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• The orness function and the normal/inverse normal distribution shape parameter are not monotonically correlated. • The orness function and the exponential/inverse exponential distribution shape parameter are monotonically correlated. • An enhanced weight generation approach for ordered weighted averaging operators is proposed. In the present paper, we demonstrate that the degree of orness, which measures the attitudes of decision-makers, does not decrease strictly with the fractile values when either the normal probability density function or its inverse form is used to generate the weights of ordered weighted averaging operators. As for the weights of ordered weighted averaging operators generated from either the exponential distribution and its inverse form, we prove the strict monotonicity of the orness function with respect to the distribution shape parameter. To solve the drawbacks of the probability-density-function-based weight generation approach, the present paper uses the interweaving method to adjust the probability-density-function-based weighting vector of an ordered weighted averaging operator based on the premise that the distribution shape parameter is excluded. This enhanced approach retains the preferences of decision-makers to the utmost when they change their attitudes toward objects. Finally, the feasibility and effectiveness of this novel paradigm for generating the weights of ordered weighted averaging operators are demonstrated with its promising application in a system for aggregating movie ratings. [ABSTRACT FROM AUTHOR]

In this paper, we point out that two theorems in a previous paper by Wei et al. (2013) are incorrect by some counterexamples in detail, and present the modified theorems. [ABSTRACT FROM AUTHOR]

Abstract: Real engineering design problems are generally characterized by the presence of many often conflicting and incommensurable objectives. Naturally, these objectives involve many parameters whose possible values may be assigned by the experts. The aim of this paper is to introduce a hybrid approach combining three optimization techniques, dynamic programming (DP), genetic algorithms and particle swarm optimization (PSO). Our approach integrates the merits of both DP and artificial optimization techniques and it has two characteristic features. Firstly, the proposed algorithm converts fuzzy multiobjective optimization problem to a sequence of a crisp nonlinear programming problems. Secondly, the proposed algorithm uses H-SOA for solving nonlinear programming problem. In which, any complex problem under certain structure can be solved and there is no need for the existence of some properties rather than traditional methods that need some features of the problem such as differentiability and continuity. Finally, with different degree of α we get different α-Pareto optimal solution of the problem. A numerical example is given to illustrate the results developed in this paper. [Copyright &y& Elsevier]

Abstract: This paper investigates decentralized bi-level multi-objective linear programming (DBL-MOLP) problems with a single decision-maker (DM) at the higher level and more than one DM at the lower level. Each DM can have more than one objective function, which is formulated as a fuzzy goal. To characterize the decision decentralization in a DBL-MOLP problem, this paper proposes an assignment scheme of relative satisfaction for the higher-level DM to ensure his leadership and therefore prevent the paradox problem reported in the literature, where lower-level DMs have higher satisfaction degrees than that of the higher-level DM. Through the assignment scheme, if the higher-level DM is not satisfied with the resulting solutions of objective functions, the re-solving process is easily conducted by adjusting the level of relative satisfaction for the associated lower-level DMs. A linearization transformation approach is also presented to facilitate the solution process. To emphasize some important fuzzy goals, a weighting scheme is considered in this paper. A numerical example is used for illustration, and comparisons with existing approaches are conducted to demonstrate the feasibility of the proposed method. [Copyright &y& Elsevier]

Abstract: Decision Making Trial and Evaluation Laboratory (DEMATEL) has been applied in many situations, such as marketing strategies, control systems, safety problems, developing the competencies of global managers and group decision making. It has been incorporated into other methods such as Analytical Network Process (ANP), Multiple Criteria Decision Making (MCDM), fuzzy set theory, etc., to vitalize these traditional methods and explore new applications for the hybrid methods. DEMATEL models the influences of components of a system with an initial direct relation matrix. Influences of components can ripple transitively to other components, which is modeled by raising the initial direct relation matrix to powers. The total influence is computed by summing up matrices of all powers based on the assumption that the matrix raising to the power of infinity would converge to zero. The current paper shows that raising the initial relation matrix to the power of infinity may not converge to zero and hence total influence may not converge. The current paper also shows that our revised DEMATEL guarantees that the initial direct-relation matrix to infinite power will converge to zero and the total influence can be obtained accordingly. The newly developed approach is illustrated with numerical examples. [Copyright &y& Elsevier]

Abstract: TOPSIS (technique for order preference by similarity to ideal solution) is a multiple criteria method to identify solutions from a finite set of alternatives based upon simultaneous minimization of distance from an ideal point and maximization of distance from a nadir point. This paper proposes a fuzzy TOPSIS algorithm to solve bi-level multi-objective decision-making (BL-MODM) problems, and in which the objective function at each level are non-linear functions which are to be maximized. The proposed model for getting the satisfactory solution of the BL-MODM problems includes the membership functions for the upper level decision variables vector with possible tolerances, the membership function of the distance function from the positive ideal solution (PIS) and the membership function of the distance function from the negative ideal solution (NIS). A numerical illustrative example is given to clarify the proposed TOPSIS approach of this paper. [Copyright &y& Elsevier]

