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This paper aims to develop a new axiomatic design-based mathematical programming method for heterogeneous multi-criteria group decision making (HMCGDM) problems with linguistic fuzzy truth degrees (LFTDs). The main contributions of this paper are summarized in five aspects: (1) The information content definitions for six types of fuzzy numbers are initially provided according to axiomatic design. (2) Considering the authority of experts on different criteria and group consensus, a bi-objective programming model is constructed to derive experts' weights by maximizing individual deviation and minimizing group discordance. (3) Each alternative is assessed on the basis of its information content to a fuzzy positive ideal solution. Information content is firstly used to define the linguistic fuzzy consistency and inconsistency indices. (4) A bi-objective linguistic fuzzy mathematic programming model is built to determine the criteria weights, which considers consistency and inconsistency indices simultaneously. This model can be dexterously transformed into a crisp linear programming model for resolution by the linguistic scale function. (5) The group information content of each alternative to fuzzy positive ideal solution is calculated to determine the ranking order of alternatives. Finally, an example of blockchain service provider selection is given to validate the proposed method. [ABSTRACT FROM AUTHOR]

• We propose a new fuzzy best-worst method (BWM) based on triangular fuzzy numbers. • We propose the concepts of fuzzy consistency index and fuzzy consistency ratio. • Four linear programming models are built to get optimal fuzzy weights, respectively. • We apply the proposed fuzzy BWM to deal with multi-criteria decision-making. • It gets a higher consistency than the ones of the existing fuzzy BWM and the BWM. In this paper, we propose a new fuzzy best-worst method (BWM) based on triangular fuzzy numbers for multi-criteria decision-making (MCDM). Aimed at the Best-to-Others vector and the Others-to-Worst vector in the form of triangular fuzzy numbers, this paper regards consistency equations as fuzzy equations. The derivation of optimal fuzzy weights of criteria is formulated as a fuzzy decision-making problem, where a mathematical programming model is constructed to derive optimal fuzzy weights of criteria to build a normalized triangular fuzzy weight vector. Then, we propose four linear programming models based on the obtained mathematical programming model for the optimistic decision maker, the pessimistic decision maker and the neutral decision maker, respectively. Through a proper selection of the values of tolerance parameters, each of the linear programming models certainly has a unique global optimal solution. Moreover, this paper proposes the concept of fuzzy consistency index and the concept of fuzzy consistency ratio. Several application examples are used to validate the proposed fuzzy BWM. The proposed fuzzy BWM provides us with a very useful way for MCDM in fuzzy environments. [ABSTRACT FROM AUTHOR]

• Ship-unloading scheduling is solved by mathematical modeling and column generation. • A mathematical programming model is established, and that is an effective means for handling practical optimization problems as encountered in this paper. • A column generation algorithm is proposed, and that is effective for solving practical large-sized integer programming problems. A ship-unloading scheduling problem (SUSP), also called "sequencing ship" problem arising from a large steel plant with bulk material port is studied in this paper. Raw materials such as iron ore, coal and stone are transported to the steel plant by ships. Each ship has an expected departure time based on a contract between the steel plant and ship-owner. If the steel plant cannot effectively schedule the unloading operation of the ship to make it leave the port before its expected departure time, a demurrage penalty cost which increases with the delay will be charged to the steel plant by the ship-owner. SUSP is to find an optimal schedule for these raw material ships so as to minimize the total demurrage costs within a given planning time horizon. The problem is formulated as a mixed integer programming, and can be regarded as a flexible job shop scheduling problem, where the ships are regarded as the jobs and the belt conveyors as the machines. A column generation approach is proposed for solving the optimization model. The computational results on the real-world data obtained from the steel plant are compared with CPLEX to verify the effectiveness and merits of the proposed model and solution. The proposed optimization technique has great potential to be applied in the steel plant, and it may save 20 million of CNY caused by the delay cost per year. [ABSTRACT FROM AUTHOR]

Highlights • A period-dependent mathematical program with equilibrium constraints (PMPEC) is presented. • A two-stage model is presented. • A new solution method is proposed. • Numerical experiments are conducted and comparisons are made with existing signal controls. Abstract For a road networked system with stochastic travel demand, a two-stage model is proposed for period-dependent area traffic signal control. In this paper, a period-dependent mathematical program with equilibrium constraints (PMPEC) is presented to minimize total travel delay over successive time periods. For stochastic travel demand over multiple time periods, a period-dependent user equilibrium traffic assignment can be formulated as a variational inequality. Due to non-linearity of equilibrium constraints, a two-stage model is presented in this paper. In order to understand feasibility of the proposed model, numerical experiments using a real-data road network are conducted. The results indicate that the proposed model attains a promising system performance and exhibit computational advantage over existing alternatives. [ABSTRACT FROM AUTHOR]

