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The oil production and price issues have been discovered a long time ago, and always be a continuous problem to the globe especially during the current global threats of the coronavirus pandemic. This paper provides a literature review that involves game theory and multi-criteria decision-making (MCDM) methods with its applications to oil production and price problems. This paper identifies and analyses the use of the game theory and MCDM methods on oil production and price to compare the situation studied, to determine the model that has been used, the trend of past literature and also the details of the basic elements for the game theory framework. Therefore, the oil production and price problem using the game theory and MCDM methods are reviewed and numerous applications studied from the past works of literature are highlighted. The trend of oil production and price which used the game theory and MCDM methods based on the year 2001 till 2021 is still lacking sources from the Web of Science and Scopus databases. The main contribution of the recent study is the employment of the game theory and MCDM methods to the oil production and price problem. Keywords: Game theory; MCDM; oil production; oil price

Circular data are common in biological studies which are involved angle and direction measurements. An outlier in circular biological data mostly related to the abnormality of the data set. The existence of outliers may affect the final outcome of a data analysis. Thus, an outliers’ identification method is essential in circular biological data to determine the stage of abnormality for the sample that has been studied. Past studies were mostly focusing on detecting outliers for multivariate circular biological data. However, identifying outlier for univariate data is more essential in the abnormality stage investigation. In this study, outliers’ identification methods for univariate circular biological data have been reviewed. The strength and weaknesses of the methods are investigated and discussed.

We propose a method to search rare cardiovascular disease symptom rules from historical health examination records according to its hazard ratio utility and further detect the disease given new medical record data. Further, we aim to assist both medical experts and patients by alerting the current symptoms and preparing the early treatments. In general, the proposed method first deals with the uncertainty of age and other continuous features using a fuzzy set. Next, we define the hazard ratio utility of each item set to assist the mining process. Based on the utility, we discover the rare cardiovascular disease patterns employing High Utility Rare Itemset Mining. At last, we add a prediction step to check the given health record data whether diagnosed cardiovascular. Subsequently, we can obtain rare symptoms of cardiovascular disease, which are later applied to detect the new related record data. The rare symptoms that are confirmed by their utility risk for cardiovascular disease can assist the medical experts' decision better than the common symptoms as it is often hard to be recognized at a glance. The proposed method evaluated on a public cardiovascular dataset. The experimental results showed that the generated rare cardiovascular disease patterns successfully applied to detect the cardiovascular given the symptoms data.

Z-numbers and intuitionistic fuzzy numbers are both important as they consider the reliability of the judgement, membership and non-membership functions of the numbers. The combination of these two numbers produce intuitionistic Z-numbers which need to be defuzzified before aggregation of multiple experts’ opinions could be done in the decision making problems. This paper presents the generalised intuitionistic Z-numbers and proposes a centroid-based defuzzification of such numbers, namely intuitive multiple centroid. The proposed defuzzification is used in the decision making model and applied to the supplier selection problem. The ranking of supplier alternatives is evaluated using the ranking function based on centroid. In the present paper, the ranking is improved since the intuitionistic fuzzy numbers (IFN) are integrated within the evaluations which were initially in form of Z-numbers, considering their membership and non-membership grades. The ranking of the proposed model gives almost similar ranking to the existing model, with simplified but detailed defuzzification method.

Choquet integral is one of the aggregation operators that mainly used to aggregate interrelated information. This operator has been successfully embedded with intuitionistic fuzzy sets in solving various decision-making problems. However, the intuitionistic fuzzy sets have some limitations particularly on boundary of constraint where the sum of two memberships never exceeded one. Pythagorean fuzzy set (PFS) was coined to overcome this limitation where the square sum of two memberships could be less than or equal to one. In most cases, it is assumed that all elements of PFSs are independent. Nonetheless, in real life of multi-criteria decision-making problems, most of the criteria are interrelated. This paper aims to introduce Choquet integral operator based on PFSs of which interactions between elements of PFSs can be dealt with fuzzy measures. The proposed operators do not only consider the importance of elements or their ordered positions, but also consider the interaction among the criteria or ordered positions in criteria of decision-making process. The proposed aggregation operator is the combination of the PFSs and Choquet integral in which Choquet integral is used to handle interactions between criteria. A case of sustainable solid waste management problem of two major cities in Malaysia is presented to illustrate the application of the proposed aggregation operators. The proposed method successfully identified that Kuala Lumpur is the better city in managing solid waste based on the values of Pythagorean fuzzy Choquet integrals. Finally, this paper gives some suggestions for future research directions.