Abstract: Soft set theory is a newly emerging mathematical tool to deal with uncertain problems. Since the trapezoidal fuzzy number, as a vital concept of fuzzy set, can express linguistic assessments by transforming them into numerical variables objectively, this paper aims to extend classical soft sets to trapezoidal fuzzy soft sets based on trapezoidal fuzzy numbers. Then, some operations on a trapezoidal fuzzy soft set are defined, such as complement operation, “AND” operation, and “OR” operation. Finally, a Multiple Criterion Decision-Making (MCDM) problem under a fuzzy environment is analyzed by trapezoidal fuzzy soft sets with the demonstration of a numerical example. This paper also uses traditional fuzzy soft sets to deal with the MCDM problem. The result shows that the method provided by this paper outperforms the traditional one. [Copyright &y& Elsevier]

Abstract: Group decision making is an active area of research within multiple attribute decision making. This paper assumes that all the decision makers (DMs) are not equally qualified to contribute equitably to the decision process. The aim of this paper is to develop an approach to determine weights of DMs, in which the decision information on alternatives with respect to attributes, provided by each DM, is represented in the form of interval data. We define the average of all individual decisions as the positive ideal decision (PID), and the maximum separation from PID as the negative ideal decision, which are characterized by a matrix, respectively. The weight of each DM is determined according to the Euclidean distances between the individual decision and ideal decisions. By using the obtained weights of DMs, all individual decisions are aggregated into a collective decision. Then the alternatives is ranked based on the collective decision. Meanwhile, this paper also gives a humanized decision method by using an optimistic coefficient, which is used in adjusting the relative importance between profit and risk. Finally, we give an example to illustrate the developed approach. [Copyright &y& Elsevier]

Abstract: In this paper, a multi-objective solid transportation problem (MOSTP) for a breakable item is considered with two different criteria: cost and time for transportation. Here breaking for the item depends on two modes- (i) type of conveyance and (ii) transported amount. The item breaks at constant rate for the modes of conveyance and randomly for the transported amount. The requirement of the destination is crisp, but due to presence of breakability, the fulfillment of demand at destination is stochastic, which is solved by the chance-constraint method. In this paper, a nested discount (IQD within AUD) is presented on the transportation cost. The considered model is formulated to minimize the total transportation cost and time to transport all units of the item with respect to the transported amounts of the item from origins to destinations. Thus the problem reduces to a multi-objective problem. A set of pareto optimal solutions are obtained by multi-objective genetic algorithm (MOGA). The best solution out of this set is presented using Analytical Hierarchy Process (AHP). The MOSTP has also been formulated with entropy function defined by Shannons measure of entropy. The entropy function is used as an additional objective function which acts as a measure of dispersion. To illustrate the model, numerical example has been presented. The effect of entropy on transported amount is illustrated. A sensitivity analysis on the total cost due to the changes in breakability rate is presented. [Copyright &y& Elsevier]

Abstract: This paper provides a review on recent efforts and development in multi-criteria location problems in three categories including bi-objective, multi-objective and multi-attribute problems and their solution methods. Also, it provides an overview on various criteria used. While there are a few chapters or sections in different location books related to this topic, we have not seen any comprehensive review papers or book chapter that can cover it. We believe this paper can be used as a complementary and updated version. [Copyright &y& Elsevier]

Abstract: The VIKOR method was developed for multi-criteria optimization of complex systems. It determines the compromise ranking list and the compromise solution obtained with the initial (given) weights. This method focuses on ranking and selecting from a set of alternatives in the presence of conflicting criteria. It introduces the multi-criteria ranking index based on the particular measure of “closeness” to the “ideal” solution. The aim of this paper is to extend the VIKOR method for decision making problems with interval number. The extended VIKOR method’s ranking is obtained through comparison of interval numbers and for doing the comparisons between intervals, we introduce α as optimism level of decision maker. Finally, a numerical example illustrates and clarifies the main results developed in this paper. [Copyright &y& Elsevier]

A great number of real world problems can be associated with multicriteria decision making. These problems are often characterized by a high degree of uncertainty. Interval-valued intuitionistic fuzzy sets are a generalized form of an ordinal fuzzy set to deal with this natural uncertainty. In this paper, an enhanced version of the ELECTRE method, called ELECTRE III, is extended under the interval-valued intuitionistic fuzzy environment. The advantages and strengths of ELECTRE III as a decision aid technique and interval-valued intuitionistic fuzzy sets as an uncertain framework make the proposed method a suitable choice in solving practical problems. The application of the proposed method is illustrated by the solution of an investment project selection problem. [ABSTRACT FROM AUTHOR]

