A Study and Estimation of Different Distance Measures in Generalized Fuzzy TOPSIS to Improve Ranking Order

2019 ◽  
pp. 207-236
Author(s):  
Martin Aruldoss ◽  
Miranda Lakshmi Travis ◽  
Prasanna Venkatesan Venkatasamy
Keyword(s):  
Fuzzy Topsis ◽  
Distance Measures ◽  
Ideal Solution ◽  
Distance Method ◽  
Distance Methods ◽  
Relative Closeness ◽  
Bit Vector ◽  
Ranking Order ◽  
Negative Ideal Solution ◽  
Target Alternative

Multi criteria decision making (MCDM) is used to solve multiple conflicting criteria. There are different methods available in MCDM out of which TOPSIS is a well- known method to solve precise and imprecise information. In this chapter, triangular fuzzy TOPSIS is considered which has different steps like normalization, weight, finding of positive ideal solution (PIS) and negative ideal solution (NIS), distance between PIS and NIS, calculating relative closeness coefficient (RCC) value and ranking the alternatives. Out of these different steps a distance method is studied. The distance measures are basically used to find the distance between the target alternative and the best and the least alternatives. The most commonly used distance method is Euclidean distance. Many other distance methods are available such as Manhattan, Bit-vector, Hamming, Chebyshev distance, etc. To obtain the appropriate distance, these methods are evaluated. The proposed approach is applied in banking domain to find the suitable user for multi criteria reporting (MCR).

Intuitionistic Fuzzy Distance-Based Intuitionistic Fuzzy TOPSIS Method and Application to MADM

2017 ◽  
pp. 72-96
Author(s):  
Jiangxia Nan ◽  
Ting Wang ◽  
Jingjing An
Keyword(s):  
Distance Measure ◽  
Fuzzy Topsis ◽  
Distance Measures ◽  
Ideal Solution ◽  
Intuitionistic Fuzzy Numbers ◽  
Metric Properties ◽  
Fuzzy Distance ◽  
Intuitionistic Fuzzy ◽  
Multi Attribute Decision Making ◽  
Negative Ideal Solution

In this paper, an intuitionistic fuzzy (IF) distance measure between two triangular intuitionistic fuzzy numbers (TIFNs) is developed. The metric properties of the proposed IF distance measures are also studied. Then, based on the IF distance, an extended TOPSIS is developed to solve multi-attribute decision making (MADM) problems with the ratings of alternatives on attributes of TIFNs. In this methodology, the IF distances between each alternative and the TIFN positive ideal-solution are calculated as well as the TIFN negative ideal-solution. Then the relative closeness degrees obtained of each alternative to the TIFN positive ideal solution are TIFNs. Based on the ranking methods of TIFNs the alternatives are ranked. A numerical example is examined to the validity and practicability of the method proposed in this paper.

Interval Rough Neutrosophic TOPSIS Strategy for Multi-Attribute Decision Making

2020 ◽  
pp. 98-118
Author(s):  
Rumi Roy ◽  
Surapati Pramanik ◽  
Tapan Kumar Roy
Keyword(s):  
Decision Making ◽  
Euclidean Distance ◽  
Hamming Distance ◽  
Ideal Solution ◽  
Numerical Example ◽  
New Strategy ◽  
Order Preference ◽  
Multi Attribute Decision Making ◽  
Ranking Order ◽  
Negative Ideal Solution

In this chapter, the authors present a new strategy for multi-attribute decision making in interval rough neutrosophic environment. They define Hamming distance and Euclidean distance between interval rough neutrosophic numbers. They also define interval rough neutrosophic relative positive ideal solution (IRNRPIS) and interval rough neutrosophic relative negative ideal solution (IRNRNIS). Then the ranking order of the alternatives is obtained by the technique for order preference by similarity to ideal solution (TOPSIS) strategy. Finally, a numerical example is provided to demonstrate the applicability and effectiveness of the proposed interval rough neutrosophic TOPSIS strategy.

An Improved Fuzzy TOPSIS Method with a New Ranking Index

2021 ◽  
pp. 1-27
Author(s):  
S. A. Sadabadi ◽  
A. Hadi-Vencheh ◽  
A. Jamshidi ◽  
M. Jalali
Keyword(s):  
Real Life ◽  
Similarity Index ◽  
Multiple Criteria Decision Making ◽  
Fuzzy Topsis ◽  
Ideal Solution ◽  
Triangular Fuzzy Numbers ◽  
Linguistic Terms ◽  
Cost Criterion ◽  
Negative Ideal Solution ◽  
Ranking Index

