Two-Stage Interactive Multi-Objective Decision-Making Method Based on the Satisfactoriness Criterion

In this paper, for multi objective decision making, the defects on the commonly used interactive methods based on the satisfactoriness criterion is studied. Then a class of two stage interactive method based on the satisfactoriness criterion is proposed for improvement with the satisfactoriness criterion being determined through the collection of the decision makers preference information. An application example is presented for illustration of applicability of the method.

A decision support system for satellite layout integrating multi-objective optimization and multi-attribute decision making

A decision support system, including a multi-objective optimization framework and a multi-attribute decision making approach is proposed for satellite equipment layout. Firstly, given three objectives (to minimize the C.G. offset, the cross moments of inertia and the space debris impact risk), we develop a threedimensional layout optimization model. Unlike most of the previous works just focusing on mass characteristics of the system, a space debris impact risk index is developed. Secondly, we develop an efficient optimization framework for the integration of computer-aided design (CAD) software as well as the optimization algorithm to obtain the Pareto front of the layout optimization problem. Thirdly, after obtaining the candidate solutions, we present a multi-attribute decision making approach, which integrates the smart Pareto filter and the correlation coefficient and standard deviation (CCSD) method to select the best tradeoff solutions on the optimal Pareto fronts. Finally, the framework and the decision making approach are applied to a case study of a satellite platform.

Improved Fuzzification Method for Multi-Objective Decision-Making and Its Application in Evaluation of Highway Planning

A new fuzzification method for multi-objective decision-making and selective sorting is proposed on the basis of the fuzzy consistent relation, and the specific algorithm is presented. The method is applied to the evaluation of highway planning of Zhanjiang city. To decrease the subjectivity in the process of decision-making, the LOWA operator is introduced, and a discussion on how to select appropriate weights involved in multi-objective sorting is made. It is concluded that it is feasible to apply the fuzzy consistent relation to multi-objective decision-making analysis, and the improved fuzzication method is workable.

Control Method of Effect of Robust Optimization in Multi-Player Multi-Objective Decision-Making

In the real situations of supply chain, there are different parts such as facilities, logistics warehouses and retail stores and they handle common kinds of products. In this research, these situations are focused on as the background of this research. They deal with the common quantities of their products, but due to their different environments, the optimal production quantity of one part can be unacceptable to another part and it may suffer a heavy loss. To avoid that kind of unacceptable situations, the common production quantities should be acceptable to all parts in one supply chain. Therefore, the motivation of this research is the necessity of the method to find the production quantities that make all decision makers acceptable is needed. However, it is difficult to find the production quantities that make all decision makers acceptable. Moreover, their acceptable ranges do not always have common ranges. In the decision making of car design, there are similar situations to this type of decision making. The performance of a car consists of purposes such as fuel efficiency, size and so on. Improving one purpose makes another worse and the relationship between these purposes is tradeoff. In these cases, Suriawase process is applied. This process consists of negotiations and reviews of the requirements of the purposes. In the step of negotiations, the requirements of the purposes are share among all decision makers and the solution that makes them as satisfied as possible. In the step of reviews of the requirements, they are reviewed based on the result of the negotiation if the result is unacceptable to some of decision makers. Therefore, through the iterations of the two steps, the solution that makes all decision makers satisfied is obtained. However, in the previous research, the effects that one decision maker reviews requirements in Suriawase process are quantified, but the mathematical model to modify the ranges of production quantities of all decision makers simultaneously is not shown. Therefore, in this research, based on Suriawase process, the mathematical model of multi-player multi-objective decision making is proposed. The mathematical model of multi-player multi-objective decision making by using linear physical programming (LPP) and robust optimization (RO) in the previous research is the basis of the methods of this research. LPP is one of the multi-objective optimization methods and RO is used to make the balance of the preference levels among decision makers. In LPP, the preference ranges of all objective functions are needed, so as the hypothesis of this research. In the research referred in this research, the method to control the effect of RO is not shown. If the effect of RO is too big, the average of the preference level becomes worse. The purpose of this research is to reproduce the mathematical model of multi-player multi-objective decision making based on Suriawase process and propose the method to control the effect of RO. In the proposed model, a set of the solutions of the negotiation problem is obtained and it is proved by the result of the numerical experiment. Therefore, the conclusion that the proposed model is available to obtain a set of the solutions of the negotiation problems in supply chain.

