Fuzzy Multi-criteria Decision Research Articles

Decision-aided evaluation of paths for routing on multi-attribute computer network consisting of encoded paths under uncertainty

The network users need to evaluate the alternative transmission pathways to avoid some routing problems such as possible network attacks, data traffic, etc. in computer networks. In order to provide a mathematical solution to this situation, in this paper the computer network system is considered as a graph, and a random data structure denoted by Bloom filter is used to forward data between computers in the network. The Bloom filter has been used for encoding the routes minimises the query response time, although it has a significant risk of producing errors indicated by false positives (FP). The study aims to assess all paths between two distinct computers on a multi-attribute computer network considering risk and FP values regarding paths. These considerations are inherently vagueness. That being the case, a novel two-stage research methodology is presented to determine the desired pathways during message transmission on a multi-attribute computer network under uncertainty. At this point, the values of the possible risks and the probability of FP of the transmission edges are defined by employing triangular fuzzy numbers to reach the theoretical solutions. The novelty of the study is proposing a research methodology based on fuzzy Multi-Criteria Decision Making (MCDM) techniques to offer alternative routes during data transmission on any multi-attribute computer network under uncertainty for the first time. Further, a sensitivity analysis is implemented. In all computational analyses, the most appropriate and reliable transmission pathways are listed, and some managerial insights and main findings are provided for the network users.

Cybernetic-parsimonious MCDM modeling with application to the adoption of Circular Economy in waste management

Construction and demolition waste (CDW) is the main contributor to economic loss, environmental pollution, and health hazards if the current linear economy model of ‘take-make-consume-dispose’ is not replaced by a Circular Economy (CE) as a solution approach to maximize the use of resources and reduce waste. However, successful CE concept implementation involves strategies that trigger construction and demolition waste management (CDWM) throughout its life cycle, rather than end-of-life strategies, such as reuse and recycling. By meticulously reviewing the literature, nineteen factors that affect CDWM from CE concept implementation throughout six stages of preconstruction, procurement, construction, demolition, transportation, and end-of-life are initially identified. A hybrid fuzzy Multi-Criteria Decision-Making approach is then utilized in two main stages, including an Enhanced Fuzzy Delphi Method in stage one, to refine the identified factors according to Tehran’s construction context, and a Cybernetic Parsimonious Fuzzy Analytic Hierarchy Process in stage two, to prioritize these factors. Three factors were identified during the first stage of the research methodology and added to the factors extracted from the literature. The results indicate that ‘on-site sorting, reusing, and recycling of waste materials’, ‘various procurement models’, and ‘precise implementation of waste management regulations and plans’ are the most important factors, respectively. A comprehensive list of the factors provided as part of the research findings has contributed to the body of knowledge to be used as a snapshot by researchers, while the ranking of the factors gives new insights to stakeholders on ways to manage CDW in projects.

MULTIMOORA‐based MCDM model for sustainable ranking of wastewater treatment technologies under picture fuzzy environment

AbstractThis study aims to provide the best vision for ranking wastewater treatment technologies using a MULTIMOORA‐based MCDM model to build a more effective technique for future generations. Nanotechnology, photocatalytic technology, automated variable filtration (AVF) technology, and membrane filtration are the technologies explored in this article. Social, monetary, and ecological elements like cost, energy utilization, water quality, capacity, environmental effect, and technical factors were considered as boundaries to extricate best from the different wastewater treatment procedures. Each technique undertook evaluation and comparison, then ranked according to the proposed MCDM model from most to least preferred. The suggested Picture fuzzy MCDM model shows that AVF (0.4081) is the most adapted technology for wastewater treatment, followed by nanotechnology (0.2657), photocatalytic technology (0.1748), and membrane filtration (−0.0962). The results of all three models (MULTIMOORA, TOPSIS, and COPRAS MCDM) showed that the AVF technology is highly effective, although other technologies are also operative.

