A class of interactive multi objective decision making method by means of evaluation criterion is proposed for problems with linear value function,in which case,the decision maker(DM) usually has only unwhole infor...A class of interactive multi objective decision making method by means of evaluation criterion is proposed for problems with linear value function,in which case,the decision maker(DM) usually has only unwhole information of weights for objectives. The concept of fault measure of the evaluation criterion is proposed to measure the deviation of the evaluation criterion from the DMs preference structure.The approach to obtain an upper boundary of fault measure of an evaluation criterion,and the approach to modify the evaluation criterion to be one with smaller fault measure,and the approach to obtain a pre optimized objective set by evaluation criterion with certain fault measure are also proposed.展开更多
In this paper, for multi objective decision making, the defects on the commonly used interactive methods based on the satisfactoriness criterion is studied. Then a class of two stage interactive method based on the...In this paper, for multi objective decision making, the defects on the commonly used interactive methods based on the satisfactoriness criterion is studied. Then a class of two stage interactive method based on the satisfactoriness criterion is proposed for improvement with the satisfactoriness criterion being determined through the collection of the decision makers preference information. An application example is presented for illustration of applicability of the method.展开更多
A decision support system, including a multi-objective optimization framework and a multi-attribute decision making approach is proposed for satellite equipment layout. Firstly, given three objectives (to minimize the...A decision support system, including a multi-objective optimization framework and a multi-attribute decision making approach is proposed for satellite equipment layout. Firstly, given three objectives (to minimize the C.G. offset, the cross moments of inertia and the space debris impact risk), we develop a threedimensional layout optimization model. Unlike most of the previous works just focusing on mass characteristics of the system, a space debris impact risk index is developed. Secondly, we develop an efficient optimization framework for the integration of computer-aided design (CAD) software as well as the optimization algorithm to obtain the Pareto front of the layout optimization problem. Thirdly, after obtaining the candidate solutions, we present a multi-attribute decision making approach, which integrates the smart Pareto filter and the correlation coefficient and standard deviation (CCSD) method to select the best tradeoff solutions on the optimal Pareto fronts. Finally, the framework and the decision making approach are applied to a case study of a satellite platform.展开更多
The spectral analysis of simulated N-team of interacting decision makers with bounded rationality constraints of Oladejo, which assumes triangular probability density function of command inputs is hereby restructured ...The spectral analysis of simulated N-team of interacting decision makers with bounded rationality constraints of Oladejo, which assumes triangular probability density function of command inputs is hereby restructured and analysed, to have hierarchical command inputs that are predicated on order statistics distributions. The results give optimal distributions.展开更多
A new fuzzification method for multi-objective decision-making and selective sorting is proposed on the basis of the fuzzy consistent relation, and the specific algorithm is presented. The method is applied to the eva...A new fuzzification method for multi-objective decision-making and selective sorting is proposed on the basis of the fuzzy consistent relation, and the specific algorithm is presented. The method is applied to the evaluation of highway planning of Zhanjiang city. To decrease the subjectivity in the process of decision-making, the LOWA operator is introduced, and a discussion on how to select appropriate weights involved in multi-objective sorting is made. It is concluded that it is feasible to apply the fuzzy consistent relation to multi-objective decision-making analysis, and the improved fuzzication method is workable.展开更多
In order to solve existing problems about the method of establishing traditional system structure of decision support system(DSS), O S chart is applied to describe object oriented system structure of general DSS, an...In order to solve existing problems about the method of establishing traditional system structure of decision support system(DSS), O S chart is applied to describe object oriented system structure of general DSS, and a new method of eight specific steps is proposed to establish object oriented system structure of DSS by using the method of O S chart, which is applied successfully to the development of the DSS for the energy system ecology engineering research of the Wangheqiu country. Supplying many scientific effective computing models, decision support ways and a lot of accurate reliable decision data, the DSS plays a critical part in helping engineering researchers to make correct decisions. Because the period for developing the DSS is relatively shorter, the new way improves the efficiency of establishing DSS greatly. It also makes the DSS of system structure more flexible and easy to expand.展开更多
The modern war features a highly distributed coordination. In the face of great time constrains, it is important to change command organizations to adapt to the real environment. Therefore it's a key step to set u...The modern war features a highly distributed coordination. In the face of great time constrains, it is important to change command organizations to adapt to the real environment. Therefore it's a key step to set up adaptive C2 teams. In this paper, the relational problems about distributed C2 organizational structure adaptation are discussed, and the methodology for team decision making design based on the object oriented technique is studied.展开更多