This study aims at investigating a scheduling problem for unloading of material ships in a large-scale steel plant. The optimization problem minimizes the cost caused by improperly delayed unloading operations of the ships for a given time horizon. The problem intends to decide the order of unloading ships and the allocation of conveyors to the ships. The solution for the practical-sized problem is NP-hard because of the dimensionality of the problem. In this paper we resolve the problem using a well-designed differential evolution algorithm (DE). In addition, a mathematical programming model is given as well for comparison. An empirical study with some comparative results from CPLXE solver and other DE variants is carried out, which shows a good potential for real-world applications. [ABSTRACT FROM AUTHOR]

In this paper, we focus on necessary and sufficient efficiency conditions for optimization problems with multiple objectives and a feasible set defined by interval-valued functions. A new concept of Fritz-John and Karush–Kuhn–Tucker-type points is introduced for this mathematical programming problem based on the gH-derivative concept. The innovation and importance of these concepts are presented from a practical and computational point of view. The problem is approached directly, without transforming it into a real-valued programming problem, thereby attaining theoretical results that are more powerful and computationally more efficient under weaker hypotheses. We also provide necessary conditions for efficiency, which have been inexistent in the relevant literature to date. The identification of necessary conditions is important for the development of future computational optimization techniques in an interval-valued environment. We introduce new generalized convexity notions for gH-differentiable interval-valued problems which are a generalization of previous concepts and we prove a sufficient efficiency condition based on these concepts. Finally, the efficiency conditions for deterministic programming problems are shown to be particular instances of the results proved in this paper. The theoretical developments are illustrated and justified through several numerical examples. [ABSTRACT FROM AUTHOR]

Real-time control is of great significance for practical plants such as intelligent manufacturing systems and transportation systems, and timing information should be integrated in their discrete models. The existing specifications expressed by generalized mutual exclusion constraints (GMECs) do not consider timing specifications in the control design of these models, which would be restrictive for the control specifications of a timed system. In the framework of time Petri net (TPN) models, this paper introduces a class of GMECs, called time GMECs (TGMECs), in which each GMEC is associated with a restricted time interval. By restricting the firing intervals of controllable transitions, an efficient method based on control functions is proposed to implement TGMECs on a TPN system in presence of uncontrollable transitions. The core of the reported method is to employ the transitions-related timing constraints in a partial modified state class graph (PMSCG) to solve mathematical programming problems. Such a PMSCG is a graph recently introduced to enhance the supervisor permissiveness for a TPN system with GMECs. In particular, the terminal condition for the construction of a PMSCG is modified. By taking advantage of the PMSCG, an online control procedure is presented to implement the supervision for TGMECs in a maximally permissive way. [ABSTRACT FROM AUTHOR]

Many real-life problems can be described as unbalanced, where the number of instances belonging to one of the classes is much larger than the numbers in other classes. Examples are spam detection, credit card fraud detection or medical diagnosis. Ensembles of classifiers have acquired popularity in this kind of problems for their ability to obtain better results than individual classifiers. The most commonly used techniques by those ensembles especially designed to deal with imbalanced problems are for example Re-weighting, Oversampling and Undersampling. Other techniques, originally intended to increase the ensemble diversity, have not been systematically studied for their effect on imbalanced problems. Among these are Random Oracles, Disturbing Neighbors, Random Feature Weights or Rotation Forest. This paper presents an overview and an experimental study of various ensemble-based methods for imbalanced problems, the methods have been tested in its original form and in conjunction with several diversity-increasing techniques, using 84 imbalanced data sets from two well known repositories. This paper shows that these diversity-increasing techniques significantly improve the performance of ensemble methods for imbalanced problems and provides some ideas about when it is more convenient to use these diversifying techniques. [ABSTRACT FROM AUTHOR]