GIS-Based Multi-Criteria Decision Analysis (MCDA) and Analytical Hierarchy Process (AHP) Techniques to Derive Flood Risks Management on Rice Productivity in Gishari Marshland

Floods are phenomenon with significant socio-economic implications mainly for human loss, agriculture, livestock, soil loss and land degradation, for which many researchers try to identify the most appropriate methodologies by analyzing their temporal and spatial development. This study therefore attempts to employ the GIS-based multi-criteria decision analysis and analytical hierarchy process techniques to derive the flood risks management on rice productivity in the Gishari Agricultural Marshland in Rwamagana district, Rwanda. Here, six influencing potential factors to flooding, including river slope, soil texture, Land Use Land Cover through Land Sat 8, rainfall, river distance and Digital Elevation Model are considered for the delineation of flood risk zones. Data acquisition like Landsat 8 images, DEM, land use land cover, slope, and soil class in the study area were considered. Results showed that if the DEM is outdated or inaccurate due to changes in the terrain, such as construction, excavation, or erosion, the predicted flood patterns might not reflect the actual water flow. This could result unexpected flood extents and depths, potentially inundating rice fields that were not previously at risk and this, expectedly explained that the increase 1 m in elevation would reduce the rice productivity by 0.17% due to unplanned flood risks in marshland. It was found that the change in rainfall distribution in Gishari agricultural marshland would also decrease the rice productivity by 0.0018%, which is a sign that rainfall is a major factor of flooding in rice scheme. Rainfall distribution plays a crucial role in flooding analysis and can directly impact rice productivity. Oppositely, another causal factor was Land Use Land Cover (LULC), where the Multivariate Logistic Regression Model Analysis findings showed that the increase of one unit in Land Use Land Cover would increase rice productivity by 0.17% of the total rice productivity from the Gishari Agricultural Marshland. Based on findings from these techniques, the Gishari Agricultural Marshlands having steeped land with grassland is classified into five classes of flooding namely very low, low, moderate, high, and very high which include 430%, 361%, 292%, 223%, and 154%. Government of Rwanda and other implementing agencies and major key actors have to contribute on soil and water conservation strategies to reduce the runoff and soil erosion as major contributors of flooding.

Multi Objective Decision Making Method Based on Evaluation Criterion for Problems with Linear Value Function

A class of interactive multi objective decision making method by means of evaluation criterion is proposed for problems with linear value function,in which case,the decision maker(DM) usually has only unwhole information of weights for objectives. The concept of fault measure of the evaluation criterion is proposed to measure the deviation of the evaluation criterion from the DMs preference structure.The approach to obtain an upper boundary of fault measure of an evaluation criterion,and the approach to modify the evaluation criterion to be one with smaller fault measure,and the approach to obtain a pre optimized objective set by evaluation criterion with certain fault measure are also proposed.

Aggregation operators on intuitionistic trapezoidal fuzzy number and its application to multi-criteria decision making problems

Intuitionistic trapezoidal fuzzy numbers and their operational laws are defined. Based on these operational laws, some aggregation operators, including intuitionistic trapezoidal fuzzy weighted arithmetic averaging operator and weighted geometric averaging operator are proposed. Expected values, score function, and accuracy function of intuitionitsic trapezoidal fuzzy numbers are defined. Based on these, a kind of intuitionistic trapezoidal fuzzy multi-criteria decision making method is proposed. By using these aggregation operators, criteria values are aggregated and integrated intuitionistic trapezoidal fuzzy numbers of alternatives are attained. By comparing score function and accuracy function values of integrated fuzzy numbers, a ranking of the whole alternative set can be attained. An example is given to show the feasibility and availability of the method.

Two-phase TOPSIS of uncertain multi-attribute group decision-making

To solve the uncertain multi-attribute group decision-making of unknown attribute weights,three optimal models are built to decide the corresponding ideal solution weights,standard deviation weights and mean deviation weights.The comprehensive attribute weights are gotten through the product of the above three kinds of weights.And each decision maker＇s weighted decision matrices are also received by using the integrated attribute weights.The closeness degrees are also gotten by use of technique for order preference by similarity to ideal solution（TOPSIS） through dealing with the weighted decision matrices.At the same time the group decision matrix and weighted group decision matrix are gotten by using each decision-maker＇s closeness degree to every project.Then the vertical TOPSIS method is used to calculate the closeness degree of each project.So these projects can be ranked according to their values of the closeness degree.The process of the method is also given step by step.Finally,a numerical example demonstrates the feasibility and effectiveness of the approach.