Multiple objects decision is used widely in many complex fields. In this paper an idea is provided to construct a train diagram intelligent multiple objects decision support system (TDIMODSS). And the reference point ...Multiple objects decision is used widely in many complex fields. In this paper an idea is provided to construct a train diagram intelligent multiple objects decision support system (TDIMODSS). And the reference point method is used to solve the complicated and large scale problems of making and adjusting train schedule. This paper focuses on the principle and framework of the model base, knowledge base of train diagram. It is shown that the TDIMODSS can solve the problems and their uncertainty in making train diagram, and can combine the expert knowledge, experience and judgement of a decision maker into the system. In addition to that, a friendly working environment is also presented, which brings together the human judgement, the adaptability to environment and the computerised information.展开更多
Curriculum design is an aspect of education profession which focuses on developing curricula for students.Educators will take many factors in consideration when design a curriculum.In practical teaching,teacher as dec...Curriculum design is an aspect of education profession which focuses on developing curricula for students.Educators will take many factors in consideration when design a curriculum.In practical teaching,teacher as decision makers to design an appropriate curricu lum and teaching activities play an important part in the whole teaching and learning.Many classroom teachers are working with students of different levels of ability,and they need to be able to adjust the curriculum to keep all of the students engaged and learning.It may also be necessary to change the pace of a curriculum to deal with problems as they arise.The essay analyse five parts in designing the curriculum as a teacher decision maker and get a conclusion according to the whole analysis course.展开更多
A hybrid control system is composed of three boxes which are analogous box, digital time box and decision maker box. A hierarchical structure of decision maker in hybrid control systems is presented in this paper, whi...A hybrid control system is composed of three boxes which are analogous box, digital time box and decision maker box. A hierarchical structure of decision maker in hybrid control systems is presented in this paper, which is that decision maker consists of two components, i.e., policy decision and coordination. Policy decision can design coordination and digital time box. And policy decision consists of two parts, i.e., steady policy decision and transient policy decision. In general,steady policy decision corresponds to steady requirements and transient policy decision corresponds to transient requirements in systems. A chemical concentration control system severs an illustrative example to show the features of the hierarchical decision maker.展开更多
The presently existing decision making method for problem of goal type, i.e. the goal programming, is popular to some extent. In this paper we analyzed the features of the problem and the method,based on which we foun...The presently existing decision making method for problem of goal type, i.e. the goal programming, is popular to some extent. In this paper we analyzed the features of the problem and the method,based on which we found some defects of the method and pointed out these defects. To overcome these defects we absorbed the spirit and exploited concepts of evaluation criterion and the fault measure of evaluation criterion. We proposed and applied a method with an evaluation criterion, after which we also p...展开更多
A distributed blackboard decision-making framework for collaborative planning based on nested genetic algorithm (NGA) is proposed. By using blackboard-based communication paradigm and shared data structure, multiple...A distributed blackboard decision-making framework for collaborative planning based on nested genetic algorithm (NGA) is proposed. By using blackboard-based communication paradigm and shared data structure, multiple decision-makers (DMs) can collaboratively solve the tasks-platforms allocation scheduling problems dynamically through the coordinator. This methodo- logy combined with NGA maximizes tasks execution accuracy, also minimizes the weighted total workload of the DM which is measured in terms of intra-DM and inter-DM coordination. The intra-DM employs an optimization-based scheduling algorithm to match the tasks-platforms assignment request with its own platforms. The inter-DM coordinates the exchange of collaborative request information and platforms among DMs using the blackboard architecture. The numerical result shows that the proposed black- board DM framework based on NGA can obtain a near-optimal solution for the tasks-platforms collaborative planning problem. The assignment of platforms-tasks and the patterns of coordination can achieve a nice trade-off between intra-DM and inter-DM coordination workload.展开更多
