Negative Ideal Point Research Articles

Multi-Attribute Decision Making Method Based on Intuitionistic Fuzzy Grey Sets

In this paper, it discussed the fuzzy multi-attribute decision making problems that are the attribute weights are known and the attribute values are intuitionistic fuzzy grey sets. Intuitionistic fuzzy grey set is given, and the positive and negative ideal points are introduced, then the definition of Hamming distance formula between the intuitionistic fuzzy grey numbers is discussed. Moreover, it puts forward multi-attribute decision making method based on intuitionistic fuzzy grey set, and discusses the steps of the method. Then, the examples are given to show that the method is reasonable and effective.

Imprecise DEA Model Based on TOPSIS

In view of the defect that TOPSIS (Technique for Order Preference by Similarity to Ideal Solution) can not deal with imprecise data properly in multiple criteria decision making. And the weights are often hard to reflect the fact because of subjective preference of decision makers. We proposed a hybrid model combines TOPSIS and imprecise DEA model to improve the disadvantages. Ideal DMU and anti-ideal DMU were built, and the corresponding positive ideal point and negative ideal point were established. Imprecise DEA was set up and an upper-lower limit method is utilized to formulate the imprecise efficiency scores of the two hypothetical DMUs. Based on the distances between DMU0 and the two hypothetical DMUs respectively, imprecise relative closeness was formulated to rank the superiority of all DMUs. The imprecise DEA model based on TOPSIS can avoid too subjective weights and make the evaluation more rational. A numerical example indicated the efficiency of the hybrid measure.

Porphyry Copper Mineral Prospectivity Mapping Using Interval Valued Fuzzy Sets Topsis Method in Central Iran

Geospatial Information System (GIS) provide tools to quantitatively analysis and combination of datasets from geological, geophysical, remote sensing and geochemical surveys for decision-making processes. Excellent coverage of well-documented and good quality data enables testing of variable exploration modeling in an efficient way. The study area of this research is the most important part of Cu (Mo) porphyry—type mineralization belt in Iran. There are some well-known porphyry copper deposits in this region like Sarcheshmeh and Meiduk mines, but certainly there are same grounds to search for new porphyry deposits. The risks of developing mineral resources need to be known as accurately as possible, with regarding to all features those are effective in mineralization. These features can be recognized respect to Critical Genetic Factors (CGF’s) using Critical Recognition Criteria (CRC) for each type of mineralization. CGF’s can be employed for designing a Conceptual Genetic Model (CGM). Evidence maps create on the basis of CGM and then integrate together for production of Mineral Prospectivity Map (MPM). This map categorizes the areas based on their exploration importance. There are several techniques for creation of MPM. Interval Valued Fuzzy Sets (IVFSs) TOPSIS method was applied in this research. This method as a knowledge-driven method, allocate appropriate weights to layers on the basis of the effective membership, non membership, and non-certainty. The fundamental concept of TOPSIS is that the chosen alternatives should have the shortest distance from the positive ideal points (A*) and the farthest distance from negative ideal points (A-).

Study on the safety production evaluation of the coal mine based on entropy-TOPSIS

In order to evaluate the safety production situation of the coal mine effectively, selected the indicators about mine production safety, applied entropy method to determine the objective weight of each index, calculated the distance and close degree between the mines and the ideal point and negative ideal point, and then evaluated the safety production situation of the mines according to the close degree. The results show that the method provides a reasonable, concise and more objective idea to evaluate the safety production situation of the mines.

Area ranking of fuzzy numbers based on positive and negative ideal points

The maximizing set and minimizing set method is a popular ranking approach for fuzzy numbers, which ranks them based on their left, right and total utilities. This paper presents an alternative ranking approach for fuzzy numbers called area ranking based on positive and negative ideal points, which defines two new alternative indices for the purpose of ranking. The two new indices are defined in terms of a decision maker (DM)’s attitude towards risks and the left and the right areas between fuzzy numbers and the two ideal points. It is shown that the area ranking approach has strong discrimination power and can rank fuzzy numbers that are unable to be discriminated by the maximizing set and minimizing set method. It is also shown that the DM’s attitude towards risks may have a significant impact on the ranking of fuzzy numbers. As a side product, a new defuzzification formula is also developed and discussed.

Research on Risk Evaluation in Supply Chain Based on Grey Relational Method

Supply chain risk evaluation is a multi-criteria decision making problem under fuzzy environments. To tackle the problem, this paper firstly identifies and discusses some of the important and critical decision criteria and constructs the evaluation indicator framework. Then this paper presents a modified grey relational analysis method based on the concepts of ideal and anti-ideal points. In the method, the weight information is partially known and the vagueness and subjectivity are handled with linguistic terms parameterized by triangular fuzzy numbers. Besides, a single objective programming model is developed to determine the relation degree between every alternative and positive ideal point or negative ideal point. By solving the programming model, the weight vector of criteria is calculated. The alternatives are ranked by the relative relation degree. Finally, a case study is given to demonstrate the proposed method’s effectiveness.

An interactive procedure for linguistic multiple attribute decision making with incomplete weight information

In this paper, we consider the multiple attribute decision making (MADM) problems, in which the information about attribute weights is partly known and the attribute values are expressed in linguistic labels. We first define the concepts of linguistic positive ideal point, linguistic negative ideal point, and satisfactory degree of alternative. Based on these concepts, we then establish some linear programming models, through which the decision maker interacts with the analyst. Furthermore, we establish a practical interactive procedure for solving the MADM problems considered in this paper. The interactive process can be realized by giving and revising the satisfactory degrees of alternatives till an optimum satisfactory solution is achieved. Finally, a practical example is given to illustrate the developed procedure.

Group decision-making based on concepts of ideal and anti-ideal points in a fuzzy environment

Decision-making problems (location selection) often involve a complex decision-making process in which multiple requirements and uncertain conditions have to be taken into consideration simultaneously. In evaluating the suitability of alternatives, quantitative/qualitative assessments are often required to deal with uncertainty, subjectiveness and imprecise data, which are best represented with fuzzy data. This paper presents a new method of analysis of multicriteria based on the incorporated efficient fuzzy model and concepts of positive ideal and negative ideal points to solve decision-making problems with multi-judges and multicriteria in real-life situations. As a result, effective decisions can be made on the basis of consistent evaluation results. Finally, this paper uses a numerical example of location selection to demonstrate the applicability of this method, with its simplicity in both concept and computation. The results show that this method can be implemented as an effective decision aid in selecting location or decision-making problems.

A note on DEA efficiency assessment using ideal point: An improvement of Wang and Luo’s model

Evaluating the efficiency of organizational units continues to be a difficult problem to solve, especially when the multiplicity of inputs (resources, costs) and outputs (services, products) associated with these units is considered. This paper considers a previous article published by Wang and Luo [Y. Wang, Y. Luo, DEA efficiency assessment using ideal and anti-ideal decision-making units, Applied Mathematics and Computation 173 (2) (2006) 902–915] in the journal of Applied Mathematics and Computation where data envelopment analysis (DEA) and the technique for order preference by similarity to ideal solution (TOPSIS) are integrated in ranking of decision-making units (DMUs). Wang and Luo (2006) contribute to a very interesting topic by showing that the TOPSIS idea can be combined to DEA for a comprehensive ranking of DMUs. However, this paper finds that their approach is problematic in employing the negative ideal point (NIP) for DEA computation. Their ideal point based models rely on using conflicting efficiency concepts. We slightly revised the models so that a DEA analysis using TOPSIS idea can be performed. Numerical demonstration reveals that our approach produces a ranking result that is consistent with that in previous studies.