Programming Technique For Multidimensional Analysis Research Articles

Fuzzy mathematical programming approach to heterogeneous multiattribute decision-making with interval-valued intuitionistic fuzzy truth degrees

Considering the hesitancy degrees on pair-wise comparisons of alternatives as interval-valued intuitionistic fuzzy (IVIF) sets (IVIFSs), we develop a new fuzzy mathematical programming method for solving heterogeneous multiattribute decision-making problems based on the Linear Programming Technique for Multidimensional Analysis of Preference. In this method, IVIFSs, intuitionistic fuzzy sets (IFSs), trapezoidal fuzzy numbers, linguistic variables, intervals and real numbers are used to represent multiple types of attribute values and the attribute weights are not completely known. The preference relations between alternatives given by decision maker are expressed with IVIFSs of ordered pairs of alternatives. The consistency and inconsistency indices are defined as IVIFSs on the basis of comparisons of alternatives with IVIF truth degrees. The attribute weights and fuzzy ideal solution (FIS) are estimated through constructing a fuzzy mathematical programming model, which is solved by the technically developed method of IVIF mathematical programming. Hereby the distances of alternatives to the FIS are computed to rank the alternatives. Some generalization and discussion on the constructed IVIF mathematical programming model are also presented. A green supplier selection example is provided to illustrate the effectiveness of the proposed model and method. The comparison analyses verify the superiorities of the proposed method.

Optimization performance and thermodynamic analysis of an irreversible nano scale Brayton cycle operating with Maxwell–Boltzmann gas

In last decades, nano technology developed. Since, nano scale thermal cycles will be possibly employed in the near future. In this research, a nano scale irreversible Brayton cycle is investigated thermodynamically for optimizing the performance of the aforementioned cycle. Ideal Maxwell–Boltzmann gas is employed as a working fluid in the system. In this paper, two scenarios are employed in the multi-objective optimization process; however, the outcomes of each of the scenarios are evaluated independently. In the first scenario, in order to maximize the dimensionless Maximum available work and energy efficiency of the system, multi-objective optimization algorithms is employed. Furthermore, in the second scenario, two objective functions comprising the dimensionless Maximum available work and the dimensionless Ecological function are maximized concurrently via employing multi objective optimization algorithms. The multi objective evolutionary approaches on the basis of non-dominated sorting genetic algorithm method are employed in this paper. Decision making is done via three methods including linear programming techniques for multidimensional analysis of preference and Technique for order of preference by similarity to ideal solution and Bellman–Zadeh. Finally, error analysis is implemented on the results obtained from each scenario.

The robust linear programming technique for multi-dimensional analysis of preferences

The linear programming technique for multi–dimensional analysis of preferences (LINMAP) is one of the noted multi–attributes decision making (MADM) techniques and has been implemented in crisp and fuzzy environments. Robust optimisation attempts to obtain a solution which is feasible in all circumstances arising due to the uncertainty of parameters. The purpose of this study is to extend the LINMAP method for addressing robustness in MADM problems. In this methodology, robust optimisation concepts are used to describe robustness in decision information and decision making processes. Each alternative is evaluated based on its weighted distance to a robust positive ideal solution (RPIS). The RPIS and the robust weights of attributes are estimated using a new robust linear programming technique. Finally, Monte Carlo simulation is applied to test the robustness of the solution. A numerical example is provided to illustrate the effectiveness of the methodology.

Integrating LINMAP and TOPSIS methods for hesitant fuzzy multiple attribute decision making

The linear programming technique for multidimensional analysis of preference LINMAP and the technique for order preference by similarity to ideal solution TOPSIS are two well-known methods for deal...

Integrating LINMAP and TOPSIS methods for hesitant fuzzy multiple attribute decision making

The linear programming technique for multidimensional analysis of preference (LINMAP) and the technique for order preference by similarity to ideal solution (TOPSIS) are two well-known methods for dealing with the multiple attribute decision making (MADM) problems. In this paper, we further extend the LINMAP to accommodate hesitant fuzzy environment and propose a new approach to solve the MADM problems with hesitant fuzzy information. Then, an integrated method that combines the LINMAP and TOPSIS is developed. In this methodology, we take advantage of the LINMAP to determine the attribute weights objectively and thus overcome the drawbacks of the TOPSIS. Meanwhile the TOPSIS that considers both the positive ideal solution (PIS) and the negative ideal solution (NIS) can make up the disadvantages of the LINMAP. In order to measure consistency and inconsistency between the ranking order of alternatives and the decision maker's preference, two indices based on PIS and NIS are defined. Moreover, a linear programming model that can be used for minimizing the total inconsistency is constructed to determine the attribute weights. By using the TOPSIS, we obtain the most appropriate alternative. Finally, two numerical examples are given to demonstrate the implementation process of the developed approach.