The neutral grounding mode of medium-voltage distribution network decides the reliability, overvoltage, relay protection and electrical safety. Therefore, a comprehensive consideration of the reliability, safety and e...The neutral grounding mode of medium-voltage distribution network decides the reliability, overvoltage, relay protection and electrical safety. Therefore, a comprehensive consideration of the reliability, safety and economy is particularly important for the decision of neutral grounding mode. This paper proposes a new decision method of neutral point grounding mode for mediumvoltage distribution network. The objective function is constructed for the decision according the life cycle cost. The reliability of the neutral point grounding mode is taken into account through treating the outage cost as an operating cost. The safety condition of the neutral point grounding mode is preserved as the constraint condition of decision models, so the decision method can generate the most economical and reliable scheme of neutral point grounding mode within a safe limit. The example is used to verify the feasibility and effectiveness of the decision method.展开更多
The uncertain multi-attribute decision-making problems because of the information about attribute weights being known partly, and the decision maker's preference information on alternatives taking the form of interva...The uncertain multi-attribute decision-making problems because of the information about attribute weights being known partly, and the decision maker's preference information on alternatives taking the form of interval numbers complementary to the judgment matrix, are investigated. First, the decision-making information, based on the subjective uncertain complementary preference matrix on alternatives is made uniform by using a translation function, and then an objective programming model is established. The attribute weights are obtained by solving the model, thus the overall values of the alternatives are gained by using the additive weighting method. Second, the alternatives are ranked, by using the continuous ordered weighted averaging (C-OWA) operator. A new approach to the uncertain multi-attribute decision-making problems, with uncertain preference information on alternatives is proposed. It is characterized by simple operations and can be easily implemented on a computer. Finally, a practical example is illustrated to show the feasibility and availability of the developed method.展开更多
Climate researchers have observed that the carbon dioxide (CO2) concentration in the atmosphere have been growing significantly over the past century. CO2 from energy represents about 75% of the greenhouse gas (GHG...Climate researchers have observed that the carbon dioxide (CO2) concentration in the atmosphere have been growing significantly over the past century. CO2 from energy represents about 75% of the greenhouse gas (GHG) emissions for Annex B (Developed) countries, and over 60% of global emissions. Because of impermeable cap rocks hydrocarbon reservoirs are able to sequester CO〉 In addition, due to high-demand for oil worldwide, injection of CO2 is a useful way to enhance oil production. Hence, applying an efficient method to co-optimize CO2 storage and oil production is vital. Lack of suitable optimization techniques in the past led most multi-objective optimization problems to be tackled in the same way as a single objective optimization issue. However, there are some basic differences between the multi and single objective optimization methods. In this study, by using a non- dominated sorting genetic algorithm (NSGA-II) for an oil reservoir, some appropriate scenarios are proposed based on simultaneous gas storage and enhanced oil recovery optimization. The advantages of this method allow us to amend production scenarios after implementing the optimization process, by regarding the variation of economic parameters such as oil price and CO2 tax. This leads to reduced risks and time duration of making new decisions based on upcoming situations.展开更多
A context-aware privacy protection framework was designed for context-aware services and privacy control methods about access personal information in pervasive environment. In the process of user's privacy decision, ...A context-aware privacy protection framework was designed for context-aware services and privacy control methods about access personal information in pervasive environment. In the process of user's privacy decision, it can produce fuzzy privacy decision as the change of personal information sensitivity and personal information receiver trust. The uncertain privacy decision model was proposed about personal information disclosure based on the change of personal information receiver trust and personal information sensitivity. A fuzzy privacy decision information system was designed according to this model. Personal privacy control policies can be extracted from this information system by using rough set theory. It also solves the problem about learning privacy control policies of personal information disclosure.展开更多
Unlike the case in Mediterranean countries, where olive oil consumption is driven by habit or tradition, in a population where olive oil consumption rates are considerably low, it appears reasonable to suppose that th...Unlike the case in Mediterranean countries, where olive oil consumption is driven by habit or tradition, in a population where olive oil consumption rates are considerably low, it appears reasonable to suppose that the initial decision to buy a fairly expensive product—as is the case with olive oil in the Uruguayan market—may result from an individual’s overall interest in health-related issues and/or their acquaintance with relevant nutritional properties of the particular product—in this case, olive oil. Consumer subjective and objective knowledge, interest in health-related issues, and demographic variables were studied for their potential relationship (explanatory capacity) with olive oil consumption frequency, using a sample of 256 inhabitants of Montevideo (Uruguay). Several of the studied variables were found to relate to olive oil consumption, such as subjective and objective knowledge, age, education level, marital status, and interest in health-related issues. Subjective knowledge was found to have the highest explanatory capacity. An increase in subjective knowledge is therefore expected to lead to an increase in consumption frequency among regular olive oil consumers, while it may also encourage less frequent or non-consumers to purchase olive oil and become acquainted with the product.展开更多