Approach to stochastic multi-attribute decision problems using rough sets theory

Multi-attribute decision problems where the performances of the alternatives are random variables are considered. The suggested approach grades the probabilities of preference of one alternative over another with respect to the same attribute. Based on the graded probabilistic dominance relation, the pairwise comparison information table is defined. The global preferences of the decision maker can be seen as a rough binary relation. The present paper proposes to approximate this preference relation by means of the graded probabilistic dominance relation with respect to the subsets of attributes. At last, the method is illustrated by an example.

Sequential maneuvering decisions based on multi-stage influence diagram in air combat

A multi-stage influence diagram is used to model the pilot＇s sequential decision making in one on one air combat. The model based on the multi-stage influence diagram graphically describes the elements of decision process, and contains a point-mass model for the dynamics of an aircraft and takes into account the decision maker＇s preferences under uncertain conditions. Considering an active opponent, the opponent＇s maneuvers can be modeled stochastically. The solution of multistage influence diagram can be obtained by converting the multistage influence diagram into a two-level optimization problem. The simulation results show the model is effective.

Multi-target Collaborative Combat Decision-Making by Improved Particle Swarm Optimizer

A decision-making problem of missile-target assignment with a novel particle swarm optimization algorithm is proposed when it comes to a multiple target collaborative combat situation.The threat function is established to describe air combat situation.Optimization function is used to find an optimal missile-target assignment.An improved particle swarm optimization algorithm is utilized to figure out the optimization function with less parameters,which is based on the adaptive random learning approach.According to the coordinated attack tactics,there are some adjustments to the assignment.Simulation example results show that it is an effective algorithm to handle with the decision-making problem of the missile-target assignment(MTA)in air combat.

Novel combinatorial algorithm for the problems of fuzzy grey multi-attribute group decision making

To study the fuzzy and grey information in the problems of multi-attribute group decision making, the basic concepts of both fuzzy grey numbers and grey interval numbers are given firstly, then a new model of fuzzy grey multi-attribute group decision making based on the theories of fuzzy mathematics and grey system is presented. Furthermore, the grey interval relative degree and deviation degree is defined, and both the optimistic algorithm of the grey interval relational degree and the algorithm of deviation degree minimization for solving this new model are also given. Finally, a decision making example to demonstrate the feasibility and rationality of this new method is given, and the results by using these two algorithms are uniform.

Method for uncertain multi-attribute decisionmaking with preference information in the form of interval numbers complementary judgment matrix

The uncertain multi-attribute decision-making problems because of the information about attribute weights being known partly, and the decision maker＇s preference information on alternatives taking the form of interval numbers complementary to the judgment matrix, are investigated. First, the decision-making information, based on the subjective uncertain complementary preference matrix on alternatives is made uniform by using a translation function, and then an objective programming model is established. The attribute weights are obtained by solving the model, thus the overall values of the alternatives are gained by using the additive weighting method. Second, the alternatives are ranked, by using the continuous ordered weighted averaging （C-OWA） operator. A new approach to the uncertain multi-attribute decision-making problems, with uncertain preference information on alternatives is proposed. It is characterized by simple operations and can be easily implemented on a computer. Finally, a practical example is illustrated to show the feasibility and availability of the developed method.

Multi-criteria linguistic interval group decision-making approach

For group decision-making problems with linguistic assessment information, a new method based on two-tuple and WC-OWA operator is proposed, in which the criteria＇s weights and the decision-makers＇ preference information might take the form of linguistic grade, or might be between two continuous linguistic grades, or might be linguistic interval, or might be default. In this method, all linguistic values are transformed into two-tuple, and an aggregative decision-making matrix is obtained by using interval operation. The group aggregative values of each criterion on alternatives are computed by using a WC-OWA operator, the aggregative values on alternatives are worked out, and transformed into two-tuple. And the rank of the alternatives is obtained by using the order property of two-tuple. An example shows the feasibility and effectiveness of the proposed method.

Co-optimization of carbon dioxide storage and enhanced oil recovery in oil reservoirs using a multi-objective genetic algorithm(NSGA-Ⅱ)

Climate researchers have observed that the carbon dioxide （CO2） concentration in the atmosphere have been growing significantly over the past century. CO2 from energy represents about 75% of the greenhouse gas （GHG） emissions for Annex B （Developed） countries, and over 60% of global emissions. Because of impermeable cap rocks hydrocarbon reservoirs are able to sequester CO〉 In addition, due to high-demand for oil worldwide, injection of CO2 is a useful way to enhance oil production. Hence, applying an efficient method to co-optimize CO2 storage and oil production is vital. Lack of suitable optimization techniques in the past led most multi-objective optimization problems to be tackled in the same way as a single objective optimization issue. However, there are some basic differences between the multi and single objective optimization methods. In this study, by using a non- dominated sorting genetic algorithm （NSGA-II） for an oil reservoir, some appropriate scenarios are proposed based on simultaneous gas storage and enhanced oil recovery optimization. The advantages of this method allow us to amend production scenarios after implementing the optimization process, by regarding the variation of economic parameters such as oil price and CO2 tax. This leads to reduced risks and time duration of making new decisions based on upcoming situations.

