Multidimensional Analysis Of Preference Research Articles

Nitrogen and phosphorus uptake, yield and agronomic traits of oat cultivars as affected by fertilizer N rates under diverse environments

Oat has been gaining renewed interest due to its role in human healthy diet. A field study was conducted across three diverse locations in Canada to determine N and P uptake, agronomic traits and yield performance of 10–12 cultivars under four fertilizer N rates. Our data showed that ‘SA060123’ and ‘OA1331-5’ were the highest-yielding cultivars, and ‘Dieter’ and ‘Morrison’ the lowest, across sites-years. Yield components were altered to adapt to soil-environmental conditions, specifically, panicles m−2 mostly accounted for yield variation at Melfort, seeds panicle−1 and 1000-seed weight at Normandin, and lodging index was an additional yield-determining factor at Ottawa. It was noted that severe crop lodging that occurred mainly at Ottawa, was logically associated with greater accumulation of straw N and plant biomass under high N supply conditions, and that crop lodging displayed a strong correlation with straw P content. Relationship of lodging index and straw P was best-fit into a split-line model with a change-point of 13.6 kg P ha−1, below which lodging rarely occurred. We speculate that high straw P content, induced by external N supply, may have exhibited similar behavior as N in weakening the strength of stem base and anchorage system, leading to crop lodging. This study also demonstrated an interactive genotype-by-environment effect on all traits except for the seed number panicle−1. Multidimensional preference analysis revealed the best performance of ‘SA060123’ for outstanding yield and 'Minstrel' for harvest index, respectively.

Multi-objective optimization of the Stirling heat engine through self-adaptive Jaya algorithm

A Stirling engine presents an excellent theoretical output equivalent to the output of a Carnot engine, and it emits low levels of pollution and requires less maintenance. In this paper, a solar-powered Stirling engine is considered for optimization with multiple criteria. Hence, the present study explores the use of an improved Jaya algorithm called the self-adaptive Jaya algorithm and the basic Jaya algorithm, which are used for maximizing output power and thermal efficiency and minimizing pressure losses of the entire Stirling system. The key feature is that the self-adaptive Jaya algorithm automatically determines the population size. Hence, the user does not need to concentrate on choosing the population size. The comparison of the proposed algorithm is made with those obtained by using the non-dominated sorting genetic-algorithm-II (NSGA-II), an optimizer inbuilt in MATLAB (function gamultiobj), Front-based Yin-Yang-Pair Optimization (FYYPO), Multi-Objective Grey Wolf Optimizers (MOGWOs), Teaching–Learning-Based Optimization (TLBO), tutorial training and self-learning inspired teaching-learning based optimization (TS-TLBO), the decision-making methods like linear programming technique for multi-dimensional analysis of preference (LINMAP), technique for order of preference by similarity to ideal solution (TOPSIS), and Bellman-Zadeh, and experimental results. The results achieved by using Jaya and self-adaptive Jaya algorithms are compared with the results achieved by using the NSGA-II, gamultiobj, FYYPO, MOGWO, TLBO, TS-TLBO, LINMAP, TOPSIS, Bellman-Zadeh, and experimental results. The Jaya algorithm and its improved version are proved to be better compared to other optimization algorithms with respect to the computational effort and function evaluations.

A robust optimization model for a decision-making problem: An application for stock market

In this paper we apply robust linear programming technique for multidimensional analysis of preference (LINMAP) method for a decision making problem. During the last two decades, many methods have been extensively used for decision making problems. However, there is no investigation among many existing studies where the uncertainty in data is possible. The robust LINMAP method with the assumption of uncertainty on parameters is implemented in the stock market in order to rank priorities of the stocks.

Influence of the addition of microencapsulated Swiss cheese bioaroma on the technical and sensory qualities of cheese bread

This study evaluated the influence of the powdered bioaroma of Swiss cheese on the technical and sensory qualities of cheese bread. The methodology of the internal preference mapping was applied. The results revealed that cheese breads containing powdered bioaroma of Swiss cheese showed high sensorial quality in terms of aroma, flavour, global acceptance and intent to purchase. The addition of the powdered bioaroma positively influenced the texture, the main parameter of acceptance. The technical quality parameters of density and water activity were constant with increasing flavouring concentration, except for samples with 6.6% Swiss cheese bioaroma powder that showed higher values of density. The multidimensional preference analysis confirmed the anova results, allowing for the clear observation of the segmentation of consumers according to the sensory characteristics of the samples (0.0, 2.2, 4.4 and 6.6% bioaroma). Sensory analysis showed that consumers preferred samples having 6.6% bioaroma.