A multi-criteria decision-making process utilizes real-time data information, which is inherently uncertain and imprecise. To be relevant in the decision-making process, real-time data information must be reliable. Because fuzziness alone is insufficient to solve decision-making problems, measuring the information’s reliability is critical. Z-number, which incorporates both restrictions and reliability in its definition is considered as a powerful tool to depict the imperfect information. In this paper, a new methodology is developed based on fuzzy Technique for Order Preference by Similarity to Ideal Solution (TOPSIS) method and fuzzy entropy for solving the multi-criteria decision-making problems where the weight information for decision makers and criteria is incomplete. The evaluation of the information is represented in the form of linguistic terms and the following calculation is performed using Z-numbers. Fuzzy entropy is applied to determine the weights of the criteria and fuzzy TOPSIS is used to rank the alternatives. An empirical study of subjective well-being of working women is used to demonstrate the proposed methodology.

More studies trend to hybrid the game theory technique with the multi-criteria decision-making (MCDM) method to aid real-life problems. This paper provides a comprehensive review of the hybrid game theory technique and MCDM method. The fundamentals of game theory concepts and models are explained to make game theory principles clear to the readers. Moreover, the definitions and models are elaborated and classified to the static game, dynamic game, cooperative game and evolutionary game. Therefore, the hybrid game theory technique and MCDM method are reviewed and numerous applications studied from the past works of literature are highlighted. The result of the previous studies shows that the fundamental elements for both frameworks were studied in various ways with most of the past studies tend to integrate the static game with AHP and TOPSIS methods. Also, the integration of game theory techniques and MCDM methods was studied in various applications such as politics, economy, supply chain, engineering, water management problem, allocation problem and telecommunication network selection. The main contribution of the recent studies of employment between game theory technique and MCDM method are analyzed and discussed in detail which includes static and dynamic games in the non-cooperative game, cooperative game, both non-cooperative and cooperative games and evolutionary game.

This paper presents a hybrid fuzzy multi criteria decision making model for z-numbers using intuitive vectorial centroid. There are two novelty discuss here: 1) development of intuitive vectorial centroid defuzzification and; 2) development ofhybrid fuzzy multi criteria decision making model based on consistent fuzzy preference relations and fuzzy technique for order performance by similarity to ideal solution for z-numbers. The implementation of z-numbers is taken into consideration, where it has more authority to describe the knowledge of human being and extensively used in the uncertain information development to deal with linguistic decision making problems. Fuzziness is not sufficient enough when dealing with real information and a degree of reliability of the information is very critical. It also highlights the combination of z-numbers with multi criteria decision making techniques allow the use of fuzzy linguistic by considering the need of human intuition in decision making problems. The proposed methodology is applied to staff recruitment problem.

This paper proposes an ensemble method based on neural network architecture and stacking generalization. The objective is to develop a novel ensemble of Artificial Neural Network models with back propagation network and dynamic Recurrent Neural Network to improve prediction accuracy. Historical meteorological parameters and rainfall intensity have been used for predicting the rainfall intensity forecast. Hourly predicted rainfall intensity forecast are compared and analyzed for all models. The result shows that for 1 h of prediction, the neural network ensemble forecast model returns 94% of precision value. The study achieves that the ensemble neural network model shows significant improvement in prediction performance as compared to the individual neural network model.