Environmental Impact Significance Assessment (EISA) is usually modeled as a multi-criteria decision making process for determining the importance of project’s impacts over involved environment, considering subjective judgments provided in a qualitative and/or quantitative way. Classical EISA methods are not efficient in handling heterogeneous contexts since experts are forced to use numerical scales even for assessing subjective environmental indicators and they also obtain numerical outputs of low interpretability. In this paper is proposed a new approach for heterogeneous EISA based on the linguistic 2-tuple fusion model for dealing with heterogeneous information. It provides a flexible evaluation framework in which experts can supply their preferences using different information domains conform to the nature and uncertainty of criteria as well as their level of knowledge and experience. Moreover the approach applies a multi-step aggregation process to obtain interpretable significance values without loss of information. [ABSTRACT FROM AUTHOR]

In the complex multi-attribute large-group decision-making (CMALGDM) problems in interval-valued intuitionistic fuzzy (IVIF) environment, attributes of the alternatives are often stratified and correlated. This paper proposes a decision-making method for these problems based on partial least squares (PLS) path modelling, which not only fully exploits the decision information of decision makers (DMs), but also effectively addresses the relativity problem in the decision attributes and objectively assigned weights to the primary decision attributes (i.e., "latent variables for decision making"). The method can be outlined in three steps. First, a two-stage method is proposed to transform the interval-valued intuitionistic fuzzy number (IVIFN) samples into single-valued samples. In this step, an improved C-OWA operator is first given to transform the IVIFN samples into intuitionistic fuzzy number (IFN) samples, which makes the preference information of the DMs more objectively aggregated. Then a proposed membership-based method is applied to reduce the information loss and transform the IFN samples into single-valued samples. Second, the estimated values and weights of the "latent variables for decision-making" are obtained by means of the PLS path modelling algorithm. Finally, a multi-alternative sorting method is devised in accordance with the estimated values and weights. An example is provided to illustrate the proposed technique and evaluate its feasibility and validity. [ABSTRACT FROM AUTHOR]

Abstract: This paper extended the concept of the technique for order preference by similarity to ideal solution (TOPSIS) to develop a methodology for solving multi-level non-linear multi-objective decision-making (MLN-MODM) problems of maximization-type. Also, two new interactive algorithms are presented for the proposed TOPSIS approach for solving these types of mathematical programming problems. The first proposed interactive TOPSIS algorithm includes the membership functions of the decision variables for each level except the lower level of the multi-level problem. These satisfactory decisions are evaluated separately by solving the corresponding single-level MODM problems. The second proposed interactive TOPSIS algorithm lexicographically solves the MODM problems of the MLN-MOLP problem by taking into consideration the decisions of the MODM problems for the upper levels. To demonstrate the proposed algorithms, a numerical example is solved and compared the solutions of proposed algorithms with the solution of the interactive algorithm of Osman et al. (2003) [4]. Also, an example of an application is presented to clarify the applicability of the proposed TOPSIS algorithms in solving real world multi-level multi-objective decision-making problems. [Copyright &y& Elsevier]

Abstract: A single valued neutrosophic set (SVNS) is an instance of a neutrosophic set, which give us an additional possibility to represent uncertainty, imprecise, incomplete, and inconsistent information which exist in real world. It would be more suitable to apply indeterminate information and inconsistent information measures. In this paper, the cross entropy of SVNSs, called single valued neutrosophic cross entropy, is proposed as an extension of the cross entropy of fuzzy sets. Then, a multicriteria decision-making method based on the proposed single valued neutrosophic cross entropy is established in which criteria values for alternatives are SVNSs. In decision making process, we utilize the single-valued neutrosophic weighted cross entropy between the ideal alternative and an alternative to rank the alternatives corresponding to the cross entropy values and to select the most desirable one(s). Finally, a practical example of the choosing problem of suppliers is provided to illustrate the application of the developed approach. [Copyright &y& Elsevier]

Abstract: In multi-objective geometric programming problem there are more than one objective functions. There is no single optimal solution which simultaneously optimizes all the objective functions. Under these conditions the decision makers always search for the most “preferred” solution, in contrast to the optimal solution. A few mathematical programming methods namely fuzzy programming, goal programming and weighting methods have been applied in the recent past to find the compromise solution. In this paper -constraint method has been applied to find the non-inferior solution. A brief solution procedure of -constraint method has been presented to find the non-inferior solution of the multi-objective programming problems. Further, the multi-objective programming problems is solved by the fuzzy programming technique to find the optimal compromise solution. Finally, two numerical examples are solved by both the methods and compared with their obtained solutions. [Copyright &y& Elsevier]

Abstract: This paper investigates an approach for multi-criterion decision making (MCDM) problems with interval-valued intuitionistic fuzzy preference relations (IVIFPRs). Based on the novel interval score function, some extended concepts associated with IVIFPRs are defined, including the score matrix, the approximate optimal transfer matrix and the possibility degree matrix. By using these new matrixes, a prioritization method for IVIFPRs is proposed. Then, we investigate an interval-valued intuitionistic fuzzy AHP method for multi-criteria decision making (MCDM) problems. In the end, a numerical example is provided to illustrate the application of the proposed approach. [Copyright &y& Elsevier]