Owing to vague concepts frequently represented in decision data, the crisp values are inadequate to model real-life situations. In this paper, the rating of each alternative and the weight of each criterion is described by linguistic terms which can be expressed in triangular fuzzy numbers. Next, we focus on fuzzy TOPSIS (FTOPSIS) method. We show that, however, the conventional FTOPSIS is interesting, but it suffers from some flaws. The shortcomings of classical FTOPSIS are shown and some solutions are given. Further, a new similarity index is proposed and then is illustrated using numerical examples. By treating the separations of an alternative from the fuzzy positive ideal solution (FPIS) and the fuzzy negative ideal solution (FNIS) as “cost” criterion and “benefit” criterion, respectively, we reduce the original fuzzy multiple criteria decision making (FMCDM) problem to a new one with two criteria. Illustrative examples are given to show the advantages of the proposed approach.

scholarly journals EVALUATION OF ALTERNATIVES APPLYING TOPSIS METHOD IN A FUZZY ENVIRONMENT

2005 ◽  
Vol 11 (4) ◽  
pp. 242-247 ◽  
Author(s):  
Jurgita Antuchevičiene
Keyword(s):  
Real Life ◽  
Fuzzy Topsis ◽  
Multiple Attribute Decision Making ◽  
Ideal Solution ◽  
Topsis Method ◽  
Fuzzy Environment ◽  
Attribute Analysis ◽  
Relative Closeness ◽  
Multiple Attribute ◽  
Topsis Technique

The paper analyses the problem of multiple attribute decision‐making (MADM) under fuzzy environment. In some cases the crisp value is inadequate to model real‐life situations. For this reason some fuzzy MADM methods have been developed. The extended TOPSIS (Technique for the Order Preference by Similarity to Ideal Solution) to fuzzy environment is presented in the current paper. Weights and ratings of each criterion are described in triangular fuzzy numbers. The relative closeness to the ideal solution of each alternative is calculated applying different approaches that were presented in different scientific papers. A computational experiment is presented to compare the results of a multiple attribute analysis that uses three modifications of fuzzy TOPSIS method in a particular situation.

Intuitionistic Fuzzy Distance Based TOPSIS Method and Application to MADM

2016 ◽  
Vol 5 (1) ◽  
pp. 43-56 ◽  
Author(s):  
Jiangxia Nan ◽  
Ting Wang ◽  
Jingjing An
Keyword(s):  
Distance Measure ◽  
Ideal Solution ◽  
Ranking Methods ◽  
Intuitionistic Fuzzy Numbers ◽  
Metric Properties ◽  
Fuzzy Distance ◽  
Intuitionistic Fuzzy ◽  
Relative Closeness ◽  
Multi Attribute Decision Making ◽  
Negative Ideal Solution

In this paper, an intuitionistic fuzzy (IF) distance measure between two triangular intuitionistic fuzzy numbers (TIFNs) is developed. The metric properties of the proposed IF distance measure are also studied. Then, based on this IF distance, an extended TOPSIS is developed to solve multi-attribute decision making (MADM) problems with the ratings of alternatives on attributes of TIFNs. In this methodology, the IF distances between each alternative and the TIFN positive ideal-solution are calculated as well as the TIFN negative ideal-solution. Then the relative closeness degrees obtained of each alternative to the TIFN positive ideal solution are TIFNs. Based on the ranking methods of TIFNs the alternatives are ranked. A numerical example is examined to the validity and practicability of the method proposed in this paper.

scholarly journals Project Delivery System Decision Making using Pythagorean Fuzzy TOPSIS

2019 ◽  
Vol 30 (4) ◽  
pp. 461-471
Author(s):  
Limin Su ◽  
Huimin Li ◽  
Yongchao Cao ◽  
Lelin Lv
Keyword(s):  
Decision Making ◽  
Fuzzy Sets ◽  
Similarity Measure ◽  
Similarity Measures ◽  
Fuzzy Topsis ◽  
Delivery Systems ◽  
Project Delivery ◽  
Ideal Solution ◽  
Negative Ideal Solution ◽  
Selection Of

The selection of project delivery systems is a complex decision-making process, which is also a critical task for owners. The complexity problem arises from the uncertainty of decision making environment and construction project itself. Pythagorean fuzzy sets (PFS), as an extension from intuitionistic fuzzy sets (IFSs) to deal with uncertainty information, has attracted more scholars’ attention in the decision making area. In this paper, we develop three similarity measures (i.e., 1-type PFSs similarity measure, 2-type PFSs weighted similarity measure, 3-type PFSs weighted similarity measure), and investigate their properties. Then an improved TOPSIS decision making framework is further established with PFSs information, in which the proposed similarity measures are employed to measure the similarity degree between each alternative and negative ideal solution and positive ideal solution. Finally, a case study of the selection of project delivery systems is presented to proof the performance of the proposed decision making method.