Fuzzy risk analysis plays an important role in mitigating the levels of harm of a risk. In real world scenarios, it is a big challenge for risk analysts to make a proper and comprehensive decision when coping with risks that are incomplete, vague and fuzzy. Many established fuzzy risk analysis approaches do not have the flexibility to deal with knowledge in the form of preferences elicitation which lead to incorrect risk decision. The inefficiency is reflected when they consider only risk analyst preferences elicitation that is partially known. Nonetheless, the preferences elicited by the risk analyst are often non-homogeneous in nature such that they can be completely known, completely unknown, partially known and partially unknown. In this case, established fuzzy risk analysis methods are considered as inefficient in handling risk, hence an appropriate fuzzy risk analysis method that can deal with the non-homogeneous nature of risk analyst’s preferences elicitation is worth developing. Therefore, this paper proposes a novel fuzzy risk analysis method that is capable to deal with the non-homogeneous risk analyst’s preferences elicitation based on grey numbers. The proposed method aims at resolving the uncertain interactions between homogeneous and non-homogeneous natures of risk analyst’s preferences elicitation by using a novel consensus reaching approach that involves transformation of grey numbers into grey parametric fuzzy numbers. Later on, a novel fuzzy risk assessment score approach is presented to correctly evaluate and distinguish the levels of harm of the risks faced, such that these evaluations are consistent with preferences elicitation of the risk analyst. A real world risk analysis problem in fiber industry is then carried out to demonstrate the novelty, validity and feasibility of the proposed method.

Ranking function acts as a predictive algorithm that is used to establish a simple ordering of documents according to its relevance and this process shows the effectiveness, quality and the accuracy for the variety type of Information Retrieval (IR) such as, Domain Specific Retrieval of Malay Translated Hadith. In this research, a Hierarchical Fuzzy Logic Controller of Mamdani-type Fuzzy Inference System has been built to define the ranking function based on the BM25 Model. The model examines four-inputs which are Ontology BM25 Score, Fabrication Rate of Hadith, Shia Rate of Hadith from the previous works of the researchers and the New additional Positive Rate of Hadith. It also examines four-output values of Final Ranking Score which consist of three triangular membership functions. The new Positive Rate of hadith is based on the score value of the automatic text summarization that was executed in pre-processing phase. The proposed system has outperformed the BM25 original score and the Vector Space Model (VM) on 5 topic of queries and 26 queries in the term of individual queries, while the BM25 original score and Vector Space Model only yielded better result in 3 and 0 queries respectively on the P@10, %no measures and MAP. P@10 represent the values of Precision at Rank 10 P@10), %no measures represent the percentage of queries with no relevant documents in the top ten retrieved and MAP represents Mean Average Precision of the queries. The results show the proposed system have capability to demote negative documents and move up the relevant documents in the ranking list with positive indicator and its capability to recall unseen document with the application of ontology in text retrieval. For the future works, the researcher would like to apply the usage of new ranking indicator such as reliability score from the expert and the lay users of the Domain Specific Retrieval of Malay Translated Hadith.

The management of uncertainty in decision making problems is a very challenging research issues. The deterministic or probabilistic classical decision approaches quite often do not fit well to real world decision making problems. This proposal presents Fuzzy Technique for Order Preference by Similarity to Ideal Solution (FTOPSIS) using fuzzy similarity for z-numbers. The classical fuzzy TOPSIS techniques use closeness coefficient to determine the rank order by calculating Fuzzy Positive Ideal Solution (FPIS) and Fuzzy Negative Ideal Solution (FNIS) simultaneously. The authors propose fuzzy similarity to replace closeness coefficient by doing ranking evaluation. Fuzzy similarity is used to calculate the similarity between two fuzzy ratings (FPIS and FNIS). Fuzziness is not sufficient enough when dealing with real information and a degree of reliability of the information is very critical. Therefore, the implementation of z-numbers is taken into consideration, where it has more authority to describe the knowledge of human being and extensively used in the uncertain information development to deal with linguistic decision making problems. A case study on group of company in Malaysia is given to illustrate the feasibility of the proposed methodology in ranking the performance assessment.