Graphics processing units (GPUs) have been utilized to improve the processing speed of many conventional data mining algorithms. DBSCAN, a popular clustering algorithm that has been often used in practice, was extended to execute on a GPU. However, existing GPU-based DBSCAN extensions still have impediments in that the distances from all objects need to be repeatedly computed to find the neighbor objects and the objects and intermediate clustering results are stored in costly off-chip memory of the GPU. This paper proposes CudaSCAN , a novel algorithm that improves the efficiency of DBSCAN by making better use of the GPU. CudaSCAN consists of three phases: (1) partitioning the entire dataset into sub-regions of size of an integer multiple of the on-chip shared memory size in the GPU; (2) local clustering within sub-regions in parallel; and (3) merging the local clustering results. CudaSCAN allows an overlap between sub-regions to ensure independent, parallel local clustering in each sub-region, which in turn enables for objects and/or intermediate results to be stored in on-chip shared memory that has an access cost a few hundred times cheaper than that of off-chip global memory. The independence also enables for merging to be parallelized. This paper proves the correctness of CudaSCAN, and according to our extensive experiments, CudaSCAN outperforms CUDA-DClust, a previous GPU-based DBSCAN extension, by up to 163.6 times. [ABSTRACT FROM AUTHOR]

In this paper, we consider a class of nonconvex problems with linear constraints appearing frequently in the area of image processing. We solve this problem by the penalty method and propose the Bregman reweighted alternating minimization algorithm. The penalty parameter is set to increase in the iterations to speed up the algorithm. A convergence result is proved for the algorithm. If another smooth assumption is promised, with the semi-algebraic property, we can prove the algorithm globally converges to a critical point of the penalty objective function. Numerical results demonstrate the efficiency of the proposed algorithm. [ABSTRACT FROM AUTHOR]

Highlights • Three search heuristics to configure extended Multi-Product Lines (MPLs) are proposed. • MPLs interrelate large scale variability models representing non-functional properties. • These heuristics were implemented in a constraint programming solver to configure products. • Configuring optimal products regarding multi-objective criteria is automated for MPLs. • These strategies improve the configuration performance as models and constraints scale. Abstract Nowadays, complex application domains require configuring multi-product lines where product features and constraints among them are specified in several variability models. These variability models are enriched with inter-model constraints representing the existing relations among domain concerns, and with non-functional properties modeled as attributes attached to product features. Multiple techniques use constraint programming to automate the cumbersome task of manually configuring a suitable product. Currently, there are some proposals to improve the performance of constraint solvers when configuring single-model product lines, however configuration scenarios with multiple interrelated and attributed models are not yet targeted. This paper proposes and evaluates three search heuristics used to configure optimal products regarding multi-objective criteria. Results are compared against the default search strategy of the Choco constraint solver. We evaluated the performance for configuring optimal products in four state-of-the-art product lines and 130 generated variability models representing multi-product lines that scale up to 6400 features and 960 constraints. As a result, we observe that the proposed heuristics perform better than the default solver strategy when the variability models scale in terms of features. In contrast, the default strategy and one of the proposed heuristics perform better as the number of interdependencies between variability models increases. [ABSTRACT FROM AUTHOR]

Abstract In this paper, the multi-goal motion planning problem of an environment with some background information about its map is addressed in detail. The motion planning goal is to find a policy in belief space for the robot to traverse through a number of goal points. This problem is modeled as an asymmetric traveling salesman problem (TSP) in the belief space using Partially Observable Markov Decision Process (POMDP) framework. Then, feedback-based information roadmap (FIRM) algorithm is utilized to reduce the computational burden and complexity. By generating a TSP-FIRM graph, the search policy is obtained and an algorithm is proposed for online execution of the policy. Moreover, approaches to cope with challenges such as map updating, large deviations and high uncertainty in localization, which are more troublesome in a real implementation, are carefully addressed. Finally, in order to evaluate applicability and performance of the proposed algorithms, it is implemented in a simulation environment as well as on a physical robot in which some challenges such as kidnapping and discrepancies between real and computational models and map are examined. [ABSTRACT FROM AUTHOR]