In this paper a Vertex Covering Obnoxious Facility Location model on a Plane has been designed with a combination of three interacting criteria as follows: 1) Minimize the overall importance of the various exist-ing f...In this paper a Vertex Covering Obnoxious Facility Location model on a Plane has been designed with a combination of three interacting criteria as follows: 1) Minimize the overall importance of the various exist-ing facility points;2) Maximize the minimum distance from the facility to be located to the existing facility points;3) Maximize the number of existing facility points covered. Area restriction concept has been incor-porated so that the facility to be located should be within certain restricted area. The model developed here is a class of maximal covering problem, that is covering maximum number of points where the facility is within the upper bounds of the corresponding mth feasible region Two types of compromise solution methods have been designed to get a satisfactory solution of the multi-objective problem. A transformed non- linear programming algorithm has been designed for the proposed non-linear model. Rectilinear dis-tance norm has been considered as the distance measure as it is more appropriate to various realistic situa-tions. A numerical example has been presented to illustrate the solution algorithm.展开更多
文摘A class of interactive multi objective decision making method by means of evaluation criterion is proposed for problems with linear value function,in which case,the decision maker(DM) usually has only unwhole information of weights for objectives. The concept of fault measure of the evaluation criterion is proposed to measure the deviation of the evaluation criterion from the DMs preference structure.The approach to obtain an upper boundary of fault measure of an evaluation criterion,and the approach to modify the evaluation criterion to be one with smaller fault measure,and the approach to obtain a pre optimized objective set by evaluation criterion with certain fault measure are also proposed.
文摘In this paper, for multi objective decision making, the defects on the commonly used interactive methods based on the satisfactoriness criterion is studied. Then a class of two stage interactive method based on the satisfactoriness criterion is proposed for improvement with the satisfactoriness criterion being determined through the collection of the decision makers preference information. An application example is presented for illustration of applicability of the method.
基金supported by the National Natural Science Foundation of China(51405499)
文摘A decision support system, including a multi-objective optimization framework and a multi-attribute decision making approach is proposed for satellite equipment layout. Firstly, given three objectives (to minimize the C.G. offset, the cross moments of inertia and the space debris impact risk), we develop a threedimensional layout optimization model. Unlike most of the previous works just focusing on mass characteristics of the system, a space debris impact risk index is developed. Secondly, we develop an efficient optimization framework for the integration of computer-aided design (CAD) software as well as the optimization algorithm to obtain the Pareto front of the layout optimization problem. Thirdly, after obtaining the candidate solutions, we present a multi-attribute decision making approach, which integrates the smart Pareto filter and the correlation coefficient and standard deviation (CCSD) method to select the best tradeoff solutions on the optimal Pareto fronts. Finally, the framework and the decision making approach are applied to a case study of a satellite platform.
文摘The spectral analysis of simulated N-team of interacting decision makers with bounded rationality constraints of Oladejo, which assumes triangular probability density function of command inputs is hereby restructured and analysed, to have hierarchical command inputs that are predicated on order statistics distributions. The results give optimal distributions.
基金SupportedbytheNationalNaturalScienceFoundationofChina (No .60 1 340 1 0 )
文摘A new fuzzification method for multi-objective decision-making and selective sorting is proposed on the basis of the fuzzy consistent relation, and the specific algorithm is presented. The method is applied to the evaluation of highway planning of Zhanjiang city. To decrease the subjectivity in the process of decision-making, the LOWA operator is introduced, and a discussion on how to select appropriate weights involved in multi-objective sorting is made. It is concluded that it is feasible to apply the fuzzy consistent relation to multi-objective decision-making analysis, and the improved fuzzication method is workable.
文摘In order to solve existing problems about the method of establishing traditional system structure of decision support system(DSS), O S chart is applied to describe object oriented system structure of general DSS, and a new method of eight specific steps is proposed to establish object oriented system structure of DSS by using the method of O S chart, which is applied successfully to the development of the DSS for the energy system ecology engineering research of the Wangheqiu country. Supplying many scientific effective computing models, decision support ways and a lot of accurate reliable decision data, the DSS plays a critical part in helping engineering researchers to make correct decisions. Because the period for developing the DSS is relatively shorter, the new way improves the efficiency of establishing DSS greatly. It also makes the DSS of system structure more flexible and easy to expand.