An interval type-2 fuzzy LINMAP method with approximate ideal solutions for multiple criteria decision analysis

The purpose of this paper is to develop a linear programming technique for multidimensional analysis of preference (LINMAP) to address multiple criteria decision analysis problems within the interval type-2 fuzzy environment based on interval type-2 trapezoidal fuzzy numbers. Considering the issue of anchor dependency, we use multiple anchor points in the decision-making process and employ approximate positive-ideal and negative-ideal solutions as the points of reference. Selected useful properties of the approximate ideal solutions are also investigated. In contrast to the classical LINMAP methods, this paper directly generates approximate ideal solutions from the characteristics of all alternatives. Next, this work presents the concept of closeness-based indices using Minkowski distances with approximate ideal solutions to develop a new approach for determining measurements of consistency and inconsistency. Under incomplete preference information on paired comparisons of the alternatives, this paper provides a novel method that uses the concept of comprehensive closeness-based indices to measure the poorness of fit and the goodness of fit. By applying the consistency indices and inconsistency indices, this work formulates an optimization problem that can be solved for the optimal weights of the criteria and thus acquires the best compromise alternative. Additionally, this paper explores the problem of supplier selection and conducts a comparative discussion to validate the effectiveness and applicability of the proposed interval type-2 fuzzy LINMAP method with approximate ideal solutions. Furthermore, the proposed method is applied to address a marketplace decision difficulty (MPDD)-prone decision-making problem to provide additional contributions for practical implications.

The Inclusion-Based LINMAP Method for Multiple Criteria Decision Analysis Within an Interval-Valued Atanassov's Intuitionistic Fuzzy Environment

The purpose of this paper is to develop an inclusion-based LINMAP (i.e., Linear Programming Technique for Multidimensional Analysis of Preference) method for multiple criteria decision analysis that is based on interval-valued Atanassov's intuitionistic fuzzy sets. Using the inclusion comparison possibility in the interval-valued Atanassov's intuitionistic fuzzy context, an inclusion-based index of interval-valued Atanassov's intuitionistic fuzzy numbers is proposed that considers positive and negative ideals. An inclusion-based consistency index and an inclusion-based inconsistency index to measure the concordance and discordance, respectively, between paired comparison judgments are suggested. An inclusion-based LINMAP model is constructed using a linear programming technique to determine the optimal criterion weights and obtain the corresponding comprehensive inclusion-based index for each alternative. Then, the priority order of the alternatives can be acquired according to the comprehensive inclusion-based indices. The feasibility of the proposed method is illustrated using a practical problem that relates to the selection of bridge construction methods. A comparative analysis of other relevant decision-making methods is conducted to validate the effectiveness of the developed methodology.

Interval programming method for hesitant fuzzy multi-attribute group decision making with incomplete preference over alternatives

The aim of this study is to employ the main structure of LINMAP (LINear programming technique for Multidimensional Analysis of Preference) to propose an interval programming method for solving multi-attribute group decision making (MAGDM) problems in which the ratings of alternatives are taken as hesitant fuzzy elements (HFEs) and all pair-wise comparison judgments over alternatives are represented by interval numbers. The contribution of this study is fivefold: (1) we define the new consistency and inconsistency indices; (2) we construct an interval programming model to determine the hesitant fuzzy positive ideal solution and the optimal weights of attributes, and at the same time present a decision algorithm; (3) we discuss several special cases of the proposed model in detail; (4) we show that compared with intuitionistic fuzzy LINMAP method (Li et al., 2010), the proposed approach reveals more useful information including the interval preference information, and does not need to transform HFEs into intuitionistic fuzzy numbers but directly deals with MAGDM problems and thus obtains better final decision results; and (5) we demonstrate the applicability and implementation process of the proposed approach by using an energy project selection example.