Interval programming is a commonly used technique in real-world situations. Its related theories and methods have been widely researched. There are a variety of approaches for assessing solutions of an interval programming problem due to the particularity of intervals. It is well-known that different assessing approaches may produce different optimal solution(s) for the same interval programming problem, and it is rather difficult to choose from these assessing approaches for users, especially for those who have little knowledge about interval arithmetic, which greatly restricts its extensive applications. In this paper, we develop an ensemble framework for assessing solutions of interval programming problems. At the start, interval dominance rules are defined, and their correlations are described via exclusion, inclusion and equivalence; then, a rule reduction strategy is developed through inspecting the impact of different rules on the sorting of solutions, and a novel ensemble dominance relation for interval programming is proposed to evaluate solutions; furthermore, their complexities are analyzed; finally, the experimental results empirically validate the correctness and effectiveness of the proposed framework. [ABSTRACT FROM AUTHOR]

This paper proposes a novel preference degree algorithm to rank intuitionistic fuzzy values (IFVs) and applies it to multi-attribute group decision making (MAGDM) with IFVs. First, the concept of preference degree of IFVs is defined according to the geometrical representation of IFVs. Some useful properties of the defined preference degree are discussed. Combining the preference degree with the hesitation margin of IFVs, a novel preference degree algorithm is designed to rank a series of IFVs. In MAGDM problems with IFVs, the attribute weights would be usually diverse for different decision makers (DMs). To derive the attribute weights for each DM objectively, a multi-objective programming model is constructed and transformed into a linear program to resolve. Then, the consensus indices are calculated from three levels based on the individual fuzzy reciprocal preference relations and the collective one. To determine DMs’ weights, a linear goal programming model is established by maximizing the consensus index of group of DMs. Using the intuitionistic fuzzy weighted average operator, the individual comprehensive values of alternatives are obtained and further integrated into the collective comprehensive values of alternatives. The ranking order of alternatives is generated by the designed preference degree algorithm. At length, the validity of the proposed method is illustrated with a construction organization selection example. [ABSTRACT FROM AUTHOR]

This paper proposes an improved constrained teaching–learning-based optimization (ICTLBO) method to efficiently solve constrained optimization problems (COPs). In the teacher phase of ICTLBO, the population is partitioned into several subpopulations, and the direction information between the mean position of each subpopulation and the best position of population guide the corresponding subpopulation to the promising region promptly. Information exchange between different subpopulations is used to discourage premature convergence of each subpopulation. Furthermore, in the learner phase, a new learning strategy is introduced to improve the population diversity and enhance the global search ability. Three different constraint handling methods are adopted for three situations, which are infeasible, semi-feasible, and feasible situations, during the evolution process. To evaluate the performance of ICTLBO, 22 benchmark functions presented in CEC2006 and 18 benchmark functions introduced in CEC2010 are chosen as the test suite. Moreover, four widely used engineering design problems are selected to test the performance of ICTLBO for real-world problems. Experimental results indicate that ICTLBO can obtain a highly competitive performance compared with other state-of-the-art algorithms. [ABSTRACT FROM AUTHOR]

In this paper we deal with the theory of rough ideals started in (Davvaz, 2004). We show that the approximation spaces built from an equivalence relation compatible with the ring structure, i.e. associated to a two-sided ideal, are too naive in order to develop practical applications. We propose the use of certain crisp equivalence relations obtained from fuzzy ideals. These relations make available more flexible approximation spaces since they are enriched with a wider class of rough ideals. Furthermore, these are fully compatible with the notion of primeness (semiprimeness). The theory is illustrated by several examples of interest in Engineering and Mathematics. [ABSTRACT FROM AUTHOR]

Considering the practical application background in peer-to-peer network system, we investigate the single-variable term semi-latticized fuzzy relation geometric programming with max-product operator in this paper. Based on the characteristics of the objective function and feasible domain, we develop a matrix approach to deal with the proposed problem. A step-by-step algorithm is proposed to find an optimal solution without solving all the minimal solutions of the constraint. Two examples are given to illustrate the feasibility and efficiency of the algorithm. [ABSTRACT FROM AUTHOR]

In order to attain better reconstruction quality from compressive sensing (CS) of images, exploitation of the dependency or correlation patterns among the transform coefficients commonly has been employed. In this paper, we study a new image sensing technique, called compressive image sensing (CIS), with computational complexity O ( m 2 ), where m denotes the length of a measurement vector y = ϕ x , which is sampled from the signal x of length n via the sampling matrix ϕ with dimensionality m × n . CIS is basically a variation on compressive sampling. The contributions of CIS include: (i) reconstruction speed is extremely fast due to a closed-form solution being derived; (ii) certain reconstruction accuracy is preserved because significant components of x can be reconstructed with higher priority via an elaborately designed ϕ ; and (iii) in addition to conventional 1D sensing, we also study 2D separate sensing to enable simultaneous acquisition and compression of large-sized images. [ABSTRACT FROM AUTHOR]