Risk analysis plays a crucial role in mitigating the levels of harm of a risk. In real world scenarios, it is a big challenge for risk analysts to make a proper and comprehensive decision when coping with the risks. Many practical risk analysis problems do not have flexibility with regards to knowledge elicitation and disagreements in the group. This is due to the non-homogeneous nature of risk analysts’ preferences that lead to inconsistent agreements in the process of group decision making. In this chapter, a novel non-homogeneous preference elicitation based on grey numbers for risk analysis problem is proposed. Grey numbers allow more flexibility for non-homogeneous preference elicitation in uncertain, vague and fuzzy environment. This work also introduces a novel theoretical non-homogeneous consensus reaching methodology that resolves disagreement between risk analysts. A case study on risk analysis decision making is also presented to demonstrate the novelty, validity and feasibility of the proposed methodology.

In this article, the researchers main contribution is to investigate three factors which may correlate in implementation of Expert Judgment Z-Numbers as new Fuzzy Logic Ranking Indicator such as: expert relevance judgment or score, the expert confidence and the level of expertise. The Expert Judgment Z-Numbers then will be an input to the Hierarchical Fuzzy Logic System of Domain Specific Text Retrieval, along with other indicators such as Ontology BM25 Score, Fabrication Rate, Shia Rate and Positive Rate of hadith document. The results showed, the proposed system, with the additional new indicator of Expert Judgment Z-Numbers, may improve the original BM25 ranking function, by yielding better results on 26 queries, on all evaluation metrics that are measured in this research such as P@10, %no measures and MAP, and has achieved better results in 28 queries on P@10 alone, compared to the BM25 original score, that only yield better results in 2 queries on all evaluation metrics, and also yield better results in 4 queries on the MAP alone. The results proved that the proposed system has a capability to utilize the expert confidence and their relevant judgment that are represented in Z-Number, as an indicator to optimize the existing ranking function system and has a potential for a further research to be conducted on these domains. For the future works, the researchers would like to enhance this research by including a variety of expert’s level confidence and their judgment, also a new calculation to represent the value of Z-Numbers.

Eco-friendly car is expected to be the next driving market force for global transportation and technology due to its paramount importance towards the sustainability of the environment and society. However, the actual sales of eco-friendly car are not that convincing and it is even decreasing because the consumer is still uncertain to consider eco-friendly as one of the criteria for them to buy their cars. This situation is worsen by the lack of information and awareness regarding sustainability transportation initiatives. Due to the uncertainty and vague understanding of the consumer about this problem, this paper attempts to investigate the current preference of consumer to buy their cars, and whether they really need to buy the eco-friendly car by using the Fuzzy Analytic Hierarchy Process (FAHP) which implements the Intuitive Vectorial Centroid (IVC). Based on FAHP, the imprecise or fuzzy judgment from the decision maker can be incorporated, to anticipate a better decision for eco-friendly car selection. The outcome of FAHP is compared with crisp Analytic Hierarchy Process (AHP), and the findings shows that FAHP can provide an accurate and consistent result with AHP, although it deals with fuzzy judgment inputs from multiple decision makers.

By gleaning insights from the data, fuzzy clustering capable to learn from data, identify patterns and make decision with minimum human intervention. However, it cannot simply study in detail regarding the quality of data, particularly knowledge of human being. Since the data are collected through decision-makers, the quality and human knowledge of the particular data are crucial factors to be considered. Compared to classical fuzzy numbers, z-numbers has ability to describe the human knowledge because it has both restraint and reliability part in its definition. Consequently, the implementation of z-numbers in fuzzy clustering algorithm is taken into consideration, where it has more authority to describe the knowledge of human being and extensively used in uncertain information development. Thus, there are two objectives of this paper; (i) to propose a reliable fuzzy clustering algorithm using z-numbers and; (ii) to cluster the Chronic Kidney Disease (CKD) patients based on the selected indicators to identify which cluster the patients belongs to (Cluster 0, Cluster 1, Cluster 2, Cluster 3 or Cluster 4) based on the membership functions defined. A case study of the CKD patients with the selected indicators is considered to demonstrate the capability of z-numbers to handle the knowledge of human being and uncertain information and also will present the idea in developing a robust and reliable fuzzy clustering algorithm particularly in dealing with knowledge of human being using z-numbers.