Abstract: The solution concept in multi-objective programming is represented by a program which reaches “the best compromise”. Many solving methods find a good compromise feasible solution and then check whether the solution is efficient or not. In this paper, using the efficiency test introduced by Lotfi et al. (2010) [12], we propose two procedures for deriving weakly and strongly efficient solutions in multi-objective linear fractional programming problems (MOLFPP) starting from any feasible solution, and present their possible applications in multiple criteria decision-making process. Then, we discuss a shortcoming of some fuzzy approaches to solving MOLFPP and modify them in order to guarantee the efficiency of the optimal solution. [Copyright &y& Elsevier]

Abstract: In this paper, a hybrid decision making approach integrating induced aggregation operators into VIKOR is proposed for tackling multicriteria problems with conflicting and noncommensurable (different units) criteria. For doing so, we develop a new distance aggregation operator called the induced ordered weighted averaging standardized distance (IOWASD) operator. It is an aggregation operator that provides a wide range of standardized distance measures between the maximum and the minimum by using the induced OWA (IOWA) operator. The main advantage of the IOWA-based VIKOR (IOWA-VIKOR) is that it is able to reflect the complex attitudinal character of the decision maker by using order inducing variables and provide much more complete information for decision making. We also studied some of the IOWASD’s main properties and different particular cases and further generalized it by using the induced generalized OWA (IGOWA) operator. Finally, we apply the integrated IOWA-VIKOR method in a multi-criteria decision making problem regarding the selection of materials and the results are compared for different types of standardized distance aggregation operators. [Copyright &y& Elsevier]

Abstract: Supplier selection is a highly important multi-criteria group decision making problem, which requires a trade-off between multiple criteria exhibiting vagueness and imprecision with the involvement of a group of experts. In this paper, a fuzzy multi-criteria group decision making approach that makes use of the quality function deployment (QFD) concept is developed for supplier selection process. The proposed methodology initially identifies the features that the purchased product should possess in order to satisfy the company’s needs, and then it seeks to establish the relevant supplier assessment criteria. Moreover, the proposed algorithm enables to consider the impacts of inner dependence among supplier assessment criteria. The upper and the lower bounds of the weights of supplier assessment criteria and ratings of suppliers are computed by using the fuzzy weighted average (FWA) method. The FWA method allows for the fusion of imprecise and subjective information expressed as linguistic variables or fuzzy numbers. The method produces less imprecise and more realistic overall desirability levels, and thus it rectifies the problem of loss of information. A fuzzy number ranking method that is based on area measurement is used to obtain the final ranking of suppliers. The computational procedure of the proposed framework is illustrated through a supplier selection problem reported in an earlier study. [Copyright &y& Elsevier]

Abstract: The purpose of this paper is to present a generalized hesitant fuzzy synergetic weighted distance (GHFSWD) measure, which is based on the generalized hesitant fuzzy weighted distance (GHFWD) measure and the generalized hesitant fuzzy ordered weighted distance (GHFOWD) measure proposed by Xu and Xia [Z. Xu, M. Xia, Distance and similarity measures for hesitant fuzzy sets, Inf. Sci. 181 (2011) 2128–2138.], and investigate its some desirable properties and special cases. The GHFSWD measure not only generalizes both the GHFWD and GHFOWD measures as well as the common hesitant fuzzy distance measures, but also reflects the importance degrees of both the given individual distances and their ordered positions. Then, based on the defined notions of positive ideal hesitant fuzzy set and negative ideal hesitant fuzzy set, we utilize the proposed GHFSWD measure to develop a method for multiple criteria decision making with hesitant fuzzy information. The method is flexible because it allows decision makers to provide preference with hesitancy and determine different decision results by choosing different decision strategies. Finally, a numerical example is provided to illustrate the feasibility and practicality of the proposed method. [Copyright &y& Elsevier]

Abstract: The multiple criteria decision making (MCDM) methods VIKOR and TOPSIS are all based on an aggregating function representing “closeness to the ideal”, which originated in the compromise programming method. The VIKOR method of compromise ranking determines a compromise solution, providing a maximum “group utility” for the “majority” and a minimum of an “individual regret” for the “opponent”, which is an effective tool in multi-criteria decision making, particularly in a situation where the decision maker is not able, or does not know to express his/her preference at the beginning of system design. The TOPSIS method determines a solution with the shortest distance to the ideal solution and the greatest distance from the negative-ideal solution, but it does not consider the relative importance of these distances. And, the hesitant fuzzy set is a very useful tool to deal with uncertainty, which can be accurately and perfectly described in terms of the opinions of decision makers. In this paper, we develop the E-VIKOR method and TOPSIS method to solve the MCDM problems with hesitant fuzzy set information. Firstly, the hesitant fuzzy set information and corresponding concepts are described, and the basic essential of the VIKOR method is introduced. Then, the problem on multiple attribute decision marking is described, and the principles and steps of the proposed E-VIKOR method and TOPSIS method are presented. Finally, a numerical example illustrates an application of the E-VIKOR method, and the result by the TOPSIS method is compared. [Copyright &y& Elsevier]