Optimal design of Stirling heat engine using an advanced optimization algorithm

The Stirling engine presents an excellent theoretical output equivalent to the output of Carnot engine and it is less pollutant and requires little maintenance. In this paper, Stirling heat engine is considered for optimization with multiple criteria. A recently developed advanced optimization algorithm namely “teaching–learning-based optimization (TLBO) algorithm” is used for maximization of output power, minimization of pressure losses and maximization of the thermal efficiency of the entire solar Stirling system. The comparisons of the proposed algorithm are made with those obtained by using the decision-making methods like linear programming technique for multi-dimensional analysis of preference (LINMAP), technique for order of preference by similarity to ideal solution (TOPSIS) and fuzzy Bellman–Zadeh method that have used the Pareto frontier gained through non-dominated sorting genetic algorithm-II (NSGA-II). The comparisons were also made with those obtained by the experimental results. It is found that the TLBO algorithm has produced comparatively better results than those given by the decision-making methods and the experimental results presented by the previous researchers.

Virtual enterprise partner selection integrating LINMAP and TOPSIS

Virtual enterprise (VE) has become an ever-increasing trend in today’s highly competitive markets. A more scientific decision-making process for selecting partner is very important during the formation phase of VE. Partner selection is formulated as a type of fuzzy hybrid multi-criteria group decision-making problems with fuzzy truth degrees of alternatives’ comparisons represented as trapezoidal fuzzy numbers (TrFNs). Integrating Technique for Order Preference by Similarity to Ideal Solution (TOPSIS) and Linear Programming Technique for Multidimensional Analysis of Preference (LINMAP), we use the relative closeness degrees to define fuzzy consistency and inconsistency indices. The decision makers’ weight vector is derived by using the relative entropy. Criteria weights are estimated through constructing a new fuzzy linear programming model with TrFNs, which is solved by the developed fast and efficient method. Collective ranking matrix of alternatives is generated through constructing multi-objective assignment model. Example analysis demonstrates the effectiveness of the proposed method.

Interval-valued intuitionistic fuzzy programming technique for multicriteria group decision making based on Shapley values and incomplete preference information

In the classical LINear programming technique for Multidimensional Analysis of Preference (LINMAP), the criteria are assumed to be independent, which may cause distorted results. The aim of this paper is to employ the LINMAP to develop an interval-valued intuitionistic fuzzy (IVIF) mathematical programming method for multicriteria group decision making considering not only the importance of criteria and that of their ordered positions but also the interactions among criteria and those among their ordered positions. In the spirit of LINMAP, new group consistency and group inconsistency indices based on cross-entropy and Shapley values are firstly defined by considering the interactions among criteria and among their ordered positions. To simultaneously determine the fuzzy measures on criteria set and on ordered set, a bi-objective IVIF programming model is then constructed by minimizing the inconsistency index and maximizing the consistency index. The proposed IVIF programming model is subsequently solved by transforming it into a multiobjective programming model. Furthermore, some generalizations of the proposed programming model are investigated. Finally, two examples are given to illustrate the application of the proposed method, and its superiority is demonstrated by comparing the performance of the proposed method with that of the existing methods.

Multi-objective optimization and exergetic-sustainability of an irreversible nano scale Braysson cycle operating with Maxwell–Boltzmann gas

Nano technology is developed in this decade and changes the way of life. Moreover, developing nano technology has effect on the performance of the materials and consequently improves the efficiency and robustness of them. So, nano scale thermal cycles will be probably engaged in the near future. In this paper, a nano scale irreversible Braysson cycle is studied thermodynamically for optimizing the performance of the Braysson cycle. In the aforementioned cycle an ideal Maxwell–Boltzmann gas is used as a working fluid. Furthermore, three different plans are used for optimizing with multi-objectives; though, the outputs of the abovementioned plans are assessed autonomously. Throughout the first plan, with the purpose of maximizing the ecological coefficient of performance and energy efficiency of the system, multi-objective optimization algorithms are used. Furthermore, in the second plan, two objective functions containing the ecological coefficient of performance and the dimensionless Maximum available work are maximized synchronously by utilizing multi-objective optimization approach. Finally, throughout the third plan, three objective functions involving the dimensionless Maximum available work, the ecological coefficient of performance and energy efficiency of the system are maximized synchronously by utilizing multi-objective optimization approach. The multi-objective evolutionary approach based on the non-dominated sorting genetic algorithm approach is used in this research. Making a decision is performed by three different decision makers comprising linear programming approaches for multidimensional analysis of preference and an approach for order of preference by comparison with ideal answer and Bellman–Zadeh. Lastly, analysis of error is employed to determine deviation of the outcomes gained from each plan.

An extended LINMAP method for MAGDM under linguistic hesitant fuzzy environment

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 the classical LINMAP method, all of the decision data is known precisely or is given as crisp values. It cannot be used to solve the MAGDM problems under the linguistic hesitant fuzzy environment. In this paper, an extended LINMAP method is proposed to solve the MAGDM problems in which all the attribute values of alternatives and the truth degrees of all pair-wise alternatives' comparisons are in the form of linguistic hesitant fuzzy sets (LHFSs). In this method, a formula is first presented to calculate the similarity coefficient for the LHFS. On the basis of this, the weight of each expert with respect to each attribute is determined using the support function of the power average (PA) operator. Meanwhile, the collective consistency and inconsistency measurements are introduced to depict the incomplete pair-wise comparison preference relations on alternatives provided by the experts. Then, a linear programming model is constructed to determine the optimal weights of attributes. Furthermore, by calculating the comprehensive ranking values, the ranking of alternatives can be determined. Finally, a numerical example is used to illustrate the use of the proposed method.

