit purchase/production cost is inversely related to the demand and replenishment/production rate is assumed to vary directly with demand. Shortages are allowed but fully backlogged. Here, for both models, demand and budgetary resource are assumed to be random. In fuzzy-stochastic model, in addition to the above assumptions, available storage space and total expenditure are imprecise in nature. Impreciseness in the parameters have been expressed with the help of linear membership functions. Assuming random variables to be independent and to follow normal distributions, the models have been formulated as stochastic and fuzzy-stochastic non-linear programming problems. The stochastic problem is first reduced to the equivalent single objective or multiple objectives problems following chance-constraint method. The problem with single objective is solved by a gradient-based technique whereas fuzzy technique is applied to the multi-objective one. In the same way, the fuzzy-stochastic programming problem is first reduced to a corresponding equivalent fuzzy non-linear programming problem and then it is solved by fuzzy non-linear programming (FNLP) following Zimmermann technique. The models are illustrated numerically and the results of different models are compared. (C) 2003 Elsevier Ltd. All rights reserved.

关键词： inventory fuzzy-stochastic programming fuzzy non-linear programming chance constraint multi-objective

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Multi-objectives fuzzy models for designing 3D trajectory in horizontal wells

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Journal of Applied Mathematics and Computing 2004年第1-2期15卷 265-275页

作者： Qian, Weiyi Feng, Enmin Department of Applied Mathematics Dalian University of Technology Dalian 116023 China Department of Mathematics Bohai University Jinzhou 121003 China

In this paper, multi-objective models for designing 3D trajectory of horizontal wells are developed in a fuzzy environment. Here, the objectives of minimizing the length of the trajectory and the error of entry target point are fuzzy in nature. Some parameters, such as initial value, end value, lower bound and upper bound of the curvature radius, tool-face angle and the arc length of each curve section, are also assumed to be vague and imprecise. The impreciseness in the above objectives have been expressed by fuzzy linear membership functions and that in the above parameters by triangular fuzzy numbers. Models have been solved by the fuzzy non-linear programming method based on Zimmermann [1] and Lee and Li [2]. Models are applied to practical design of the horizontal wells. Numerical results illustrate the accuracy and efficiency of the fuzzy models.

关键词： fuzzy non-linear programming fuzzy number Genetic algorithm Horizontal wells Membership function

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Multi-item fuzzy EOQ models using genetic algorithm

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COMPUTERS & INDUSTRIAL ENGINEERING 2003年第1期44卷 105-117页

作者： Mondal, S Maiti, M Vidyasagar Univ Dept Appl Math Oceanol & Comp Programming Midnapore 721102 India Rabindra Satabarsiki Mahavidyalaya Dept Math Ghatal India

A soft computing approach is proposed to solve non-linear programming problems under fuzzy objective goal and resources with/without fuzzy parameters in the objective function. It uses genetic algorithms (GAs) with mutation and whole arithmetic crossover. Here, mutation is carried out along the weighted gradient direction using the random step lengths based on Erlang and Chi-square distributions. These methodologies have been applied to solve multi-item fuzzy EOQ models under fuzzy objective goal of cost minimization and imprecise constraints on warehouse space and number of production runs with crisp/imprecise inventory costs. The fuzzy inventory models have been formulated as fuzzy non-linear decision making problems and solved by both GAs and fuzzy non-linear programming (FNLP) method based on Zimmermann's approach. The models are illustrated numerically and the results from different methods are compared. (C) 2002 Elsevier Science Ltd. All rights reserved.

关键词： fuzzy inventory genetic algorithm soft computing fuzzy non-linear programming erlang distribution Chi-square distribution

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