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Various representations of real‐life scenarios by algebraic structures are of vital importance in the modern era of Industrial Revolution 4.0 as it enables such data to be interpreted and processed by artificial intelligence, thus bridging the interaction gap between humans and machines. In response to that, this article proposes a new decision making model for traffic control among shopping complexes utilizing the novel concept of the complex intuitionistic fuzzy soft lattice of the circular type (CIFSL‐C), which takes the time within a day as truly directional entities. As a result, CIFSL‐C possesses the combined structural complexity and the level of sophistication of all the previous algebraic models which they are derived from, enabling them to be utilized in representing many real‐life scenarios, including those related to the pandemic, which will be rigorously discussed in this article. In addition, the complex intuitionistic fuzzy soft lattice of the quaternion type (CIFSL‐Q) will also be established.

In this paper, we introduce the notion of bipolar-valued neutrosophic subbisemiring (BVNSBS), level sets of BVNSBS, and bipolar valued neutrosophic normal subbisemiring (BVNNSBS) of a bisemiring. The concept of BVNSBS is a new generalization of subbisemiring over bisemirings. We discussed the theory of (ξ, τ )- BVNSBS and (ξ, τ )-BVNNSBS over bisemirings and presented several illustrative examples to demonstrate the sufficiency and validity of the proposed theorems, lemmas, and propositions.

This paper proposed a novel first-order single-valued neutrosophic hesitant fuzzy time series (SVNHFTS) forecasting model. Our aim is to improve the previously proposed neutrosophic time series (NTS) model by incorporating the degree of the hesitancy using single-valued neutrosophic hesitant fuzzy set (SVNHFS) model instead of single-valued neutrosophic set (SVNS). Our paper's novelty is that we incorporate an algorithm that automatically converts the crisp dataset into the neutrosophic set that eliminates the need for experts' input or opinions in determining the membership in each of the partitioned neutrosophic set. We also incorporate Markov Chain algorithm in the de-neutrosophication process to include the weightage of the repeating neutrosophic logical relationships (NLRs). Our paper's significant contribution is to add to the existing body of knowledge related to fuzzy time series (FTS) by developing a new FTS model based on SVNHFS, one of the improved version of fuzzy sets, since this area of research is still relatively underdeveloped. To determine our proposed model's capability, we apply our proposed SVNHFTS model to three real datasets while also comparing the result to the other FTS models based on improved versions of fuzzy sets. Our datasets include benchmark enrollment data of University of Alabama, IDX Composite (Indonesian composite stock index), and MERVAL index (Argentinian composite stock index). The result shows that our proposed SVNHFTS model outperforms most of the other FTS models in terms of AFE and RMSE, especially the previously proposed NTS model.

We introduced the theory of Single valued neutrosophic hypergroup as the initial theory of single valued neutrosophic hyper algebra and also developed some results on single valued neutrosophic hypergroup.

In this paper, we introduced the concepts of Single-valued neutrosophic hyperring and Single-valued neutrosophic hyperideal. The algebraic properties and structural characteristics of the single-val-ued neutrosophic hyperrings and hyperideals are investigated and verified.

This paper proposes a multi-criteria decision making method called the neutrosophic data analytic hierarchy process (NDAHP) for the single-valued neutrosophic set (SVNS). This method is an extension of the neutrosophic analytic hierarchy process (NAHP) designed to handle actual datasets which consist of crisp values. The proposed NDAHP method uses an objective weighting mechanism whereas all other existing versions of the AHP, fuzzy AHP, and other fuzzy based AHP method in literature such as the NAHP and picture fuzzy AHP uses a subjective weighting mechanism to arrive at the decision. This makes the proposed NDAHP method effective as the weightage of the criteria which forms the input of the evaluation matrix are determined in an objective manner using actual data collected for the problem, and hence will not change according to the opinions of different decision makers which are subjective. The proposed NDAHP method is applied to a multi-criteria decision making problem related to the ranking of the financial performance of five public listed petrochemical companies trading in the main board of the Kuala Lumpur Stock Exchange (KLSE). Actual dataset of 15 financial indices for the five petrochemical companies for 2017 obtained from Yahoo! Finance was used in this paper. Following this, a brief comparative study is conducted to evaluate the performance of our NDAHP algorithm against the results of other existing SVNS-based decision making methods in the literature. The results are compared against actual results obtained from KLSE. To further verify the rankings obtained through each method, the Spearman and Pearson ranking tests are carried out on each of the decision making methods that are studied. It is proved that NDAHP produces the most accurate results, and this was further verified from the results of the Spearman and Pearson ranking tests.

This paper proposes an integration of two neutrosophic based multi-criteria decision making methods, namely the neutrosophic data analytical hierarchy process (NDAHP) and the Technique of Order Preference by Similarity to Ideal Solution (TOPSIS) with maximizing deviation method, both based on the single-valued neutrosophic set (SVNS) to evaluate the efficiency of general insurance companies in Malaysia. The level of efficiency of insurance companies is a subjective and vague matter, as the efficiency can be further branched into operational efficiency, investment efficiency, underwriting efficiency, and risk management efficiency. Hence relying on entirely objective decision making methods based on crisp data might not address the problem effectively, and therefore fuzzy based decision making methods are highly appropriate to be used in this situation. Our proposed decision making algorithm uses an integrated weighting mechanism that takes into consideration both the objective and subjective weights of the data attributes. The objective weighting mechanism handles the actual datasets that were used which consists of crisp values, whereas the subjective weighing mechanism handles the opinions of the experts in the general insurance industry who were surveyed in this study. This makes the proposed method a more holistic approach to evaluate the efficiency of general insurance companies in Malaysia as previous researches in this area are generally based on the actual datasets without consideration of the opinions and evaluations of the industry experts, or vice-versa. The proposed decision making algorithm is applied on actual datasets of management expenses, net commission, net earned premium and the net investment income for 19 selected general insurance companies in Malaysia over a two-year period from 2016 to 2017. The results obtained are then discussed and the possible reasons for the results are analyzed. A comprehensive comparative study of the results obtained via our proposed method and two other commonly used methods are then presented, analyzed and discussed.

