An exploration of issues and limitations in current methods of TOPSIS and fuzzy TOPSIS

Decision making is an important process for organizations. Common practice involves evaluation of prioritized alternatives based on a given set of criteria. These criteria conflict with each other and commonly no solution can satisfy all criteria simultaneously. This problem is known as Multi Criteria Decision Making (MCDM) or Multi Criteria Decision Analysis (MCDA) problem. One of the well-known techniques in MCDM is the ‘Technique for Order Preference by Similarity to Ideal Solution’ (TOPSIS) which was introduced by Hwang and Yoon in 1981 [1]. However, this technique uses crisp information which is impractical in many real world situations because decision makers usually express opinions in natural language such as Poor and Good. Information in the form of natural language, i.e. words, in turn is characterized by fuzziness and uncertainty (i.e. ‘what is the meaning of poor’). This uncertainty can be a challenge for decision makers. Zadeh [2] introduced the concept of fuzzy sets, which enables systematic reasoning with imprecise and fuzzy information by using fuzzy sets to represent linguistic terms numerically to then handle uncertain human judgement

A comparison between two types of Fuzzy TOPSIS method

Multi Criteria Decision Making methods have been developed to solve complex real-world decision problems. The Technique for Order Preference by Similarity to Ideal Solution (TOPSIS) is currently one of the most popular methods and has been shown to provide helpful outputs in various application areas. In recent years, a variety of extensions, including fuzzy extensions of TOPSIS have been proposed. One challenge that has arisen is that it is not straightforward to differentiate between the multiple variants of TOPSIS existing today. Thus, in this paper, a comparison between the classical Fuzzy TOPSIS method proposed by Chen in 2000 and the recently Fuzzy TOPSIS proposed extension by Yuen in 2014 is made. The purpose of this comparative study is to show the difference between both methods and to provide context for their respective strengths and limitations both in complexity of application, and expressiveness of results. A detailed synthetic numeric example and comparison of both methods are provided

A comparison between two types of Fuzzy TOPSIS method

Multi Criteria Decision Making methods have been developed to solve complex real-world decision problems. The Technique for Order Preference by Similarity to Ideal Solution (TOPSIS) is currently one of the most popular methods and has been shown to provide helpful outputs in various application areas. In recent years, a variety of extensions, including fuzzy extensions of TOPSIS have been proposed. One challenge that has arisen is that it is not straightforward to differentiate between the multiple variants of TOPSIS existing today. Thus, in this paper, a comparison between the classical Fuzzy TOPSIS method proposed by Chen in 2000 and the recently Fuzzy TOPSIS proposed extension by Yuen in 2014 is made. The purpose of this comparative study is to show the difference between both methods and to provide context for their respective strengths and limitations both in complexity of application, and expressiveness of results. A detailed synthetic numeric example and comparison of both methods are provided

Fuzzy TOPSIS method in the selection of Investment Boards by incorporating operational risks

Multi Criteria Decision Making (MCDM) involves not only attributes that are precise or crisp, but also values that are not deterministic. Currently, Fuzzy TOPSIS presents a solution for decision makers when dealing with real world data that are usually multi attributes and involves a complex decision making process. In this work, an application of this method is demonstrated in the selection of Investment Boards by taking into account the operational risks involved

An improved uncertainty in multi-criteria decision making model based on type-2 fuzzy TOPSIS

