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

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

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

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

DECISION SUPPORT SYSTEM MODEL FOR EVALUATING FINAL YEAR PROJECT USING INTEGRATED FMCDM

Abstract Final Year Project (FYP) evaluation is an important issue in technology based program especially in Information Technology due to its multi-criteria assessment and the subjective nature of the evaluation. A group of panels and a supervisor for each project are also involved in the process. Therefore, a Decision Support System (DSS) is required to assist the supervisor and the panels during the process of FYP evaluation. In DSS, human intuitions is also taken into consideration especially in the evaluation which involved the subjective criteria which sometimes are fuzzy in nature. Fuzzy criteria makes the evaluation process very intricate and complicated. The conventional methods for evaluating FYP are inadequate for dealing with the imprecise or vague nature of linguistic assessment. To overcome this difficulty, it is important to create and develop a DSS that is embedded with integrated Fuzzy Multi Criteria Decision Making (FMCDM) models and Weighted Model as a decision analysis. Integrated FMCDM model consists of Fuzzy Analytical Hierarchy Process (FAHP) and Fuzzy Technique for Order Performance by Similarity to Ideal Solution (FTOPSIS) to evaluate FYP in computer-based programme. Weighted Model is used to rank the criteria. The FAHP is used to analyze the structure of the FYP criteria and determine the appropriate weights of the criteria while FTOPSIS is used to determine the final ranking of FYPs. The evaluation process takes into consideration a number of phases based on the FYP evaluation framework. To show the applicability of the method, a prototype system is developed for FYP evaluation process

Fractional Dynamics of Vector-Borne Infection with Sexual Transmission Rate and Vaccination

New fractional operators have the aim of attracting nonlocal problems that display fractal behaviour; and thus fractional derivatives have applications in long-term relation description along with micro-scaled and macro-scaled phenomena. Formulated by fractional operators, the formulation of a dynamical system is used in applications for the description of systems with long-range interactions. Vector-borne illnesses are one of the world’s most serious public health issues with a large economic impact on the nations that are impacted. Population increase, urbanization, globalization, and a lack of public health infrastructure have all had a role in the introduction and reemergence of vector-borne illnesses during the last four decades. The control of these infections are important to lessen the economic burden of vector-borne diseases in infected regions. In this research work, we formulate the transmission process of Zika virus with the impact of sexual incidence rate and vaccination in terms of mathematics. We presented the fundamental theory of fractional operators Caputo–Fabrizio (CF) and Atangana–Baleanu (AB) for the analysis of the proposed system. We examine our system of Zika infection and determined the endemic indicator through a next-generation matrix technique. The uniqueness and existence of the solution has been investigated through fixed point theory. Accordingly, a numerical method has been introduced to investigate the dynamical nature of the system and make a comparison of the outcomes of the operators. The impact of different input factors has been conceptualized through dynamical behaviour of the system. We observed that lowering the index of memory, the fractional system provides accurate results about the recommended Zika dynamics and dramatically reduces infected people. It has been proved that high efficacy of a vaccine can lower the level of infection. Moreover, the impact of other parameters on the system of Zika virus infection are highlighted through numerical results

Fractional Dynamics of Vector-Borne Infection with Sexual Transmission Rate and Vaccination

New fractional operators have the aim of attracting nonlocal problems that display fractal behaviour; and thus fractional derivatives have applications in long-term relation description along with micro-scaled and macro-scaled phenomena. Formulated by fractional operators, the formulation of a dynamical system is used in applications for the description of systems with long-range interactions. Vector-borne illnesses are one of the world’s most serious public health issues with a large economic impact on the nations that are impacted. Population increase, urbanization, globalization, and a lack of public health infrastructure have all had a role in the introduction and reemergence of vector-borne illnesses during the last four decades. The control of these infections are important to lessen the economic burden of vector-borne diseases in infected regions. In this research work, we formulate the transmission process of Zika virus with the impact of sexual incidence rate and vaccination in terms of mathematics. We presented the fundamental theory of fractional operators Caputo–Fabrizio (CF) and Atangana–Baleanu (AB) for the analysis of the proposed system. We examine our system of Zika infection and determined the endemic indicator through a next-generation matrix technique. The uniqueness and existence of the solution has been investigated through fixed point theory. Accordingly, a numerical method has been introduced to investigate the dynamical nature of the system and make a comparison of the outcomes of the operators. The impact of different input factors has been conceptualized through dynamical behaviour of the system. We observed that lowering the index of memory, the fractional system provides accurate results about the recommended Zika dynamics and dramatically reduces infected people. It has been proved that high efficacy of a vaccine can lower the level of infection. Moreover, the impact of other parameters on the system of Zika virus infection are highlighted through numerical results