文摘The modern war features a highly distributed coordination. In the face of great time constrains, it is important to change command organizations to adapt to the real environment. Therefore it's a key step to set up adaptive C2 teams. In this paper, the relational problems about distributed C2 organizational structure adaptation are discussed, and the methodology for team decision making design based on the object oriented technique is studied.
文摘Multiple objects decision is used widely in many complex fields. In this paper an idea is provided to construct a train diagram intelligent multiple objects decision support system (TDIMODSS). And the reference point method is used to solve the complicated and large scale problems of making and adjusting train schedule. This paper focuses on the principle and framework of the model base, knowledge base of train diagram. It is shown that the TDIMODSS can solve the problems and their uncertainty in making train diagram, and can combine the expert knowledge, experience and judgement of a decision maker into the system. In addition to that, a friendly working environment is also presented, which brings together the human judgement, the adaptability to environment and the computerised information.
文摘Curriculum design is an aspect of education profession which focuses on developing curricula for students.Educators will take many factors in consideration when design a curriculum.In practical teaching,teacher as decision makers to design an appropriate curricu lum and teaching activities play an important part in the whole teaching and learning.Many classroom teachers are working with students of different levels of ability,and they need to be able to adjust the curriculum to keep all of the students engaged and learning.It may also be necessary to change the pace of a curriculum to deal with problems as they arise.The essay analyse five parts in designing the curriculum as a teacher decision maker and get a conclusion according to the whole analysis course.
文摘A hybrid control system is composed of three boxes which are analogous box, digital time box and decision maker box. A hierarchical structure of decision maker in hybrid control systems is presented in this paper, which is that decision maker consists of two components, i.e., policy decision and coordination. Policy decision can design coordination and digital time box. And policy decision consists of two parts, i.e., steady policy decision and transient policy decision. In general,steady policy decision corresponds to steady requirements and transient policy decision corresponds to transient requirements in systems. A chemical concentration control system severs an illustrative example to show the features of the hierarchical decision maker.
文摘The presently existing decision making method for problem of goal type, i.e. the goal programming, is popular to some extent. In this paper we analyzed the features of the problem and the method,based on which we found some defects of the method and pointed out these defects. To overcome these defects we absorbed the spirit and exploited concepts of evaluation criterion and the fault measure of evaluation criterion. We proposed and applied a method with an evaluation criterion, after which we also p...
基金supported by the National Aerospace Science Foundation of China(20138053038)the Graduate Starting Seed Fund of Northwestern Polytechnical University(Z2015111)
文摘A distributed blackboard decision-making framework for collaborative planning based on nested genetic algorithm (NGA) is proposed. By using blackboard-based communication paradigm and shared data structure, multiple decision-makers (DMs) can collaboratively solve the tasks-platforms allocation scheduling problems dynamically through the coordinator. This methodo- logy combined with NGA maximizes tasks execution accuracy, also minimizes the weighted total workload of the DM which is measured in terms of intra-DM and inter-DM coordination. The intra-DM employs an optimization-based scheduling algorithm to match the tasks-platforms assignment request with its own platforms. The inter-DM coordinates the exchange of collaborative request information and platforms among DMs using the blackboard architecture. The numerical result shows that the proposed black- board DM framework based on NGA can obtain a near-optimal solution for the tasks-platforms collaborative planning problem. The assignment of platforms-tasks and the patterns of coordination can achieve a nice trade-off between intra-DM and inter-DM coordination workload.
文摘The neutral grounding mode of medium-voltage distribution network decides the reliability, overvoltage, relay protection and electrical safety. Therefore, a comprehensive consideration of the reliability, safety and economy is particularly important for the decision of neutral grounding mode. This paper proposes a new decision method of neutral point grounding mode for mediumvoltage distribution network. The objective function is constructed for the decision according the life cycle cost. The reliability of the neutral point grounding mode is taken into account through treating the outage cost as an operating cost. The safety condition of the neutral point grounding mode is preserved as the constraint condition of decision models, so the decision method can generate the most economical and reliable scheme of neutral point grounding mode within a safe limit. The example is used to verify the feasibility and effectiveness of the decision method.