The diversity of solutions is of great importance for multi-objective evolutionary algorithms. In this paper, a new multi-objective particle swarm optimization algorithm based on decomposition (MPSO/D) is proposed. Firstly, the objective space of a multi-objective problem is decomposed into a set of sub-regions based on a set of direction vectors. Then MPSO/D makes each sub-region have a solution to maintain the diversity. Secondly, considering the convergence of solutions, MPSO/D uses the crowding distance to calculate the fitness values of the reserved solutions for selection operator, and uses the neighboring particles of a particle to determine the global best historical position ( gbest ) of the particle. The proposed algorithm has been compared with NSGAII, MOEA/D and NNIA on sixteen test sets. The experimental results illustrate that the proposed algorithm outperforms NSGAII, MOEA/D and NNIA in terms of convergence and diversity. [ABSTRACT FROM AUTHOR]

Graph construction from data constitutes a pre-stage in many machine learning and computer vision tasks, like semi-supervised learning, manifold learning, and spectral clustering. The influence of graph construction procedures on learning tasks and their related applications has only received limited study despite its critical impact on accuracy. State-of-the-art graphs are built via sparse coding adopting ℓ 1 regularization. Those graphs exhibit good performance in many computer vision applications. However, the locality and similarity among instances are not explicitly used in the coding scheme. Furthermore, due to the use of ℓ 1 regularization, these construction approaches can be computationally expensive. In this paper, we investigate graph construction using the data self-representativeness property. By incorporating a variant of locality-constrained linear coding (LLC), we introduce and derive four variants for graph construction. These variants adopt a two phase LLC (TPLLC). Compared with the recent ℓ 1 graphs, our proposed objective function, associated with three variants, has an analytical solution, and thus, is more efficient. A key element of the proposed methods is the second phase of coding that allows data closeness, or locality, to be naturally incorporated. It performs a coding over some selected relevant samples and reinforces the individual regularization terms by exploiting the coefficients estimated in the first phase. Comprehensive experimental results using several benchmark datasets show that it can achieve or outperform existing state-of-the-art results. Furthermore, it is shown to be more efficient than the robust ℓ 1 graph construction schemes. [ABSTRACT FROM AUTHOR]

To avoid traffic accidents, drivers must constantly be aware of nearby vehicles. Unfortunately, nearby vehicles often go unnoticed because of various obstacles such as other vehicles, buildings, or poor weather. In this paper, we study Moving range k -nearest neighbor (MR k NN) queries as a tool for continuously monitoring nearby moving objects. A simple approach to processing MR k NN queries is to have each object periodically broadcast information regarding its movements (i.e., location and velocity at a particular time) to other objects. However, this simple technique cannot be used to process MR k NN queries owing to the limited network bandwidth in mobile peer-to-peer environments. Therefore, we address this bandwidth limitation by proposing a probabilistic algorithm, called MINT, for M ov I ng range k - N N queries with quali T y guarantee over uncertain moving objects. MINT provides users with approximate answers with a quality guarantee, rather than exact answers, with near optimal communication costs. Using a series of simulations, we demonstrate the efficiency and efficacy of MINT in evaluating MR k NN queries with a quality guarantee. [ABSTRACT FROM AUTHOR]

Tuple extraction from streaming XML should be cost effective for real-time query evaluation. Recently, StreamTX exhibits a good performance in terms of both running time and memory usage to support the tuple extraction queries for streaming XML. However, we empirically observe that StreamTX incurs computational overhead unnecessarily, since it builds on TwigStack , an XML query processing algorithm originally developed for stored XML. In this paper, we first design a non-recursive XQStream algorithm to handle inefficient recursive calls of StreamTX . Subsequently, we extend the basic XQStream by incorporating two novel schemes: (1) the relational pointer to efficiently and effectively evaluate the structural relationship of elements, and (2) the pattern reuse to reduce redundant path evaluations for pattern matching. The performance evaluation on various datasets provides new empirical findings. First, XQStream++ , which incorporates the relational pointer and the pattern reuse scheme into XQStream , significantly outperforms the state-of-the-art algorithms in running time with a small, nearly constant memory usage. Second, the most recently released XQuery engines outperform StreamTX in running time. [ABSTRACT FROM AUTHOR]