A Method of Job Scheduling on SMEs' Key Equipments Based on Hybrid Multi-attribute Decision Making

An analysis of the key factors affecting on the single production process job scheduling of the parts waiting for be- ing processed on the key equipments for SMEs (Small Manufacturing Enterprises) is given in this paper,which include interval number,real number and uncertain linguistic value.A kind of hybrid multi-attribute decision making method for the single pro- duction process job scheduling is presented in this paper,that the parts are firstly sorted about each factor,and then the total evalu- ative attributive value of each part is calculated with the method of weighted arithmetic average,and thus the part with the highest total evaluative attributive value is chosen for being processed firstly.The mathematic model corresponding to the method is set up in this paper.An example is studied in this paper,and the results of the example testify the correctness of this model.

Multi-criteria decision-making approach with incomplete certain information based on ternary AHP

It is not uncommon in multiple criteria decision-making that the numerical values of alternatives of some criteria are subject to imprecision, uncertainty and indetermination and the information on weights of criteria is incomplete certain. A new multiple criteria decision- making method with incomplete certain information based on ternary AHP is proposed. This improves on Takeda＇s method. In this method, the ternary comparison matrix of the alternatives under each pseudo-criteria is constructed, the eigenvector associated with the maximum eigenvalue of the ternary comparison matrix is attained as to normalize priority vector of the alternatives, then the order of alternatives is obtained by solving two kinds of linear programming problems. Finally, an example is given to show the feasibility and effectiveness of the method.

Multi-criteria group decision making with fuzzy data:an extension of the VIKOR method

The VIKOR method is a multi-criteria decision making aid, which employs linear normalization to offer compromise solu- tions and has been successfully applied to various group decision making problems. However, the conventional VIKOR techniques used to integrate group judgments and the information loss arising from defuzzification are problematic and distort final outcomes. An improved integration method, which is optimization-based, is proposed. And it can handle fuzzy criteria values and weights. The precondition for accurately defuzzifying triangular fuzzy num- bers is identified. Several effective defuzzification procedures are proposed to improve the extant VIKOR, and a comprehensive evaluation framework is offered to aid multi-criteria group decision making. Finally, a numerical example is provided to illustrate the practicability of the proposed method.

A Comprehensive Overview of the ELECTRE Method in Multi-Criteria Decision-Making

The ELECTRE(ELimination Et Choix Traduisant la REalite)method has gained widespread recognition as one of the most effective multi-criteria decision-making(MCDM)methods.Its versatility allows it to be applied in a wide range of areas such as engineering,economics,business,environmental management and many others.This paper aims to provide an overview of the ELECTRE method,including its fundamental concepts,applications,advantages,and limitations.At its core,the ELECTRE method is an outranking family of MCDM techniques,which allows for the direct comparison of alternatives based on a set of criteria.The method takes into account the preferences and importance of decision-makers and generates a ranking of the alternatives based on their relative strengths and weaknesses.The ELECTRE method is a powerful tool for decision-making,and its applicability to a wide range of fields demonstrates its versatility and adaptability.By understanding its concepts,applications,merits,and demerits,decision-makers can use the ELECTRE method to make informed and effective decisions in a variety of contexts.

Extension of TOPSIS for fuzzy multi-attribute decision making problem based on experimental analysis

This paper is concerned with a technique for order performance by similarity to ideal solution（TOPSIS） method for fuzzy multi-attribute decision making,in which the information about attribute weights is partly known and the attribute values take form of triangular fuzzy numbers.Considering the fact that the triangular fuzzy TOPSIS results yielded by different distance measures are different from others,a comparative analysis of triangular fuzzy TOPSIS ranking from each distance measure is illustrated with discussion on standard deviation.By applying the most reasonable distance,the deviation degrees between attribute values are measured.A linear programming model based on the maximal deviation of weighted attribute values is established to obtain the attribute weights.Therefore,alternatives are ranked by using TOPSIS method.Finally,a numerical example is given to show the feasibility and effectiveness of the method.