Abstract: This paper deals with multiattribute group decision making (MAGDM) problems with interval-valued 2-tuple linguistic information. First, we introduce some new aggregation operators, such as the interval-valued 2-tuple weighted geometric (IVTWG) operator, the interval-valued 2-tuple ordered weighted geometric (IVTOWG) operator, the generalized interval-valued 2-tuple weighted average (GIVTWA) operator and the generalized interval-valued 2-tuple ordered weighted average (GIVTOWA). Then, we discuss their desired properties and relationships among them. Furthermore, we put forward a new method to determine the weight vector of interval-valued 2-tuple aggregation operator based on the concept of degree of precision. Finally, a numerical example is provided to illustrate the efficiency of the proposed method in dealing with interval-valued 2-tuple linguistic information under multi-granular linguistic contexts. [Copyright &y& Elsevier]

Abstract: The purpose of this paper is to design a new extension of the ELECTRE, known as the elimination and choice translating reality method, for multi-criteria group decision-making problems based on intuitionistic fuzzy sets. This method is widely utilized when a set of alternatives should be identified and evaluated with respect to a set of conflicting criteria by reflecting decision makers’ (DMs’) preferences. However, handling the exact data and numerical measure is difficult to be precisely focused because the DMs’ judgments are often vague in real-life decision problems and applications. A more realistic and practical approach can be to use linguistic variables expressed in intuitionistic fuzzy numbers instead of numerical data to model DMs’ judgments and to describe the inputs in the ELECTRE method. The proposed intuitionsitic fuzzy ELECTRE utilizes the truth-membership function and non-truth-membership function to indicate the degrees of satisfiability and non-satisfiability of each alternative with respect to each criterion and the relative importance of each criterion, respectively. Then, a new discordance intuitionistic index is introduced, which is extended from the concept of the fuzzy distance measure. Outranking relations are defined by pairwise comparisons and a decision graph is depicted to determine which alternative is preferable, incomparable or indifferent in the intuitionistic fuzzy environment. Finally, a comprehensive sensitivity analysis is employed to further study regarding the impact of threshold values on the final evaluation, and a comparative analysis is demonstrated with an application example in flexible manufacturing systems between the proposed ELECTRE method and the existing intuitionistic fuzzy technique for order preference by similarity to ideal solution (IF-TOPSIS) method. [Copyright &y& Elsevier]

Abstract: Owing to the increasing complexity in various management, aggregating experts’ knowledge and experiences to make an appropriate decision is an important research area. However, with aggregation of information in decision process, some information may be lost. The aim of this paper is to present a systematic methodology avoiding information loss for group decision making. An extended TOPSIS method is twice used to the current method, which is first used to determine the weights of decision makers, and second used to rank the preference order of alternatives. The proposed approach is straightforward and has no aggregation of information. A comparison of proposed method with other methods is also done. Finally, a numerical example for supplier selection is given to illustrate the application of the introduced method. [Copyright &y& Elsevier]

Abstract: Scoring rules are an important disputable subject in data envelopment analysis (DEA). Various organizations use voting systems whose main object is to rank alternatives. In these methods, the ranks of alternatives are obtained by their associated weights. The method for determining the ranks of alternatives by their weights is an important issue. This problem has been the subject at hand of some authors. We suggest a three-stage method for the ranking of alternatives. In the first stage, the rank position of each alternative is computed based on the best and worst weights in the optimistic and pessimistic cases, respectively. The vector of weights obtained in the first stage is not a singleton. Hence, to deal with this problem, a secondary goal is used in the second stage. In the third stage of our method, the ranks of the alternatives approach the optimistic or pessimistic case. It is mentionable that the model proposed in the third stage is a multi-criteria decision making (MCDM) model and there are several methods for solving it; we use the weighted sum method in this paper. The model is solved by mixed integer programming. Also, we obtain an interval for the rank of each alternative. We present two models on the basis of the average of ranks in the optimistic and pessimistic cases. The aim of these models is to compute the rank by common weights. [Copyright &y& Elsevier]

Abstract: This paper proposes the concept of the reduct intuitionistic fuzzy sets of interval-valued intuitionistic fuzzy sets (IVIFSs) with respect to adjustable weight vectors and the Dice similarity measure based on the reduct intuitionistic fuzzy sets to explore the effects of optimism, neutralism, and pessimism in decision making. Then a decision-making method with the pessimistic, optimistic, and neutral schemes desired by the decision maker is established by combining adjustable weight vectors and the Dice similarity measure for IVIFSs. The proposed decision-making method is more flexible and adjustable in practical problems and can determine the ranking order of alternatives and the optimal one(s), so that it can overcome the difficulty of the ranking order and decision making when there exist the same measure values of some alternatives in some cases. This adjustable feature can provide the decision maker with more selecting schemes and actionable results for the decision-making analysis. Finally, two illustrative examples are employed to show the feasibility of the proposed method in practical applications. [Copyright &y& Elsevier]