Thermodynamic design of Stirling engine using multi-objective particle swarm optimization algorithm

In the recent years, the interest in Stirling engine has remarkably increased due to its ability to use any heat source from outside including solar energy, fossil fuels and biomass. A large number of studies have been done on Stirling cycle analysis. In the present study, a mathematical model based on thermodynamic analysis of Stirling engine considering regenerative losses and internal irreversibilities has been developed. Power output, thermal efficiency and the cycle irreversibility parameter of Stirling engine are optimized simultaneously using Particle Swarm Optimization (PSO) algorithm, which is more effective than traditional genetic algorithms. In this optimization problem, some important parameters of Stirling engine are considered as decision variables, such as temperatures of the working fluid both in the high temperature isothermal process and in the low temperature isothermal process, dead volume ratios of each heat exchanger, volumes of each working spaces, effectiveness of the regenerator, and the system charge pressure. The Pareto optimal frontier is obtained and the final design solution has been selected by Linear Programming Technique for Multidimensional Analysis of Preference (LINMAP). Results show that the proposed multi-objective optimization approach can significantly outperform traditional single objective approaches.

A bi-level constraint-oriented outsourcing framework for orchestration of an ERP system

Outputs of each enterprise resource planning (ERP) process in an ERP system could constraint outputs of the next ERP processes. Therefore, it is necessary to determine the ability of ERP processes to support the orchestration of an ERP system. This paper presents a bi-level constraint-oriented outsourcing framework to identify any ERP process that effects on the orchestration of an ERP system. The contribution of the proposed bi-level constraint-oriented outsourcing framework for orchestration of ERP is twofold: (1) it develops the traditional constraints management from a crisp single-criteria environment to a fuzzy multi-criteria environment; and (2) it develops a linear programming technique for multidimensional analysis of preference (LINMAP) model to a fuzzy group bi-level LINMAP model. A case study demonstrates the applicability of the proposed constraint-oriented outsourcing framework for orchestration of ERP modules and processes.

Identification of e-Health reference architecture using a bi-objective medical informatics decision support framework: the optimal lean and six sigma alignment

Because of the trade-off between e-Health Lean and Six Sigma, their independent implementation does not ensure the optimality of patient-centric service deliver in e-Health architectures. There is a significant gap in the current research literature to utilize the optimal Lean and Six Sigma alignment in e-Health architectures. Therefore, this paper develops a fuzzy group bi-objective medical informatics decision support framework to optimize Lean and Six Sigma alignment in the identification of e-health reference architecture. As The e-Health architecture is made up of the best-practice e-Health modules and layers, a fuzzy group bi-objective Linear Programming technique for Multidimensional Analysis of Preference (LINMAP) is presented: (1) to demonstrate conformity of core modules and layers of e-Health architectures with Lean criteria and Six Sigma criteria; and (2) to optimize the strategic Lean and Six Sigma alignment and identify e-Health reference architecture.

Fuzzy linear programming approach to multiattribute decision making with multiple types of attribute values and incomplete weight information

In the classical Linear Programming Technique for Multidimensional Analysis of Preference (LINMAP), the decision maker (DM) gives the pair-wise comparisons of alternatives with crisp truth degree 0 or 1. However, in the real world, DM is not sure enough in all comparisons and can express his/her opinion with some fuzzy truth degree. Thus, DM's preferences are given through pair-wise comparisons of alternatives with fuzzy truth degrees, which may be represented as trapezoidal fuzzy numbers (TrFNs). Considered such fuzzy truth degrees, the aim of this paper is to develop a new fuzzy linear programming technique for solving multiattribute decision making (MADM) problems with multiple types of attribute values and incomplete weight information. In this method, TrFNs, real numbers, and intervals are used to represent the multiple types of decision information. The fuzzy consistency and inconsistency indices are defined as TrFNs due to the alternatives’ comparisons with fuzzy truth degrees. Hereby a new fuzzy linear programming model is constructed and solved by the possibility linear programming method with TrFNs developed in this paper. The fuzzy ideal solution (IS) and the attribute weights are then obtained. The distances of alternatives from the fuzzy IS can be calculated to determine their ranking order. The implementation process of the method proposed in this paper is illustrated with a strategy partner selection example. The comparison analyzes show that the method proposed in this paper generalizes the classical LINMAP, fuzzy LINMAP and possibility LINMAP.