Designing and Evaluating Safety Accident Emergency Management for Construction Project under Fuzzy Environment

2011 ◽  
Vol 243-249 ◽  
pp. 6307-6311
Author(s):  
Cheng Hua Li ◽  
Yun Xiu Sai ◽  
Hui Mao
Keyword(s):  
Emergency Management ◽  
Construction Industry ◽  
Fuzzy Numbers ◽  
Construction Project ◽  
Fuzzy Topsis ◽  
Ideal Solution ◽  
Triangular Fuzzy Numbers ◽  
Fuzzy Environment ◽  
Safety Accident ◽  
Negative Ideal Solution

Recently, safety accident emergency management of construction project is an important issue not only for investors and governments but also for the companies that are in construction industry. Designing and evaluating safety accident emergency management is also crucial for the same sector’s development. Proposed method is based on fuzzy TOPSIS, which combined TOPSIS with triangular fuzzy numbers both in the rating of alternative and the weight of criterion. The closeness coefficient under fuzzy environment is calculated by using the concept of fuzzy positive-ideal solution and fuzzy negative-ideal solution. Then the rankings of the projects are determined according to their results.

ERP selection using picture fuzzy CODAS method

2021 ◽  
pp. 1-11
Author(s):  
Hacer Yumurtacı Aydoğmuş ◽  
Eren Kamber ◽  
Cengiz Kahraman
Keyword(s):  
Decision Analysis ◽  
Fuzzy Sets ◽  
Fuzzy Numbers ◽  
Ideal Solution ◽  
Application Area ◽  
Erp System ◽  
Mcdm Method ◽  
Negative Ideal Solution ◽  
Picture Fuzzy Sets ◽  
System Selection

The purpose of this study is to develop an extension of CODAS method using picture fuzzy sets. In this respect, a new methodology is introduced to figure out how picture fuzzy numbers can be applied to CODAS method. COmbinative Distance-based Assessment (CODAS) is a new MCDM method proposed by Ghorabaee et al. Picture fuzzy sets (PFSs) are a new extension of ordinary fuzzy sets for representing human’s judgments having possibility more than two answers such as yes, no, refusal and neutral. Compared with other studies, the proposed method integrates multi-criteria decision analysis with picture fuzzy uncertainty based on Euclidean and Taxicab distances and negative ideal solution. ERP system selection problem is handled as the application area of the developed method, picture fuzzy CODAS. Results indicate that the new proposed method finds meaningful rankings through picture fuzzy sets. Comparative analyzes show that the presented method gives successful and robust results for the solutions of MCDM problems under fuzziness.

scholarly journals Prioritization in Strategic Environmental Assessment Using Fuzzy TOPSIS Method with Random Generation for Absent Information in South Korea

2021 ◽  
Vol 13 (3) ◽  
pp. 1458
Author(s):  
Daeryong Park ◽  
Huan-Jung Fan ◽  
Jun-Jie Zhu ◽  
Taesoon Kim ◽  
Myoung-Jin Um ◽  
...  
Keyword(s):  
Decision Making ◽  
Multicriteria Decision Making ◽  
Fuzzy Topsis ◽  
River Basins ◽  
Ideal Solution ◽  
Missing Information ◽  
Nakdong River ◽  
Han River ◽  
Priority Ranking ◽  
The Nakdong River

This study evaluated a fuzzy technique for order performance by similarity to ideal solution (TOPSIS) as a multicriteria decision making system that compensates for missing information with undefined weight factor criteria. The suggested Fuzzy TOPSIS was applied to ten potential dam sites in three river basins (the Han River, the Geum River, and the Nakdong River basins) in South Korea. To assess potential dam sites, the strategic environment assessment (SEA) monitored four categories: national preservation, endangered species, water quality, and toxic environment. To consider missing information, this study applied the Monte Carlo Simulation method with uniform and normal distributions. The results show that effects of missing information generation with one fuzzy set in GB1 site of the Geum River basin are not great in fuzzy positive-ideal solution (FPIS) and fuzzy negative-ideal solution (FNIS) estimations. However, the combination of two fuzzy sets considering missing information in Gohyun stream (NG) and Hoenggye stream (NH) sites of the Nakdong River basin has a great effect on estimating FPIS, FNIS, and priority ranking in Fuzzy TOPSIS applications. The sites with the highest priority ranking in the Han River, Geum River, and Nakdong River basins based on Fuzzy TOPSIS are the Dal stream 1 (HD1), Bocheong stream 2 (GB2) and NG sites. Among the sites in all river basins, the GB2 site had the highest priority ranking. Consequently, the results coincided with findings of previous studies based on multicriteria decision making with missing information and show the applicability of Fuzzy TOPSIS when evaluating priority rankings in cases with missing information.

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