There is, I think, something ethereal about i —the square root of minus one. I remember first hearing about it at school. It seemed an odd beast at that time—an intruder hovering on the edge of reality.

Usually familiarity dulls this sense of the bizarre, but in the case of i it was the reverse: over the years the sense of its surreal nature intensified. It seemed that it was impossible to write mathematics that described the real world in …

I and i

Multi-Criteria Decision Aid (MCDA) or Multi-Criteria Decision Making (MCDM) methods have received much attention from researchers and practitioners in evaluating, assessing and ranking alternatives across diverse industries. Among numerous MCDA/MCDM methods developed to solve real-world decision problems, the Technique for Order Preference by Similarity to Ideal Solution (TOPSIS) continues to work satisfactorily across different application areas. In this paper, we conduct a state-of-the-art literature survey to taxonomize the research on TOPSIS applications and methodologies. The classification scheme for this review contains 266 scholarly papers from 103 journals since the year 2000, separated into nine application areas: (1) Supply Chain Management and Logistics, (2) Design, Engineering and Manufacturing Systems, (3) Business and Marketing Management, (4) Health, Safety and Environment Management, (5) Human Resources Management, (6) Energy Management, (7) Chemical Engineering, (8) Water Resources Management and (9) Other topics. Scholarly papers in the TOPSIS discipline are further interpreted based on (1) publication year, (2) publication journal, (3) authors' nationality and (4) other methods combined or compared with TOPSIS. We end our review paper with recommendations for future research in TOPSIS decision-making that is both forward-looking and practically oriented. This paper provides useful insights into the TOPSIS method and suggests a framework for future attempts in this area for academic researchers and practitioners.

Review: A state-of the-art survey of TOPSIS applications

Recently, a new model based on Pythagorean fuzzy set PFS has been presented to manage the uncertainty in real-world decision-making problems. PFS has much stronger ability than intuitionistic fuzzy set to model such uncertainty. In this paper, we define some novel operational laws of PFSs and discuss their desirable properties. For the multicriteria decision-making problems with PFSs, we propose an extended technique for order preference by similarity to ideal solution method to deal effectively with them. In this approach, we first propose a score function based comparison method to identify the Pythagorean fuzzy positive ideal solution and the Pythagorean fuzzy negative ideal solution. Then, we define a distance measure to calculate the distances between each alternative and the Pythagorean fuzzy positive ideal solution as well as the Pythagorean fuzzy negative ideal solution, respectively. Afterward, a revised closeness is introduced to identify the optimal alternative. At length, a practical example is given to illustrate the developed method and to make a comparative analysis.

Extension of TOPSIS to Multiple Criteria Decision Making with Pythagorean Fuzzy Sets

In the current era of sustainable development, energy planning has become complex due to the involvement of multiple benchmarks like technical, social, economic and environmental. This in turn puts major constraints for decision makers to optimize energy alternatives independently and discretely especially in case of rural communities. In addition, topographical limitations concerning renewable energy systems which are mostly distributed in nature, the energy planning becomes more complicated. In such cases, decision analysis plays a vital role for designing such systems by considering various criteria and objectives even at disintegrated levels of electrification. Multiple criteria decision making (MCDM) is a branch of operational research dealing with finding optimal results in complex scenarios including various indicators, conflicting objectives and criteria. This tool is becoming popular in the field of energy planning due to the flexibility it provides to the decision makers to take decisions while considering all the criteria and objectives simultaneously. This article develops an insight into various MCDM techniques, progress made by considering renewable energy applications over MCDM methods and future prospects in this area. An extensive review in the sphere of sustainable energy has been performed by utilizing MCDM technique.