Identifying Waste Supply Chain Coordination Barriers with Fuzzy MCDM

The stability and efficiency of the waste supply chain (WSC) is related to the urban environment. This study constructed a framework of barriers to coordinating the WSC based on four perspectives: the costs and benefits, mechanisms involved, behaviors of the subjects, and technologies and standards used. We used an analytic network process based on the fuzzy decision-making trial and evaluation laboratory to calculate the centrality and weight of each barrier factor, and we determined the critical barriers to coordination by combining their results. A causality diagram of the barriers was drawn, and a scheme of coordination of the WSC was designed based on a closed-loop supply chain around the critical barriers. The results show that contradictions in benefits between subjects, contradictions between economic and social benefits, excessive subsidies, the failure of the market mechanism, the lack of a mechanism for supervision, and blocked information and distrust among the subjects are the five most critical barriers to the coordination of the WSC, with excessive subsidies the root cause of the lack of coordination. The subsidy for direct waste disposal should be used to reduce the cost of the operation of the WSC, waste recycling should be improved, an information-sharing platform should be built, and the cost of recyclable waste for manufacturers should be reduced to improve the efficiency of the WSC.

A novel normal wiggly hesitant fuzzy multi-criteria group decision making method and its application to electric vehicle charging station location

Electric vehicle charging station location (EVCSL) is critical to promoting the electric vehicle industry and how it is evaluated is typically a MCDM issue. In this paper, an applicable multi-criteria group decision support model is developed to evaluate the electric vehicle charging station location. To do this, we used normal wiggly hesitant fuzzy set to describe the fuzzy decision-making information, which can further dig the potential uncertainty. Considering that the experts’ preference can lead to significant changes in the results, k-means clustering method is used to group the experts in different fields. Moreover, the improved correlation coefficient and standard deviation (CCSD) method is used to determine the criterion weights, and considering that prospect theory can reflect the mental behavior of experts and the simplicity and efficiency of weighted aggregated sum product assessment (WASPAS) method, a combined ranking model is proposed to evaluate the alternatives comprehensively. The procedure of the model is given in detail, and the example of electric vehicle charging station location evaluation is employed to demonstrate our results. Comparative analyses and discussion show that the proposed model has powerful effectiveness, performs better than other existing methods, and largely extends the applicability of the method with theoretical and practical implications.

Additive manufacturing process selection for automotive industry using Pythagorean fuzzy CRITIC EDAS.

For many different types of businesses, additive manufacturing has great potential for new product and process development in many different types of businesses including automotive industry. On the other hand, there are a variety of additive manufacturing alternatives available today, each with its own unique characteristics, and selecting the most suitable one has become a necessity for relevant bodies. The evaluation of additive manufacturing alternatives can be viewed as an uncertain multi-criteria decision-making (MCDM) problem due to the potential number of criteria and candidates as well as the inherent subjectivity of various decision-experts engaging in the process. Pythagorean fuzzy sets are an extension of intuitionistic fuzzy sets that are effective in handling ambiguity and uncertainty in decision-making. This study offers an integrated fuzzy MCDM approach based on Pythagorean fuzzy sets for assessing additive manufacturing alternatives for the automotive industry. Objective significance levels of criteria are determined using the Criteria Importance Through Inter-criteria Correlation (CRITIC) technique, and additive manufacturing alternatives are prioritized using the Evaluation based on Distance from Average Solution (EDAS) method. A sensitivity analysis is performed to examine the variations against varying criterion and decision-maker weights. Moreover, a comparative analysis is conducted to validate the acquired findings.

Ensemble feature selection using q-rung orthopair hesitant fuzzy multi criteria decision making extended to VIKOR

ABSTRACT This paper investigates ensemble feature selection using the q-rung orthopair hesitant fuzzy multi-criteria decision-making (MCDM) process. A novel algorithm is proposed for the study of ensemble feature selection and it is called as q-rung orthopair hesitant fuzzy MCDM extended to the Visekriterijumska optimizacija Ikompromisno Resenje (VIKOR) (q-ROHFS VIKOR). This is the first time in the literature an ensemble feature selection problem is modelled as a q-rung orthopair hesitant fuzzy MCDM extended to VIKOR technique. In the proposed method, every feature is ranked based on different available rankers and a preference matrix is obtained. In the sigmoidal transformation, the tuning parameter plays a vital role in the fuzzification process. This tuning parameter reduces the computation run-time in the fuzzification process for different high-dimensional datasets that are considered in this paper. By using q-ROHFS VIKOR method, a score is assigned to each feature based on the values of the preference matrix. At last, an output rank vector is produced for all features from which the user can select the desired number of features. To prove the efficiency and optimality of the proposed method, the comparison with basic filter-based feature selections and ensemble feature selection using feature ranking strategy is obtained. The proposed method in this paper is superior and efficient than the ensemble methods based on the accuracy and F-score levels upto 0.96.