The warm and humid condition is the characteristic of Malaysia tropical climate. Prediction of rain occurrences is important for the daily operations and decisions for the country that rely on agriculture needs. However predicting rainfall is a complex problem because it is effected by the dynamic nature of the tropical weather parameters of atmospheric pressure, temperature, humidity, dew point and wind speed. Those parameters have been used in this study. The rainfall prediction are compared and analyzed. Fuzzy Logic and Fuzzy Inference System can deal with ambiguity that often occurred in meteorological prediction; it can easily incorporate with expert knowledge and empirical study into standard mathematical. This paper will determine the dependability of Fuzzy Logic approach in rainfall prediction within the given approximation of rainfall rate, exploring the use of Fuzzy Logic and to develop the fuzzified model for rainfall prediction. The accuracy of the proposed Fuzzy Inference System model yields 72%

A prior distributions in standard Bayesian knowledge are assumed to be classical probability distribution. It is required to representable those probabilities of fuzzy events based on Bayesian knowledge. Propelled by such real applications, in this research study, the theoretical foundations of Vectorial Centroid of interval type-2 fuzzy set with Bayesian logistic regression is introduced. As opposed of utilising type-1 fuzzy set, type-2 fuzzy set is recommended based on the involvement of uncertainty quantity. It additionally highlights the association of fuzzy sets with Bayesian logistic regression permits the use of fuzzy attributes by considering the need of human intuition in data analysis. It may be worth including here that this proposed methodology then applied for BUPA liver-disorder dataset and validated theoretically and empirically.

The paper considers fuzzy rule based system for multi criteria group decision making problem. A novel version of TOPSIS method using interval type 2 fuzzy rule based system approach is proposed with the objective of improving the type 2 TOPSIS ability to deal with ambiguity through the combination of the mathematical process involved in the type 2 TOPSIS with the expert empirical knowledge. On the other hand, a hybrid analysis of decision making process that requires the use of human sensitivity to reflect influence degree of decision maker can be expressed by a fuzzy rule base. To ensure practicality and effectiveness of proposed method, stock selection problem is studied. The ranking based on proposed method is validated comparatively using Kendall's Tau rank correlation. Based on the result, the proposed method outperforms the established non-rule based version of type 2 TOPSIS in term of ranking performance.

In this paper, the theoretical foundations of generalised fuzzy Bayesian Network based on Vectorial Centroid defuzzification is introduced. The extension of Bayesi-an Network takes a broad view by examples labelled by a fuzzy set of attributes, instead of a classical set. Com-bining fuzzy set theory and Bayesian Network’s knowledge allows the use of fuzzy variables or attrib-utes that widely used in various applications in science and engineering. It is so highlights the integration of both knowledge’s considers the need of human intuition in data analysis. Through the experimental comparison and analysis on the BUPA-liver disorder dataset, the proposed methodology is then validated theoretically and empirically.

A concept of interval type-2 fuzzy numbers is introduced in decision making analysis as this concept is capable to effectively deal with the uncertainty in the information about a decision. It considers two types of uncertainty namely inter and intra personal uncertainties, in enhancing the representation of type-1 fuzzy numbers in the literature of fuzzy sets. As interval type-2 fuzzy numbers are crucial in decision making, this paper proposes a methodology for ranking interval type-2 fuzzy numbers. This methodology consists of two parts namely the interval type-2 fuzzy numbers reduction methodology as the first part and ranking of type- 1 fuzzy numbers as the second part. In this study, established reduction methodology of interval type-2 fuzzy numbers into type-1 fuzzy numbers is extended to reduction into standardised generalised type-1 fuzzy numbers as the extension complements the capability of the methodology on dealing with both positive and negative data values. It is worth adding here that this methodology is analysed using thorough empirical comparison with some established ranking methods for consistency evaluation. This methodology is considered as a generic decision making procedure, especially when interval type-2 fuzzy numbers are applied to real decision making problems.