Abstract: The distributions of empirical data are often complex. Such complexity cannot be sufficiently addressed by the individual theoretical statistical distribution function. Furthermore, the selection of the distribution function becomes more complicated when the empirical data present a multi-peak feature. In such a case, the multiple testing criteria and the mixed model must be considered during the selection of an appropriate distribution function. Aiming at this vague challenge, the present paper proposes a novel method for establishing a mixed model that can describe accurately the distribution characteristics of empirical data. Apart from combining the Akike and Bayesian information criteria to define the feasible solutions of the mixed model, this study also utilizes the root mean squared deviation, coefficient of determination, Kolmogorov–Smirnov test statistic, average deviation in cumulative distribution function, and average deviation in probability distribution function as the testing criteria. In addition, a non-linear programming is used to find the weighting factors of each criterion. The multi-criteria decision-making technology is adopted to comprehensively and objectively integrate these testing criteria into a synthetic indicator. Finally, an optimization algorithm is proposed to determine the optimal number of components in the mixed model. The illustrated results of the simulated data and measured signals confirm that this approach can estimate precisely the number of components as well as establish a highly accurate mixed model. [Copyright &y& Elsevier]

Abstract: Based on the grey system theory and methods, the grey-target decision-making problem is discussed, in which the attribute values are grey numbers and the maximum probability of the value of grey number is known. Firstly, the optimal effect vector is the positive bull’s-eye and positive bull’s-eye distance of each scheme is defined. Subjectively or objectively weighting method is integrated to determine the index weight and integrated optimization model of index weight is established. Finally, the critical effect vector is the negative bull’s-eye and negative bull’s-eye distance of each scheme is defined, then relative bull’s-eye distance and comprehensive the bull’s-eye distance of grey target decision-making are given. An example is also presented to illustrate the usefulness and effectiveness of the methods obtained in this paper and provides a new idea for grey target decision-making method research. [Copyright &y& Elsevier]

Abstract: There are several methods in the literature for solving transportation problems by representing the parameters as normal fuzzy numbers. Chiang [J. Chiang, The optimal solution of the transportation problem with fuzzy demand and fuzzy product, J. Inform. Sci. Eng. 21 (2005) 439–451] pointed out that it is better to represent the parameters as (λ, ρ) interval-valued fuzzy numbers instead of normal fuzzy numbers and proposed a method to find the optimal solution of single objective transportation problems by representing the availability and demand as (λ, ρ) interval-valued fuzzy numbers. In this paper, the shortcomings of the existing method are pointed out and to overcome these shortcomings, a new method is proposed to find solution of a linear multi-objective transportation problem by representing all the parameters as (λ, ρ) interval-valued fuzzy numbers. To illustrate the proposed method a numerical example is solved. The advantages of the proposed method over existing method are also discussed. [Copyright &y& Elsevier]

Abstract: City logistics initiatives are steps taken by municipal administrations to ameliorate the condition of goods transport in cities and reduce their negative impacts on city residents and their environment. Examples of city logistics initiatives are urban distribution centers, congestion pricing, delivery timing and access restrictions. In this paper, we present a hybrid approach based on Affinity Diagram, AHP and fuzzy TOPSIS for evaluating city logistics initiatives. Four initiatives namely vehicle sizing restrictions, congestion charging schemes, urban distribution center and access timing restrictions are considered. The proposed approach consists of four steps. The first step involves identification of criteria for assessing performance of city logistics initiatives using Affinity Diagram. The results are four categories of criteria namely technical, social, economical and environmental. In step 2, a decision making committee comprising of representatives of city logistics stakeholders is formed. These stakeholders are shippers, receivers, transport operators, end consumers and public administrators. The committee members weight the selected criteria using AHP. In step 3, the decision makers provide linguistic ratings to the alternatives (city logistics initiatives) to assess their performance against the selected criteria. These linguistic ratings are then aggregated using fuzzy TOPSIS to generate an overall performance score for each alternative. The alternative with the highest score is finally chosen as most suitable city logistics initiative for improving city sustainability. In the fourth step, we perform sensitivity analysis to evaluate the influence of criteria weights on the selection of the best alternative. The proposed approach is novel and can be practically applied for selecting sustainable city logistics initiatives for cities. Another advantage is its ability to generate solutions under limited quantitative information. An empirical application of the proposed approach is provided. [Copyright &y& Elsevier]

Abstract: In this paper, we develop a multi-objective approach for proactive routing in a Mobile Ad Hoc Network (MANET). We consider three routing objectives: minimizing average end-to-end delay, maximizing network energy lifetime, and maximizing packet delivery ratio. Accordingly, we develop three routing metrics: mean queuing delay on each node, energy cost on each node, and link stability on each link. For the proposed multi-objective approach, we develop efficient prediction methods: (a) predicting queuing delay and energy consumption using double exponential smoothing, and (b) predicting residual link lifetime using a heuristic of the distributions of the link lifetimes in MANET. Extensive simulation (by using ns2) is performed for the comparison of this multi-objective OLSR with existing OLSRs. The results show that the multi-objective OLSR is effective in finding optimal routing by tradeoffs among proposed objectives. [ABSTRACT FROM AUTHOR]