An interval-valued intuitionistic fuzzy LINMAP method with inclusion comparison possibilities and hybrid averaging operations for multiple criteria group decision making

An interval-valued intuitionistic fuzzy set contains membership and non-membership values that are crisp intervals and represent an extension of the ordinary fuzzy sets that are widely used because of their usefulness in handling imprecise or uncertain information. The linear programming technique for multidimensional analysis of preference (LINMAP) is a representative decision-making method with respect to preference information for given alternatives. In this paper, we present a new linear programming technique with weight assessment, an extended LINMAP method, for addressing multiple criteria group decision-making problems in the interval-valued intuitionistic fuzzy framework. With consideration given to the degrees of relative agreement and the importance weights of multiple decision makers, this paper presents an inclusion-based hybrid averaging operation with an inclusion comparison approach for forming a collective decision environment. The concept of inclusion-based indices that relate to anchor dependency with multiple points of reference is developed as the core of the extended LINMAP method. We also establish a linear programming model to handle the incomplete preference information for alternatives. The optimal weights of the criteria can be determined, and the priority order of the alternatives can be obtained according to the resulting comprehensive inclusion-based indices. The feasibility and applicability of the proposed methods are illustrated with an example addressing graduate admission, and a comparative analysis is performed with another interval-valued intuitionistic fuzzy LINMAP approach to validate the effectiveness of the proposed methodology.

An Extended LINMAP Method for Multi-Attribute Group Decision Making under Interval-Valued Intuitionistic Fuzzy Environment

The linear programming technique for multidimensional analysis of preference (LINMAP) is one of the well-known methods for multiple attribute group decision making (MAGDM). In this paper, we extend the LINMAP method to solve MAGDM problems in interval-valued intuitionistic fuzzy environment in which all the preference information provided by the decision- makers is presented as interval-valued intuitionistic fuzzy decision matrices and the preference information about the alterna- tives is completely unknown. We introduce two definitions of distances between interval-valued intuitionistic fuzzy sets. To calculate the weights of attributes we develop a new linear programming model based on the group consistency and incon- sistency index defined on the basis of pairwise comparison preference relations on alternatives given by the decision makers, the weighted distance of each alternative to the interval-valued intuitionistic fuzzy positive ideal solution can be calculated to determine the ranking order of all alternatives for the decision makers, and the ranking order of alternatives and the best alternative(s) for the group are generated by using the Borda's function.

A fuzzy group linear programming technique for multidimentional analysis of preference

Although crisp data are fundamentally indispensable in the conventional linear programming technique for multidimensional analysis of preference LINMAP, the observed values in the real-world problems are often imprecise or vague. These imprecise or vague data can be suitably characterized by linguistic terms which are fuzzy in nature. LINMAP has been widely used to solve multi-attribute decision making MADM problems. This paper extends the conventional LINMAP model to a fuzzy group decision making framework using trapezoidal fuzzy numbers. The ranking approach is used to transform the fuzzy model into a crisp model. The fuzzy LINMAP method proposed in this paper is a simple and effective tool for tackling the uncertainty and imprecision associated with the group MADM problems. A case study in fast food industry is presented to demonstrate the applicability of the proposed framework and exhibit the efficacy of the procedures.

Fuzzy LINMAP approach to heterogeneous MADM considering comparisons of alternatives with hesitation degrees

Multiattribute decision making (MADM) with multiple formats of information, which is called heterogeneous MADM for short, is very complex and interesting in applications. The purpose of this paper is to extend the Linear Programming Technique for Multidimensional Analysis of Preference (LINMAP) for solving heterogeneous MADM problems which involve intuitionistic fuzzy (IF) sets (IFSs), trapezoidal fuzzy numbers (TrFNs), intervals and real numbers. In this method, DM's preference is given through pair-wise comparisons of alternatives with hesitation degrees which are represented as IFSs. The IF consistency and inconsistency indices are defined on the basis of pair-wise comparisons of alternatives. Each alternative is assessed on the basis of its distance to a fuzzy ideal solution (FIS) unknown a priori. Based on the defined IF consistency and inconsistency indices, we construct a new fuzzy mathematical programming model, which is solved by the developed method of fuzzy mathematical programming with IFSs. Once the FIS and the attribute weights are obtained, we can calculate the distances of all alternatives to the FIS, which are used to determine the ranking order of the alternatives. A supplier selection example is presented to demonstrate the validity and applicability of the proposed method.