A fuzzy MCDM approach to support customer-centric innovation in virtual reality (VR) metaverse headset design

Nowadays, customer-centric innovation is important in affective design, leading to the design and development of a product that fits the needs of a group of target customers for sales and marketing. Though there is much research on customer-centric innovation and affective product design, designing a novel and innovative product that appeals to customers remains difficult. This is not only due to the difficulty of knowing a customer's preference, enabling the product functionality, etc., but it is also very complex to optimize both the technical and aesthetical design factors and parameters for a group of customers. The technical design specification is one of the critical aspects in designing innovative technological products. In fact, a similar group of target customers usually has hidden preferences that provide us with clues for identifying the design of a product. To this end, we propose a sophisticated optimization technique using the Hybrid Fuzzy-based Analytical Hierarchy Process and the Integral-based Taguchi Method called the Fuzzy multi-criteria decision-making (MCDM) approach to determine the essential factors and design parameters in order to understand the preferences of customers and the technical requirements of engineers for designing the enclosure of a product. We demonstrate our methodology using the virtual reality (VR) Headset, which can be used for visualizing the metaverse in the virtual environment. The fuzzy MCDM approach suggested combines technical and aesthetical features to enhance the robustness of product design.

Smartphone Addiction Assessment Using Pythagorean Fuzzy CRITIC-TOPSIS

Addiction to smartphones, particularly among adolescents, has reached alarming proportions, rivaling or perhaps exceeding internet addiction as the most widespread kind of dependence in modern culture. Evaluating the degree of problematic smartphone use habits by experts and identifying the vulnerable ones to steer to the right treatment program has become a critical issue. Since such a task may involve an abundance of criteria and candidates, as well as the inherent subjectivity of multiple decision experts participating in the process, the assessment of smartphone addiction can be framed as an uncertain multi-criteria decision-making (MCDM) problem. As an extension of intuitionistic fuzzy sets, Pythagorean fuzzy sets can be used to efficiently manage ambiguity and uncertainty during decision-making. This study provides an integrated fuzzy MCDM methodology based on Pythagorean fuzzy sets for evaluating the smartphone addiction level of adolescents. The Criteria Importance Through Inter-criteria Correlation (CRITIC) method is used to determine the importance levels of criteria in an objective manner, and smartphone addiction levels of the selected candidates are ranked using the Technique for Order of Preference by Similarity to Ideal Solution (TOPSIS) approach. A sensitivity analysis is conducted to examine the variations in candidate rankings caused by changes to the criteria and weights of the decision experts. Moreover, in the context of comparative analysis, the Evaluation based on Distance from Average Solution (EDAS) approach is used to validate the acquired findings.

Aczel–Alsina Hamy Mean Aggregation Operators in T-Spherical Fuzzy Multi-Criteria Decision-Making

A T-spherical fuzzy set is a more powerful mathematical tool to handle uncertain and vague information than several fuzzy sets, such as fuzzy set, intuitionistic fuzzy set, Pythagorean fuzzy set, q-rung orthopair fuzzy set, and picture fuzzy set. The Aczel–Alsina t-norm and s-norm are significant mathematical operations with a high premium on affectability with parameter activity, which are extremely conducive to handling imprecise and undetermined data. On the other hand, the Hamy mean operator is able to catch the interconnection among multiple input data and achieve great results in the fusion process of evaluation information. Based on the above advantages, the purpose of this study is to propose some novel aggregation operators (AOs) integrated by the Hamy mean and Aczel–Alsina operations to settle T-spherical fuzzy multi-criteria decision-making (MCDM) issues. First, a series of T-spherical fuzzy Aczel–Alsina Hamy mean AOs are advanced, including the T-spherical fuzzy Aczel–Alsina Hamy mean (TSFAAHM) operator, T-spherical fuzzy Aczel–Alsina dual Hamy mean (TSFAADHM) operator, and their weighted forms, i.e., the T-spherical fuzzy Aczel–Alsina-weighted Hamy mean (TSFAAWHM) and T-spherical fuzzy Aczel–Alsina-weighted dual Hamy mean (TSFAAWDHM) operators. Moreover, some related properties are discussed. Then, a MCDM model based on the proposed AOs is built. Lastly, a numerical example is provided to show the applicability and feasibility of the developed AOs, and the effectiveness of this study is verified by the implementation of a parameters influence test and comparison with available methods.