A review of multi criteria decision making (MCDM) towards sustainable renewable energy development

Despite the importance of decision-making (DM) techniques for construction of effective decision models for supplier selection, there is a lack of a systematic literature review for it. This paper provides a systematic literature review on articles published from 2008 to 2012 on the application of DM techniques for supplier selection. By using a methodological decision analysis in four aspects including decision problems, decision makers, decision environments, and decision approaches, we finally selected and reviewed 123 journal articles. To examine the research trend on uncertain supplier selection, these articles are roughly classified into seven categories according to different uncertainties. Under such classification framework, 26 DM techniques are identified from three perspectives: (1) Multicriteria decision making (MCDM) techniques, (2) Mathematical programming (MP) techniques, and (3) Artificial intelligence (AI) techniques. We reviewed each of the 26 techniques and analyzed the means of integrating these techniques for supplier selection. Our survey provides the recommendation for future research and facilitates knowledge accumulation and creation concerning the application of DM techniques in supplier selection.

Application of decision-making techniques in supplier selection: A systematic review of literature

Supplier selection, the process of finding the right suppliers who are able to provide the buyer with the right quality products and/or services at the right price, at the right time and in the right quantities, is one of the most critical activities for establishing an effective supply chain. On the other hand, it is a hard problem since supplier selection is typically a multi criteria group decision-making problem involving several conflicting criteria on which decision maker's knowledge is usually vague and imprecise. In this study, TOPSIS method combined with intuitionistic fuzzy set is proposed to select appropriate supplier in group decision making environment. Intuitionistic fuzzy weighted averaging (IFWA) operator is utilized to aggregate individual opinions of decision makers for rating the importance of criteria and alternatives. Finally, a numerical example for supplier selection is given to illustrate application of intuitionistic fuzzy TOPSIS method.

A multi-criteria intuitionistic fuzzy group decision making for supplier selection with TOPSIS method

A biparametric similarity measure on intuitionistic fuzzy sets with applications to pattern recognition

Due to global warming and climate changes, the utilization of renewable energy not only plays a key role in reducing emissions of greenhouse gases in the world but also will supply global energy in the future. Renewable energy technologies are efficient and effective solutions for clean and sustainable energy development in Turkey due to the advantages of Turkey's geographical location for the extensive usage of most renewable energy resources. In this article, the evaluation of renewable energy technologies for electricity generation in Turkey has been accomplished using intuitionistic fuzzy TOPSIS. Photovoltaic, hydro, wind and geothermal energy have been evaluated for long-term renewable technologies for Turkey.

The Evaluation of Renewable Energy Technologies for Electricity Generation in Turkey Using Intuitionistic Fuzzy TOPSIS

Interval multiplicative transitivity for consistency, missing values and priority weights of interval fuzzy preference relations

One of the most important activities carried out by human resource management is personnel selection, concerned with identifying an individual from a pool of candidates suitable for a vacant position. Traditionally, personnel selection is a group decision-making problem under multiple criteria containing subjectivity, imprecision, and vagueness, which are best represented with fuzzy data. In this article, the Technique for Order Preference by Similarity to Ideal Solution (TOPSIS) method extended to intuitionistic fuzzy environments is proposed to select appropriate personnel among candidates. An intuitionistic fuzzy set (IFS), which is characterized by membership function, nonmembership function, and hesitation margin, is a more suitable way to deal with vagueness when compared to a fuzzy set. To demonstrate the applicability and effectiveness of the intuitionistic fuzzy TOPSIS method, a numerical example of personnel selection in a manufacturing company for a sales manager position is given. © 2011 Wiley Periodicals, Inc. © 2011 Wiley Periodicals, Inc.

Fatih Emre Boran

Papers

A multi-criteria intuitionistic fuzzy group decision making for supplier selection with TOPSIS method

A biparametric similarity measure on intuitionistic fuzzy sets with applications to pattern recognition

The Evaluation of Renewable Energy Technologies for Electricity Generation in Turkey Using Intuitionistic Fuzzy TOPSIS

Interval multiplicative transitivity for consistency, missing values and priority weights of interval fuzzy preference relations

Personnel selection based on intuitionistic fuzzy sets