EXTENSIONS OF LINMAP MODEL FOR MULTI CRITERIA DECISION MAKING WITH GREY NUMBERS

The linear programming technique for multidimensional analysis of preference, known as LINMAP is one of the existing well-known ideal seeking methods for multi attribute decision making problems. This method originally is proposed under crisp and deterministic circumstances. However, uncertainty is an indubitable property of decision making problems. In this paper, a new version of LINMAP-G is proposed where the decision maker's judgments are expressed as grey numbers. Like original LINMAP method, the grey ideal solution and attributes weight vector is determined and alternatives are ranked according to their weighted distance from determined ideal point. Application of the proposed method is illustrated in two numerical examples.

WEEE treatment strategies’ evaluation using fuzzy LINMAP method

Electrical and electronic equipments (EEE) have already begun to be accumulated at the garbage dumps. This garbage accumulation brings big danger to the environment and human health. That’s why one should look for exploring the ways to dispose of these wastes and emphasize the waste treatment strategies. Waste treatment strategies also contribute either to local or global economies by creating a new sector and employment opportunities, and by reducing use of scarce resources. In this paper, a linear programming technique for multidimensional analysis of preference (LINMAP) method for solving multi-attribute group decision making (MAGDM) problems with preference information on alternatives in fuzzy environment is developed. The aim is to develop a fuzzy LINMAP model for evaluation and select of a waste treatment strategy for EEE. Thus, three treatment strategy alternatives and eight criteria are determined. The best strategy is selected and the key criterion is found accordingly. The best alternative is found to be treating waste electrical and electronic equipments (WEEE) by reuse and recycling methods.

Risk identification and assessment for build–operate–transfer projects: A fuzzy multi attribute decision making model

In recent years, BOT approach has provided an increasingly popular project financing to move toward infrastructure development in Asian countries such as Iran. There are many complexities in projects because of the variety of factors in project’s trend and also the dependence of project on mainly national factors. Due to these complexities and their long-term operating, the projects meet with uncertainty and numerous risks. In this paper, an attempt is made at identifying common risks in BOT projects. A novel hierarchical structure of risks is presented on the basis of the project-oriented point of view; next, some effective criteria for risk ranking in BOT projects are introduced. Then, the problem is defined in Fuzzy Multi Attribute Decision Making (FMADM) field. Therefore, Fuzzy Technique for Order Preference by Similarity to Ideal Solution (FTOPSIS) and Fuzzy Linear Programming Technique for Multidimensional Analysis of Preference (FLINMAP) methods are presented in order to rank high risks in BOT projects. In this study, these two methods are compared in four respects: separation among alternatives, fuzzy error in criteria’s weights, risk response planning, and numerousness of alternatives in proportion to criteria. The proposed model is used for identifying and assessing risks in Iran BOT power plant project. Finally, the rankings of high risks are determined according to their results at the end of this paper.

Leveraging technological knowledge transfer by using fuzzy linear programming technique for multiattribute group decision making with fuzzy decision variables

Despite the importance of knowledge transfer for firms involved in foreign direct investment activities, this area has not received appropriate attention from the perspectives of both the knowledge transferor (i.e., MNC parent) and the knowledge recipient. To fill in the gap in the current literature we propose a model to understand the links between criteria complicating the transfer of knowledge and preferences that the company has to focus. This model is based on both the existing literature as well as views of company representatives and provides a useful methodology for identifying decision making problems on the transfer of knowledge. In this paper, we investigate the fuzzy linear programming technique (FLP) to analyze these links and for multiple attribute group decision making (MAGDM) problems with preference information on criteria. To reflect the decision maker’s subjective preference information and to determine the weight vector of attributes, the technique for order preference by similarity to ideal solution (TOPSIS) developed by Hwang and Yoon (1995) and the linear programming technique for multidimensional analysis of preference (LINMAP) developed by Sirinivasan and Shocker (Psychometrica 38:337–369, 1973) are used.