Fuzzy dynamic MCDM method based on PRSRV for financial risk evaluation of new energy vehicle industry

The financial risk evaluation of new energy vehicle (NEV) industry is conducive to the popularization of NEVs, to encourage more investment into the NEV industry, and to promote the improvement of the risk control system. When evaluating the performance of NEV industry in China, it is usually full of uncertainty and dynamic. q-Rung orthopair fuzzy set (q-ROFS) has the characteristics of non-membership and membership with adjustable parameterization q, which is a very effective mathematical model to capture uncertainty. In this paper, the q-rung orthopair fuzzy (q-ROF) distance measure based triangle orthocenter is given. Then, q-ROF score function (SF) based distance measure is proposed for disposing of comparison issue. Moreover, we present nonlinear comprehensive weighting method by integrating subjective weight information and objective weight information (determining by water-filling theory). In order to solve the counter-intuitive phenomena and dynamic trend issue, the dynamic q-ROF aggregation operators are investigated and their properties are proved. Whereafter, q-ROF multi-criteria decision making (MCDM) approach based projection ranking by similarity to referencing vector (PRSRV) is proposed for evaluating financial risk of NEV industry, along with the sensitivity analysis. Finally, a comparison with some existing MCDM methods states that the presented method has strong data adaptability.

Toward a Sustainable Transportation Industry: Oil Company Benchmarking Based on the Extension of Linear Diophantine Fuzzy Rough Sets and Multicriteria Decision-Making Methods

Building a sustainable transportation system without involving international oil companies (IOCs) is an unrealistic feat. To date, no study has determined the best IOC and low-performing ones with respect to sustainable oil transportation, which is considered a benchmarking challenge requiring an urgent solution. Despite this limitation, the benchmarking of IOCs falls under the complex multicriteria decision making (MCDM) because of the use of several evaluation criteria and their varying datasets and the varying importance of these criteria. Moreover, the issues involving the use of imprecise, unclear, and ambiguous information remain unresolved in the existing multiattribute decision-making methods. The robustness of the multiobjective optimization on the basis of ratio analysis (MULTIMOORA, i.e., an updated version of MOORA) plus full-multiplicative form method and that of the fuzzy-weighted with zero inconsistency (FWZIC) method have been proven. Therefore, in this article, we propose a novel benchmarking of oil companies by extending the linear Diophantine fuzzy rough sets (LDFRSs) into the MCDM methods to help build a sustainable transportation industry. The proposed methodology consists of two phases. The initial phase involves assigning values to the evaluation criteria of IOCs to formulate the evaluation decision matrix. The second phase involves the development of two fuzzy MCDM methods, namely, the LDFRS with the FWZIC method (hereafter called LDFRS–FWZIC) for weighting the criterion of each IOC and the LDFRS with the MULTIMOORA method (hereafter called LDFRS–MULTIMOORA) for benchmarking the IOCs. The IOCs were evaluated based on 2 criteria, 9 subcriteria, and 47 measurement items by 483 experts from 11 IOCs. Results revealed the following: 1) LDFRS–FWZIC can effectively weigh the evaluation criteria of IOCs. The highest final weight of 0.2594 was for “cost leadership” (C2-1), whereas the lowest weights of 0.1148 was for “priority of other external matters” (C1-2) and “insufficient supply”(C1-4), and 2) LDFRS–MULTIMOORA can successfully benchmark the IOCs. IOC11 ranked first, followed by IOC10 and IOC3 in the second and third ranks, respectively. IOC4 ranked the lowest (rank <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">= 11</i> ). A sensitivity analysis was conducted to determine the robustness of the developed fuzzy MCDM methods.

Toward Sustainable Transportation: A Pavement Strategy Selection Based on the Extension of Dual-Hesitant Fuzzy Multicriteria Decision-Making Methods

Pavement strategy is critical for achieving sustainable transportation. However, the presence of many evaluation criteria, criteria tradeoffs, criteria conflict, and criteria importance categorize the evaluation and selection of pavement strategies under complex multicriteria decision-making (MCDM) problems. To date, no study has presented an evaluation framework for selecting the most optimal pavement strategy to be utilized as a way to achieve sustainable transportation considering multicriteria evaluation of pavement strategies and sustainable solutions. This article presents a pavement strategy selection based on a new extension of fuzzy MCDM methods. The methodology is developed in two phases. First, the evaluation decision matrix is formulated on the basis of intersecting the “evaluation criteria” and “pavement strategies list.” Second, the proposed MCDM methods are developed: multilayer dual hesitant fuzzy weighted zero inconsistency (DH-FWZIC) to assign weights to the pavement's evaluation criteria followed by dual hesitant fuzzy decision by opinion score method (DH-FDOSM) for selecting the best pavement strategy. Four alternatives, namely, flexible/asphalt, rigid/concrete, reflective, and permeable alternatives pavement strategies, are evaluated on the basis of 30 criteria. Results show the following. 1) The multilayer DH-FWZIC method has weighted the pavement strategies’ evaluation criteria at three layers in a consistent manner, showing that a region's environment criterion has the highest final weight (0.1215) and the lowest importance value (0.0089) assigned for its windy criterion. 2) According to DH-FDOSM, the flexible/asphalt pavement achieved the first rank among the four pavement strategies. Finally, the robustness of the developed framework was assessed by conducting sensitivity analysis and comparison study.

