Solving fuzzy multi-objective linear programming problems using deviation degree measures and weighted max–min method

Cheng, Haifang; Huang, Weilai; Zhou, Quan; Cai, Jianhu

doi:10.1016/j.apm.2013.01.048

Cited by 42 publications

(24 citation statements)

References 38 publications

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“…As a typical aggregation function, we may recall arithmetic mean, geometric mean, minimum operator, product operator. Among the several choices, weighted arithmetic mean (Lai and Lai 2000) and minimum operator (Cheng et al 2013) are widely used in literature to aggregate the objectives. However, as mentioned earlier, due to the effectiveness of the product operator (Cheng and Li 1996;Deep et al 2011) over the other existing aggregation functions, we adopt product operator as aggregation function which may be written as…”

Section: Normalization Of Values Of Linguistic Variables Involved In mentioning

confidence: 99%

Multi-objective optimization problem under fuzzy rule constraints using particle swarm optimization

Chakraborty

Guha

2015

Soft Comput

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In this paper, a fuzzy multi-objective programming problem is considered where functional relationships between decision variables and objective functions are not completely known to us. Due to uncertainty in real decision situations sometimes it is difficult to find the exact functional relationship between objectives and decision variables. It is assumed that information source from where some knowledge may be obtained about the objective functions consists of a block of fuzzy if-then rules. In such situations, the decision making is difficult and the presence of multiple objectives gives rise to multi-objective optimization problem under fuzzy rule constraints. In order to tackle the problem, appropriate fuzzy reasoning schemes are used to determine crisp functional relationship between the objective functions and the decision variables. Thus a multi-objective optimization problem is formulated from the original fuzzy rule-based multi-objective optimization model. In order to solve the resultant problem, a deterministic single-objective non-linear optimization problem is reformulated with the help of fuzzy optimization technique. Finally, PSO (Particle Swarm Optimization) algorithm is employed to solve the resultant singleobjective non-linear optimization model and the computation procedure is illustrated by means of numerical examples. Communicated by V. Loia.

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Section: Normalization Of Values Of Linguistic Variables Involved In mentioning

confidence: 99%

Multi-objective optimization problem under fuzzy rule constraints using particle swarm optimization

Chakraborty

Guha

2015

Soft Comput

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“…Numbers. Next, we introduce the concept of deviation distances and give the definition of deviation degrees of two triangular fuzzy numbers used in [31,32].…”

Section: Deviation Degree Of Triangular Fuzzymentioning

confidence: 99%

“…Definition 5 (see [32]). Let̃= ( (1) , (2) , (3) ) and̃= ( (1) , (2) , (3) ) be two triangular fuzzy numbers; then (1) the deviation distance of̃from̃is…”

Section: Deviation Degree Of Triangular Fuzzymentioning

confidence: 99%

Solving the Fully Fuzzy Bilevel Linear Programming Problem through Deviation Degree Measures and a Ranking Function Method

Ren

2016

Mathematical Problems in Engineering

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This paper is concerned with a class of fully fuzzy bilevel linear programming problems where all the coefficients and decision variables of both objective functions and the constraints are fuzzy numbers. A new approach based on deviation degree measures and a ranking function method is proposed to solve these problems. We first introduce concepts of the feasible region and the fuzzy optimal solution of a fully fuzzy bilevel linear programming problem. In order to obtain a fuzzy optimal solution of the problem, we apply deviation degree measures to deal with the fuzzy constraints and use a ranking function method of fuzzy numbers to rank the upper and lower level fuzzy objective functions. Then the fully fuzzy bilevel linear programming problem can be transformed into a deterministic bilevel programming problem. Considering the overall balance between improving objective function values and decreasing allowed deviation degrees, the computational procedure for finding a fuzzy optimal solution is proposed. Finally, a numerical example is provided to illustrate the proposed approach. The results indicate that the proposed approach gives a better optimal solution in comparison with the existing method.

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“…But the real decision environment often are fuzzy and a lot scholars start to study on this case in combination with fuzzy set theory [4]. Reference [5] presented a fuzzy multiobjective model for supplier selection in reverse logistics systems for the suitability inconsistency problems of candidates; [6] proposed a fuzzy multi-objective model for solving project network management problem with bonus and incremental penalty cost; [7] constructed a fuzzy multiobjective model reflecting service fees and product quality for supplier selection under the electronic commerce environment; [8] proposed a method for solving fuzzy multiobjective programming with triangular fuzzy number coefficients and fuzzy equality or inequality constraints using deviation degree measures and weighted max-min method; [9] develop an interactive two-phase method to solve the fuzzy multi-objective decision problems; [10] proposed a new measure Me under fuzzy environment and established a general fuzzy multi-objective model with expected objectives and chance constraints (ECM) based on the Me.…”

Section: Introductionmentioning

confidence: 99%

A New Approach to Multi-objective Programming Based on Satisfied Degree under Fuzzy Environment

Jie¹,

Li²,

Jin³

2015

2015 10th International Conference on Intelligent Systems and Knowledge Engineering (ISKE)

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Fuzziness is a common uncertainty who exists widespread in decision process and how to process fuzziness is a widespread context in academic and application fields. For the multi-objective programming under fuzzy environment, this paper firstly analyze the essential characteristics of fuzzy objectives. Then fuzzy objectives are divided into three kinds and represent by fuzzy number by introducing deviation parameter α . Then, regarding membership of fuzzy number as the satisfied degree, we establish the multi-objective programming based on satisfied degree (denotes as MP-SD) and a new solving strategy based on MP-SD is further given. Finally, we illustrate the validity of MP-SD through a case. The analytical results show that the proposed approach is effective in fuzzy decision environment and provide rich decision theories for integrated multi-objective programming problems in artificial intelligence and resource management and so on.

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Solving fuzzy multi-objective linear programming problems using deviation degree measures and weighted max–min method

Cited by 42 publications

References 38 publications

Multi-objective optimization problem under fuzzy rule constraints using particle swarm optimization

Multi-objective optimization problem under fuzzy rule constraints using particle swarm optimization

Solving the Fully Fuzzy Bilevel Linear Programming Problem through Deviation Degree Measures and a Ranking Function Method

A New Approach to Multi-objective Programming Based on Satisfied Degree under Fuzzy Environment

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