文摘The uncertain multi-attribute decision-making problems because of the information about attribute weights being known partly, and the decision maker's preference information on alternatives taking the form of interval numbers complementary to the judgment matrix, are investigated. First, the decision-making information, based on the subjective uncertain complementary preference matrix on alternatives is made uniform by using a translation function, and then an objective programming model is established. The attribute weights are obtained by solving the model, thus the overall values of the alternatives are gained by using the additive weighting method. Second, the alternatives are ranked, by using the continuous ordered weighted averaging (C-OWA) operator. A new approach to the uncertain multi-attribute decision-making problems, with uncertain preference information on alternatives is proposed. It is characterized by simple operations and can be easily implemented on a computer. Finally, a practical example is illustrated to show the feasibility and availability of the developed method.
文摘Climate researchers have observed that the carbon dioxide (CO2) concentration in the atmosphere have been growing significantly over the past century. CO2 from energy represents about 75% of the greenhouse gas (GHG) emissions for Annex B (Developed) countries, and over 60% of global emissions. Because of impermeable cap rocks hydrocarbon reservoirs are able to sequester CO〉 In addition, due to high-demand for oil worldwide, injection of CO2 is a useful way to enhance oil production. Hence, applying an efficient method to co-optimize CO2 storage and oil production is vital. Lack of suitable optimization techniques in the past led most multi-objective optimization problems to be tackled in the same way as a single objective optimization issue. However, there are some basic differences between the multi and single objective optimization methods. In this study, by using a non- dominated sorting genetic algorithm (NSGA-II) for an oil reservoir, some appropriate scenarios are proposed based on simultaneous gas storage and enhanced oil recovery optimization. The advantages of this method allow us to amend production scenarios after implementing the optimization process, by regarding the variation of economic parameters such as oil price and CO2 tax. This leads to reduced risks and time duration of making new decisions based on upcoming situations.
基金Supported by the National Natural Science Foundation of China (60573119, 604973098) and IBM joint project
文摘A context-aware privacy protection framework was designed for context-aware services and privacy control methods about access personal information in pervasive environment. In the process of user's privacy decision, it can produce fuzzy privacy decision as the change of personal information sensitivity and personal information receiver trust. The uncertain privacy decision model was proposed about personal information disclosure based on the change of personal information receiver trust and personal information sensitivity. A fuzzy privacy decision information system was designed according to this model. Personal privacy control policies can be extracted from this information system by using rough set theory. It also solves the problem about learning privacy control policies of personal information disclosure.
文摘Unlike the case in Mediterranean countries, where olive oil consumption is driven by habit or tradition, in a population where olive oil consumption rates are considerably low, it appears reasonable to suppose that the initial decision to buy a fairly expensive product—as is the case with olive oil in the Uruguayan market—may result from an individual’s overall interest in health-related issues and/or their acquaintance with relevant nutritional properties of the particular product—in this case, olive oil. Consumer subjective and objective knowledge, interest in health-related issues, and demographic variables were studied for their potential relationship (explanatory capacity) with olive oil consumption frequency, using a sample of 256 inhabitants of Montevideo (Uruguay). Several of the studied variables were found to relate to olive oil consumption, such as subjective and objective knowledge, age, education level, marital status, and interest in health-related issues. Subjective knowledge was found to have the highest explanatory capacity. An increase in subjective knowledge is therefore expected to lead to an increase in consumption frequency among regular olive oil consumers, while it may also encourage less frequent or non-consumers to purchase olive oil and become acquainted with the product.
文摘In this paper a Vertex Covering Obnoxious Facility Location model on a Plane has been designed with a combination of three interacting criteria as follows: 1) Minimize the overall importance of the various exist-ing facility points;2) Maximize the minimum distance from the facility to be located to the existing facility points;3) Maximize the number of existing facility points covered. Area restriction concept has been incor-porated so that the facility to be located should be within certain restricted area. The model developed here is a class of maximal covering problem, that is covering maximum number of points where the facility is within the upper bounds of the corresponding mth feasible region Two types of compromise solution methods have been designed to get a satisfactory solution of the multi-objective problem. A transformed non- linear programming algorithm has been designed for the proposed non-linear model. Rectilinear dis-tance norm has been considered as the distance measure as it is more appropriate to various realistic situa-tions. A numerical example has been presented to illustrate the solution algorithm.