Electric Vehicles Charging Dispatch and Optimal Bidding for Frequency Regulation Based on Intuitionistic Fuzzy Decision Making

The spread of electric vehicles (EVs) could reduce greenhouse gas emissions and achieve sustainable travel patterns. However, the rapidly increasing charging demand will bring challenges to the operation of charging stations and power systems. Therefore, a two-stage EV management scheme is introduced in this article to overcome these challenges and promote sustainable transport. A charging dispatch model based on fuzzy multicriteria decision making is proposed in the first stage, where users' preferences are in the form of intuitionistic fuzzy sets to address the fuzziness and uncertainty of subjective factors and human judgment. A <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\sigma$</tex-math></inline-formula> -cut similarity matrix is proposed to increase the users' satisfaction by excluding options with lower similarity. In the second stage, a noncooperative game model is proposed to incentive EVs to participate in supplementary frequency regulation (SFR). A fuzzy set is employed to reflect users' willingness to adjust charging power. The existence and uniqueness of the Nash equilibrium are investigated. Moreover, a distributed proximal best response algorithm with linear convergence is employed to find Nash equilibrium. Numerical simulations indicate that the proposed method can reduce charging costs while meeting users' preferences and facilitate EVs to participate in SFR.

An Integrated Fuzzy MCDM Method for the Evaluation of R&amp;D Projects

Research and development (R&amp;amp;D) activities are essential to guarantee continuity of firms, meet customer requirements and keep ahead in competition. R&amp;amp;D project selection constitutes a significant part of project management in order to achieve the desired results and outputs. In this study, an integrated fuzzy multi-criteria group decision making approach is developed for R&amp;amp;D project selection. The problem includes a hierarchical structure of the criteria, uncertainty in evaluating the relative importance of criteria/sub-criteria and rating of candidate projects. The method employs the ordered weighted average (OWA) operator as the aggregation operator, which helps to fully reflect the real behavior of the decision makers in group decision making problems. Fuzzy integral method, which does not require the assumption of the mutual independence of criteria, is used to rank the alternatives. The case study is conducted in a small-sized company in Turkey, which designs and produces special purpose machines. A R&amp;amp;D project selection model is developed to maximize the desired outputs. The results of the analysis show that technological, environmental, marketing, organizational, national and financial issues should be considered simultaneously in the evaluation process. The proposed method is shown to be efficient, generalizable and practical and it has several significant merits compared to the other methods.

An integrated fuzzy MCDM model for prioritizing strategies for successful implementation and operation of the bus rapid transit system.

The selection and prioritization of suitable strategies to address the challenges to the successful operation and implementation of the bus rapid transit (BRT) system is a common problem faced by practitioners and decision-makers. Recent research has widely discussed the issue, but such assessments have remained limited in the city of Dar es Salaam, Tanzania context, where there are mobility difficulties. The present study addresses this research gap and identifies the most critical challenges to BRT implementation and operation, and recommends the most appropriate strategy for overcoming them. Seven strategies are defined. To prioritize these strategies, five criteria are determined. An integrated multi-criteria decision-making model is introduced. Improved Fuzzy Step-Wise Weight Assessment Ratio Analysis based on the Bonferroni operator was used to determine the importance of the criteria. Measurement of alternatives and ranking according to compromise solution was applied to assess and rank the strategies. The results indicate that "frequent flooding at the Jangwani bridge bus terminal" and "long waiting time at bus stops" are the most critical challenges while the fourth alternative "strengthening the operation and management" is the appropriate strategy to be implemented for successful operation and implementation of the BRT system. After that, a five-phase sensitivity analysis is performed to observe the robustness of the proposed approach. The results indicate the flexibility and applicability of the proposed approach can address real-life problems. The proposed methodology in this work can be instrumental in assisting mass transit operators with the successful implementation and operation of the BRT system.