Abstract: In this paper, we consider the problem of alternative-fuel buses selection using two novel fuzzy multiple criteria decision-making (MCDM) methods. Several types of fuels are considered as fuel modes, i.e., electricity, fuel cell (hydrogen), and methanol. For the purpose of determining appropriate fuel buses, many factors including quantitative and qualitative ones such as efficiency, price, and capability must be taken into account. In the first proposed method, linguistic variables are used to assess the ratings and weights for factors. These linguistic ratings can be expressed in trapezoidal or triangular fuzzy numbers. Then, a hierarchical MCDM method based on fuzzy-sets theory is proposed to deal with the fuel buses selection problem. To simultaneously determine the ranking order of all alternatives based on the concept of the TOPSIS by calculating the distances to the both fuzzy positive-ideal solution (FPIS) and fuzzy negative-ideal solution (FNIS), a closeness coefficient is defined. In the second presented method we extend preference selection index (PSI) method for fuzzy environment. In this method performance ratings of criteria evaluate by linguistic variable which can be expressed in trapezoidal fuzzy numbers. Finally, an example is shown to highlight the procedure of the proposed methods and compare the results of these methods with each other. [ABSTRACT FROM AUTHOR]

Abstract: In this paper, we present a novel decision support system for order acceptance/rejection in a hybrid Make-to-Stock/Make-to-Order production environment. The proposed decision support system is comprised of five steps. At the first step, the customers are prioritized based on a fuzzy TOPSIS method. Rough-cut capacity and rough-cut inventory are calculated in the second step and in case of unavailability in capacity and materials, some undesirable orders are rejected. Also, proper decisions are made about non-rejected orders. At the next step, prices and delivery dates of the non-rejected orders are determined by running a mixed-integer mathematical programming model. At the fourth step, a set of guidelines are proposed to help the organization negotiate over price and due date with the customers. In the next step, if the customer accepts the offered price and delivery date, the order is accepted and later considered in the production schedule of the shop floor, otherwise the order is rejected. Finally, numerical experiments are conducted to show the tractability of the applied mathematical programming model. [ABSTRACT FROM AUTHOR]

Abstract: Different models have been proposed in the field of preventive maintenance planning for finding optimal age replacement policies. While previous studies have focused mainly on classical cost objectives, this paper presents a novel multi-objective model for preventive replacement of a part over a planning horizon. The proposed model considers different objectives and practical issues, such as corrective replacement and its consequences, residual lifetime objective, and kind of productivity index. Also, the model determines number of spare parts, required for replacement with the defected part, to be provided at the beginning of the planning horizon. The multi-objective model is applicable for machines or equipments which are repaired through replacing their defected part with new spare part. For solving the multi-objective model, regarding to ability of ε-constraint method to generate different pareto-optimal solutions, a procedure is developed based on this method. The procedure shows how the ε-constraint method can be used for finding preferred solution in situations where there is no access to decision maker. The model and solution procedure are illustrated by a numerical example. [ABSTRACT FROM AUTHOR]

Abstract: Most of research in production scheduling is concerned with the optimization of a single criterion. However the analysis of the performance of a schedule often involves more than one aspect and therefore requires a multi-objective treatment. In this research, with combination of two multiple objective decision-making methods, min–max and weighted techniques, a new solution presentation method and a robust hybrid metaheuristic, we solved sequence-dependent setup time hybrid flowshop scheduling problems. In this paper for reflecting real-world situation adequately, we assume the processing time of each job depends on the speed of machine and amount of resource allocated to each machine at the stage which is processed on it. In formulation of min–max type, the decision-maker can have the flexibility of mixed use of weights and distance parameter in expressing desired improvement on produced Pareto optimal solutions. To minimize makespan and total resource allocation costs, the proposed hybrid approach is robust, fast, and simply structured, and comprises two components: genetic algorithm and a variable neighborhood search. The comparison shows the proposal to be very efficient for different structure instances. [ABSTRACT FROM AUTHOR]

Abstract: Curve fitting is an interesting and important subject in mathematics and engineering. It has been studied extensively and a number of approaches, mostly based on polynomials and piecewise polynomials, have been employed. In the usual setting, some data points are given and one wants to find a polynomial function with the minimum violations measured by a norm in the given data points. In these approaches, norms are applied to aggregate all violations as a scalar. In this paper, the polynomial curve fitting problem is considered from the viewpoint of decision making. Taking into account some weaknesses of the norm-based approaches, a multiobjective programming model for curve fitting is given in which the violations are minimized simultaneously as a vector. This approach is more flexible for the curve fitting problem. Indeed, using the concept of efficiency in multiobjective programming, it enables us to impose some additional helpful secondary preferences. Especially, this approach can obtain a fitted curve with efficient violations and minimum average curvature or minimum average slope. [ABSTRACT FROM AUTHOR]