A multiple attribute interval type-2 fuzzy group decision making and its application to supplier selection with extended LINMAP method

Supplier selection is a key issue in supply chain management, which directly impacts the manufacturer's performance. The problem can be viewed as a multiple attribute group decision making (MAGDM) that concerns many conflicting evaluation attributes, both being of qualitative and quantitative nature. Due to the increasing complexity and uncertainty of socio-economic environment, some evaluations of attributes are not adequately represented by numerical assessments and type-1 fuzzy sets. In this paper, we develop some linear programming models with the aid of multidimensional analysis of preference (LINMAP) method to solve interval type-2 fuzzy MAGDM problems, in which the information about attribute weights is incompletely known, and all pairwise comparison judgments over alternatives are represented by IT2FSs. First, we introduce a new distance measure based on the centroid interval between the IT2FSs. Then, we construct the linear programming model to determine the interval type-2 fuzzy positive ideal solution (IT2PIS) and corresponding attributes weight vector. Based on it, an extended LINMAP method to solve MAGDM problem under IT2FSs environment is developed. Finally, a supplier selection example is provided to demonstrate the usefulness of the proposed method.

Regret theory-based group decision-making with multidimensional preference and incomplete weight information

In this paper, we study fuzzy multi-attribute group decision-making (FMAGDM) problems with multidimensional preference information in the form of pairwise alternatives and incomplete weight information. We develop a new group decision-making (GDM) method considering regret aversion of the decision-makers (DMs). Firstly, we define a fuzzy regret/rejoice function and a computational formula for the perceived utility of alternative decisions. We propose a perceived utility value-based group consistency index (which reflects the total consistency) and a group inconsistency index (which represents the total inconsistency) for pairwise rankings of alternatives based on regret theory and an a priori multidimensional preference order given by the DMs. Then, under the circumstances of an unknown fuzzy ideal solution, we set up a mathematical programming model to determine the optimal attribute weights and a defuzzified fuzzy ideal solution with the idea of the Linear Programming Technique for Multidimensional Analysis of Preference (LINMAP). We compute the DMs’ optimal comprehensive perceived utility values and obtain the ranking order of alternatives. Finally, we illustrate the application of the developed procedures with an air-fighter selection problem. The rationality and validity of the proposed method is demonstrated by comparing with two other GDM methods, including the fuzzy LINMAP (FLINMAP) method and the prospect theory-based GDM method.

Hesitant fuzzy programming technique for multidimensional analysis of hesitant fuzzy preferences

The linear programming technique for multidimensional analysis of preferences (LINMAP) is the most representative method for handling the multiple criteria decision making (MCDM) problems with respect to the preference information over alternatives. This paper utilizes the main structure of LINMAP to develop a novel hesitant fuzzy mathematical programming technique to handle MCDM problems within the decision environment of hesitant fuzzy elements (HFEs). Considering the hesitancy of the decision maker, both the pair-wise comparison preference information over alternatives and the evaluation information of alternatives with criteria are represented by the HFEs. Based on the incomplete pair-wise preference judgments over alternatives, we propose the concepts of the hesitant fuzzy consistency and inconsistency indices. Furthermore, we construct a hesitant fuzzy mathematical programming model to derive the weights of criteria and the positive-ideal solution. In this hesitant fuzzy programming model both the objective function and partial constraints' coefficients take the form of HFEs, and an effective approach based on the ranking method of HFEs is further developed to solve the new derived model. To address the incomplete and inconsistent preference structures of criteria weights, we introduce several deviation variables and establish the bi-objective nonlinear programming model. At length, we employ a green supplier selection problem to illustrate the feasibility and applicability of the proposed technique and conduct a comparison analysis to validate its effectiveness.

Hesitant fuzzy linguistic linear programming technique for multidimensional analysis of preference for multi-attribute group decision making

Hesitant fuzzy linguistic term sets (HFLTSs), one of the extensions of the hesitant fuzzy sets, are used to deal with several possible linguistic values or richer expressions than a single term for an alternative, variable, etc. In this paper, we develop a new method called hesitant fuzzy linguistic Linear Programming Technique for Multidimensional Analysis of Preference (LINMAP), which combines the HFLTSs with LINMAP method. By the method, we can get the attributes weights and ideal solution. Furthermore, other generalizations of the method are provided in detail. A practical example is provided to show that our method is very effective in solving multi-criteria decision making problems with hesitant fuzzy linguistic information. Comparative analyses with TOPSIS method are also furnished to show the advantages of the proposed method.

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 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.