This thesis presents a detailed study about one of the Multiple Criteria Decision Making (MCDM) models, namely Technique for Order Preference by Similarity to Ideal Solution (TOPSIS), based on fuzzy set theory (FST) by focusing on improving modelling uncertain information provided by a group of decision makers (DMs). An exploration of issues and limitations in current models of standard TOPSIS and fuzzy TOPSIS were made. Despite many variations of type-1 fuzzy TOPSIS (T1-TOPSIS) model, none of the studies explaining the details of the key stages of standard TOPSIS (non-fuzzy) and T1-TOPSIS are based on a step-wise procedure. A detailed study was conducted which involve the process of identifying the limitations of standard TOPSIS and T1-TOPSIS. Based on this, a novel contribution on the comparison between these two models in systematic stepwise procedure was given. This study successfully identified and discussed the limitations, issues and challenges which have not been investigated sufficiently in the context of T1-TOPSIS model. Based on this exploration, further investigation of multiple variants of the extension of the fuzzy TOPSIS model for solving the MCDM problem was made with the primary aim of detailing the steps involved. One challenge that has risen is that it is not straightforward to differentiate between the multiple variants of TOPSIS existing today. A systematic comparison was made between standard T1-TOPSIS model with the recently extended model to show the differences between both models and to provide context for their respective strengths and limitations both in the complexity of application and expressiveness of results. Based on the resulting comparison, the differences in the steps implemented by these two Fuzzy TOPSIS models were highlighted throughout the worked example. Furthermore, this task highlights the ability of both models to handle different levels of uncertainty. Following the exploration of issues and limitations of the current model, as well as a comparative study, a novel extension of type-2 fuzzy TOPSIS model is proposed in this thesis which suggests providing an interval-valued output to reflect the uncertainties and to model subjective information. The proposed model enables to uniquely captures input uncertainty (i.e., decision-makers’ preferences) in the decision-making outputs and provide a direct mapping of uncertainty in the inputs to outputs. By keeping the output values in interval form, the proposed model reduces the loss of information and maximises the potential benefit of using Interval Type-2 Fuzzy Sets (IT2 FSs). To demonstrate the MCDM problems when a various level of uncertainty is introduced, a novel experimental method was proposed in this study. The primary aim is to explore the use of IT2 FSs in handling uncertainty based on the TOPSIS model. This experiment was conducted to show how the variation of uncertainty levels in the input affects the final outputs. An implementation of the proposed model to two different case studies was conducted to evaluate the proposed model. The proposed model for the first time generates an interval-valued output. As intervals can, for example, exhibit partial overlap, a novel extended measure is proposed to compare the resulting interval-valued output from various cases (i.e., overlapping and non-overlapping) of the interval with considering uncertainty

An improved uncertainty in multi-criteria decision making model based on type-2 fuzzy TOPSIS

This thesis presents a detailed study about one of the Multiple Criteria Decision Making (MCDM) models, namely Technique for Order Preference by Similarity to Ideal Solution (TOPSIS), based on fuzzy set theory (FST) by focusing on improving modelling uncertain information provided by a group of decision makers (DMs). An exploration of issues and limitations in current models of standard TOPSIS and fuzzy TOPSIS were made. Despite many variations of type-1 fuzzy TOPSIS (T1-TOPSIS) model, none of the studies explaining the details of the key stages of standard TOPSIS (non-fuzzy) and T1-TOPSIS are based on a step-wise procedure. A detailed study was conducted which involve the process of identifying the limitations of standard TOPSIS and T1-TOPSIS. Based on this, a novel contribution on the comparison between these two models in systematic stepwise procedure was given. This study successfully identified and discussed the limitations, issues and challenges which have not been investigated sufficiently in the context of T1-TOPSIS model. Based on this exploration, further investigation of multiple variants of the extension of the fuzzy TOPSIS model for solving the MCDM problem was made with the primary aim of detailing the steps involved. One challenge that has risen is that it is not straightforward to differentiate between the multiple variants of TOPSIS existing today. A systematic comparison was made between standard T1-TOPSIS model with the recently extended model to show the differences between both models and to provide context for their respective strengths and limitations both in the complexity of application and expressiveness of results. Based on the resulting comparison, the differences in the steps implemented by these two Fuzzy TOPSIS models were highlighted throughout the worked example. Furthermore, this task highlights the ability of both models to handle different levels of uncertainty. Following the exploration of issues and limitations of the current model, as well as a comparative study, a novel extension of type-2 fuzzy TOPSIS model is proposed in this thesis which suggests providing an interval-valued output to reflect the uncertainties and to model subjective information. The proposed model enables to uniquely captures input uncertainty (i.e., decision-makers’ preferences) in the decision-making outputs and provide a direct mapping of uncertainty in the inputs to outputs. By keeping the output values in interval form, the proposed model reduces the loss of information and maximises the potential benefit of using Interval Type-2 Fuzzy Sets (IT2 FSs). To demonstrate the MCDM problems when a various level of uncertainty is introduced, a novel experimental method was proposed in this study. The primary aim is to explore the use of IT2 FSs in handling uncertainty based on the TOPSIS model. This experiment was conducted to show how the variation of uncertainty levels in the input affects the final outputs. An implementation of the proposed model to two different case studies was conducted to evaluate the proposed model. The proposed model for the first time generates an interval-valued output. As intervals can, for example, exhibit partial overlap, a novel extended measure is proposed to compare the resulting interval-valued output from various cases (i.e., overlapping and non-overlapping) of the interval with considering uncertainty