Abstract: In a multi-objective linear fractional programming problem (MOLFPP), it is often useful to check the efficiency of a given feasible solution, and if the solution is efficient, it is useful to check strong or weak efficiency. In this paper, by applying a geometrical interpretation, a linear programming approach is achieved to test weak efficiency. Also, in order to test strong efficiency for a given weakly efficient point, a linear programming approach is constructed. [Copyright &y& Elsevier]

Abstract: Harnessing the supply base is an important but complex task for enterprises. Supplier performance evaluation is increasingly seen as a strategic issue for companies to maintain and enhance the competitive edge. However, evaluating suppliers is complicated by the fact that various criteria must be considered in the decision-making process, and is inherently a multicriteria decision-making (MCDM) problem. It also concerns the evaluation by different experts of multiple attributes, both qualitative and quantitative. To perceive and to estimate effectively the capability of suppliers are real arduous tasks for executives. This paper takes advantage of the 2-tuple linguistic computing to coping with the heterogeneity and information loss problems while the evaluation processes of subjective integration. The proposed approach based on the group decision-making scenario assists executives in adroit manipulation of the heterogeneity during integration processes and averts the information loss effectively. Finally, we demonstrate the validity and feasibility by means of a high-technology company in Taiwan. [Copyright &y& Elsevier]

Abstract: This paper proposes a fuzzy-robust stochastic multiobjective programming (FRSMOP) approach, which integrates fuzzy-robust linear programming and stochastic linear programming into a general multiobjective programming framework. A chosen number of noninferior solutions can be generated for reflecting the decision-makers’ preferences and subjectivity. The FRSMOP method can effectively deal with the uncertainties in the parameters expressed as fuzzy membership functions and probability distribution. The robustness of the optimization processes and solutions can be significantly enhanced through dimensional enlargement of the fuzzy constraints. The developed FRSMOP was then applied to a case study of planning petroleum waste-flow-allocation options and managing the related activities in an integrated petroleum waste management system under uncertainty. Two objectives are considered: minimization of system cost and minimization of waste flows directly to landfill. Lower waste flows directly to landfill would lead to higher system costs due to high transportation and operational costs for recycling and incinerating facilities, while higher waste flows directly to landfill corresponding to lower system costs could not meet waste diversion objective environmentally. The results indicate that uncertainties and complexities can be effectively reflected, and useful information can be generated for providing decision support. [Copyright &y& Elsevier]

Abstract: In this paper, two new algorithms are presented to solve multi-level multi-objective linear programming (ML-MOLP) problems through the fuzzy goal programming (FGP) approach. The membership functions for the defined fuzzy goals of all objective functions at all levels are developed in the model formulation of the problem; so also are the membership functions for vectors of fuzzy goals of the decision variables, controlled by decision makers at the top levels. Then the fuzzy goal programming approach is used to achieve the highest degree of each of the membership goals by minimizing their deviational variables and thereby obtain the most satisfactory solution for all decision makers. The first suggested algorithm groups the membership functions for the defined fuzzy goals of the objective functions at all levels and the decision variables for each level except the lower level of the multi-level problem. The second proposed algorithm lexicographically solves MOLP problems of the ML-MOLP problem by taking into consideration the decisions of the MOLP problems for the upper levels. An illustrative numerical example is given to demonstrate the algorithms. [Copyright &y& Elsevier]

Abstract: One of the most difficult tasks in multiple criteria decision analysis (MCDA) is determining the weights of individual criteria so that all alternatives can be compared based on the aggregate performance of all criteria. This problem can be transformed into the compromise programming of seeking alternatives with a shorter distance to the ideal or a longer distance to the anti-ideal despite the rankings based on the two distance measures possibly not being the same. In order to obtain consistent rankings, this paper proposes a measure of relative distance, which involves the calculation of the relative position of an alternative between the anti-ideal and the ideal for ranking. In this case, minimizing the distance to the ideal is equivalent to maximizing the distance to the anti-ideal, so the rankings obtained from the two criteria are the same. An example is used to discuss the advantages and disadvantages of the proposed method, and the results are compared with those obtained from the TOPSIS method. [Copyright &y& Elsevier]

Abstract: In this paper, we present a method to determine the stability of nondominated criterion vectors using a modified weighted achievement scalarization metric. This method is based on the application of a particular objective function which scalarizes and parameterizes the original multiobjective nonlinear programming problem. Also, we show that this modified weighted achievement metric coincides with the metric introduced by Choo and Atkins [E.-U. Choo, D.R. Atkins, Proper efficiency in nonconvex multicriteria programming, Math. Oper. Res. 8 (1983) 467–470] and Kaliszewski [I. Kaliszewski, A modified weighted Tchebycheff metric for multiple objective programming, Comput. Oper. Res. 14 (1987) 315–323] in cases when sets of all criterion vectors are finite or polyhedral. [Copyright &y& Elsevier]