The proliferation of rich information available for real world entities and their relationships gives rise to a general type of graph, namely multi-valued attributed graph , where graph vertices are associated with a number of attributes and a vertex may have multiple values on an attribute. It would be useful if we can cluster such graphs into densely connected components with homogeneous attribute values. Recent work has studied graph clustering in attributed graphs considering the full attribute space. However, full space clustering often leads to poor results due to irrelevant attributes. In this paper, we study subspace clustering in multi-valued attributed graph and propose an algorithm SCMAG for community detection. Our algorithm uses a cell-based subspace clustering approach and identifies cells with dense connectivity in the subspaces. Random walk with restart is used to measure the structural connectivity and attribute similarity. An indexing scheme is designed to support efficiently calculating cell connectivity from random walk scores. We also propose a new cell combining strategy on dimensions of categorical attributes and a novel mechanism to handle multi-valued attributes. Experimental results on IMDB data and bibliographic data demonstrate that SCMAG significantly outperforms the state-of-the-art subspace clustering algorithm and attributed graph clustering algorithm. Case studies show SCMAG can find dense communities with homogeneous properties under different subspaces. [ABSTRACT FROM AUTHOR]

This paper proposes a Pareto-based grouping discrete harmony search algorithm (PGDHS) to solve the multi-objective flexible job shop scheduling problem (FJSP). Two objectives, namely the maximum completion time (makespan) and the mean of earliness and tardiness, are considered simultaneously. Firstly, two novel heuristics and several existing heuristics are employed to initialize the harmony memory. Secondly, multiple harmony generation strategies are proposed to improve the performance of harmony search algorithm. The operation sequence in a new harmony is produced based on the encoding method and the characteristics of FJSP. Thirdly, two local search methods based on critical path and due date are embedded to enhance the exploitation capability. Finally, extensive computational experiments are carried out using well-known benchmark instances. Three widely used performance measures, number of non-dominated solutions, diversification metric and quality metric, are employed to test the performance of PGDHS algorithm. Computational results and comparisons show the efficiency and effectiveness of the proposed PGDHS algorithm for solving multi-objective flexible job-shop scheduling problem. [ABSTRACT FROM AUTHOR]

Quantum-behaved particle swarm optimization (QPSO), a novel variant of PSO inspired by quantum mechanics, is a global convergence guaranteed algorithm, which outperforms the original PSO in search ability and has fewer parameters to control. But as many other PSOs, it is easy to fall into local optimum in solving high-dimensional complex optimization problems. This paper proposes an improved QPSO algorithm for continuous non-linear large scale problems based on memetic algorithm and memory mechanism. The memetic algorithm is used to make all particles (each particle corresponding to a memetic) gain some experience through a local search before being involved in the evolutionary process, and the memory mechanism is used to introduce a so-called ‘bird kingdom’ with memory capacity, both of which can improve the global search ability of the algorithm. Another difference compared to the previous QPSOs is that we let each dimension of a particle update with the same random number, thus increasing the speed of convergence and enhancing the ability of local search. Numerical experiments are conducted to compare the proposed algorithm with different variants of PSO and other swarm intelligence algorithms. The experimental results show the superiority of the proposed approach on benchmark test functions. [ABSTRACT FROM AUTHOR]

Abstract: This paper aims to solve the problem of multiple-objective linear optimization model subject to a system of inf- composition fuzzy relation equations, where is R-, S- or QL-implications generated by continuous Archimedean t-norm (s-norm). Since the feasible domain of inf- relation equations constraint is nonconvex, these traditional mathematical programming techniques may have difficulty in computing efficient solutions for this problem. Therefore, we firstly investigate the solution sets of a system of inf- composition fuzzy relation equations in order to characterize the feasible domain of this problem. And then employing the smallest solution of constraint equation, we yield the optimal values of linear objective functions subject to a system of inf- composition fuzzy relation equations. Secondly, the two-phase approach is applied to generate an efficient solution for the problem of multiple-objective linear optimization model subject to a system of inf- composition fuzzy relation equations. Finally, a procedure is represented to compute the optimal solution of multiple-objective linear programming with inf- composition fuzzy relation equations constraint. In addition, three numerical examples are provided to illustrate the proposed procedure. [Copyright &y& Elsevier]