An integrated fuzzy MCDM approach for manufacturing process improvement in MSMEs

An integrated fuzzy MCDM approach for manufacturing process improvement in MSMEs

Sustainable supplier selection using an intuitionistic and interval-valued fuzzy MCDM approach based on cumulative prospect theory

The sustainable supplier selection is treated as a type of complex decision-making problem due to involving lots of uncertain information, and the appropriate linguistic terms are usually used to handle such uncertainties. However, the descriptions of linguistic terms in the form of traditional fuzzy sets are not perfectly supported in the sustainable supplier selection process. Luckily, the intuitionistic fuzzy sets and interval-valued fuzzy sets can effectively deal with this uncertain and incomplete data information when selecting evaluation criteria and facing with the ambiguity of human thinking, whereas providing us with a helpful tool to resolve fuzzy multi-criteria decision-making (MCDM) problems in a more flexible way. Moreover, the cumulative prospect theory can be introduced to well depict decision-makers’ risk preferences and psychological behaviors. Therefore, this study develops a novel fuzzy MCDM approach based on the combination of intuitionistic fuzzy sets, interval-valued fuzzy sets and cumulative prospect theory for selecting the most sustainable supplier. A case study from the sustainable recycling supplier selection of e-bike sharing is studied to illustrate applicability of the proposed method. By comparing with other methods, the rationality and feasibility of the proposed method are verified. This can provide an insightful implication for decision-makers with different risk preferences to select the most sustainable supplier under uncertain environment.

Risk assessment of circular economy practices in construction industry of Pakistan

The construction industry (CI) is responsible for consuming 3 billion tons of natural raw materials annually. Also, as per the survey by World Resources Institute, the CI accounts for 40 % of the total waste generated globally. The solution to this inefficient resource usage and adverse effects on the ecosystem is implementing Circular Economy (CE) practices in CI. However, the concept of circular construction is in developmental stages. Therefore, it is more prone to damaging risks than traditional construction. The primary aim of this study is to identify and assess the risk related to implementing CE practices in developing country construction sector. To achieve this aim, 25 risks were shortlisted from the literature review and evaluated upon the probability, detection, and severity risk criteria. This study proposed a novel hybrid fuzzy Multi-Criteria Decision Making (MCDM) approach to analyze the shortlisted risks. Fuzzy Step Wise Assessment Ratio Analysis (FSWARA) is employed to gauge the risk criterion weightage. Moreover, Fuzzy VIKOR (FVIKOR) is used to determine the risks' ranking as per the weightage of the risk criterion. The analyses ranked “lack of political support and incentives for circular construction”, “difficulty in selection of circular construction experts”, “profit uncertainty”, and “circular material quality” as the most critical risks. Therefore, it is recommended for legislative authority to devise a framework that promotes and provides support to circular construction. Moreover, this study fills the literature gap by assessing the risks of CE practices in the CI of Pakistan.

An Extended Interval Type-2 Fuzzy VIKOR Technique with Equitable Linguistic Scales and Z-Numbers for Solving Water Security Problems in Malaysia

Interval Type-2 Fuzzy VIseKriterijumska Optimizacija I Kompromisno Resenje (IT2FVIKOR) technique is one of the techniques of Interval Type-2 Fuzzy Multi-Criteria Decision Making (IT2FMCDM), which was developed to solve problems involving conflicting and multiple objectives. Most of the IT2FVIKOR methods are created from linguistic variables based on Interval Type-2 Fuzzy Set (IT2FS) and its generalization, such as Interval Type-2 Fuzzy Numbers (IT2FNs). Recent literature suggests that equitable linguistic scales can offer a better alternative, particularly when IT2FSs have some limitations in handling uncertainty and imbalance. This paper proposes the extended IT2FVIKOR with an equitable linguistic scale and Z-Numbers, where its linguistic scale introduces an equitable balance of positive and negative scales added to the restriction and reliability approach. Different from the typical IT2FVIKOR, which directly utilizes IT2FNs with a positive membership, the proposed method introduces positive and negative membership where each side considers a restriction and reliability approach. Besides, this paper also offers objective weights using fuzzy entropy-based IT2FS to calculate the weights of the extended IT2FVIKOR. The obtained solutions would help decision makers (DMs) identify the best solution to enhance water security projects in terms of finding the best strategies for water supply security in Malaysia.