On fuzzy financial planning model

Financial Planning Model is adapted with the hybrid of fuzzy logic. The fuzzy logic displays the morphology of the results that help us to think efficiently based on the knowledge systems. The study is done on randomly selected college students in Terengganu. The result shows that students have different spending behaviors based on two different financial sources. Our analysis also shows the pattern of financial planning in the campus and their level of understanding of financial planning

Exploring the use of Type-2 fuzzy sets in multi-criteria decision making based on TOPSIS

Multi-criteria decision making (MCDM) problems are a well known category of decision making problem that has received much attention in the literature, with a key approach being the Technique for Order Preference by Similarity to Ideal Solution (TOPSIS). While TOPSIS has been developed towards the use of Type-2 Fuzzy Sets (T2FS), to date, the additional information provided by T2FSs in TOPSIS has been largely ignored since the final output, the Closeness Coefficient (CC), has remained a crisp value. In this paper, we develop an alternative approach to T2 fuzzy TOPSIS, where the final CC values adopt an interval-valued form. We show in a series of systematically designed experiments, how increasing uncertainty in the T2 membership functions affects the interval-valued CC outputs. Specifically, we highlight the complex behaviour in terms of the relationship of the uncertainty levels and the outputs, including non-symmetric and non-linear growth in the CC intervals in response to linearly growing levels of uncertainty. As the first TOPSIS approach which provides an interval-valued output to capture output uncertainty, the proposed method is designed to reduce the loss of information and to maximize the benefit of using T2FSs. The initial results indicate substantial potential in the further development and exploration of the proposed and similar approaches and the paper highlights promising next steps

Toward Effective Uncertainty Management in Decision-Making Models Based on Type-2 Fuzzy TOPSIS

Over the past century, there has been a dramatic increasing interest in the multi-criteria group decision-making (MCGDM) technique, with a considerable amount of studies published regarding it. One of the well-known approaches in the MCGDM paradigm is Technique for Order Preference by Similarity to Ideal Solution (TOPSIS). The integration of the TOPSIS method with fuzzy set theory has proven to be successful in various applications. Recently, a wide array of publications has proposed implementing a type-2 fuzzy set with TOPSIS. However, the additional degree of uncertainty represented by type 2 has largely been ignored, especially in a few specific mathematical operations in the model. We propose constructing interval type-2 fuzzy membership functions (IT2 MFs) using interval-based data gathered from a survey, where this is used to generate a new scale to represent ratings for each alternative. This procedure utilized all information gathered from decision makers. In addition, we present a complete algorithm for TOPSIS based on IT2 fuzzy sets (IT2 FSs) which preserve the interval-based form output. The output in the form of intervals offers decision makers (DMs) with more detailed information, enabling them to make more nuanced decisions. This can include cautious decisions when intervals are wider and overlapping. Although understanding the exact meaning of these intervals and their widths in a decision-making context is challenging, this paper introduces a systematic method for connecting input uncertainty to output uncertainty in the TOPSIS technique. This approach establishes a solid foundation for future research. Thus far, no other researchers have suggested a data-driven method that combines TOPSIS with fuzzification and provides intervals as the final output