Rural areas are often difficult to access reliably with medicine and vaccines. This study aimed to examine rural health care workers’ attitude towards drone delivery for medicine and vaccines and the factors that influenced it. Health care workers from four rural health care facilities were sampled. Participants self-reported their demographic information, attitude towards medicine and vaccine delivery using drones, perception of benefits and risks of using drones, and perceived leadership innovativeness through an online or a pen-and-paper questionnaire. A total of 272 health care workers (mean age = 36.19, SD = 8.10) from all of the sites participated in this study. More than half of the study participants agreed or strongly agreed that using a drone to deliver medicine and vaccines is a good idea (54.2%, 95% CI [47.5, 60.8]), a wise idea (54.6%, 95% CI [47.9, 61.2]), and is desirable (52.5%, 95% CI [45.7, 59.0]). Males (β = 0.223), workers from the Obstetrics and Gynaecology department (β = 0.135), a lower perceived delivery risk (β = −0.237), and higher leadership innovativeness (β = 0.336) predicted positive attitudes towards drone usage. Assistant medical officers (β = −0.172) had a negative attitude. There is a need to further understand the roles of occupation and leadership innovativeness in predicting health care workers’ attitude towards drone usage, as these differences could be embedded within their roles in the health care system.

Production of electricity from the burning of fossil fuels has caused an increase in the emission of greenhouse gases. In the long run, greenhouse gases cause harm to the environment. To reduce these gases, it is important to accurately forecast electricity production, supply and consumption. Forecasting of electricity consumption is, in particular, useful for minimizing problems of overproduction and oversupply of electricity. This research study focuses on forecasting electricity consumption based on time series data using different artificial intelligence and metaheuristic methods. The aim of the study is to determine which model among the artificial neural network (ANN), adaptive neuro-fuzzy inference system (ANFIS), least squares support vector machines (LSSVMs) and fuzzy time series (FTS) produces the highest level of accuracy in forecasting electricity consumption. The variables considered in this research include the monthly electricity consumption over the years for different countries. The monthly electricity consumption data for seven countries, namely, Norway, Switzerland, Malaysia, Egypt, Algeria, Bulgaria and Kenya, for 10 years were used in this research. The performance of all of the models was evaluated and compared using error metrics such as the root mean squared error (RMSE), average forecasting error (AFE) and performance parameter (PP). The differences in the results obtained via the different methods are analyzed and discussed, and it is shown that the different models performed better for different countries in different forecasting periods. Overall, it was found that the FTS model performed the best for most of the countries studied compared to the other three models. The research results can allow electricity management companies to have better strategic planning when deciding on the optimal levels of electricity production and supply, with the overall aim of preventing surpluses or shortages in the electricity supply.

Neutrosophic set is a generalization of classical set, fuzzy set, and intuitionistic fuzzy set by employing a degree of truth (T), a degree of indeterminacy (I), and a degree of falsehood (F) associated with an element of the dataset. One of the most essential problems is studying set-theoretic operators in order to be applied to practical applications. Developing Matlab toolboxes for computing the operational matrices in neutrosophic environments is essential to gain more widely-used of neutrosophic algorithms. In this paper, we propose some computing procedures in Matlab for neutrosophic operational matrices, especially i) computing the single-valued neutrosophic matrix; ii) determining complement of a single-valued neutrosophic matrix; iii) computing max-min-min and min-max-max of two single-valued neutrosophic matrices; v) computing power of a single-valued neutrosophic matrix; vi) computing additional operation and subtraction of two single-valued neutrosophic matrices; and ix) computing transpose of a single-valued neutrosophic matrix. Numerical examples are given to illustrate their applicability.

The adoption of innovative technology has always been a complex issue. The agriculture sectors of developing countries are following unsustainable farming policies. The currently adopted intensive farming practices need to replace with conservative agriculture practices (CAPs). However, the adoption of CAPs has remained low since its emergence and reports have suggested that the use of CAPs is scant for sustainable farm performance. This article aims to study three scenarios: Firstly, the influence of personal and CAPs level factors on the intention to adopt CAPs; secondly, the influence intention to adopt CAPs, facilitating conditions and voluntariness of use on the actual use of CAPs; and thirdly, the impact of the actual use of CAPs on sustainable farm performance. This study is based on survey data collected by structured interviews of rice farmers in rural Pakistan, which consists of 336 samples. The final analysis is performed using two methods: (1) a well-established and conventional way of Partial Least Squares Structural Equation Modeling (PLS-SEM) using Smart PLS 3.0, and (2) a frontier technology of computing using an artificial neural network (ANN), which is generated through a deep learning algorithm to achieve maximum possible accuracy. The results reveal that profit orientation and environment attitude as behavioural inclination significantly predicts the intention to adopt CAPs. The perception of effort expectancy can significantly predict the intention to adopt CAPs. Low intention to adopt CAPs caused by the low-level trust on extension, low-performance expectancy, and low social influence for the CAPs. The adoption of CAPs is affected by facilitating conditions, voluntary use of CAPs, and the intention to adopt CAPs. Lastly, the use of CAPs can positively and significantly forecast the perception of sustainable farm performance. Thus, it is concluded that right policies are required to enhance the farmers’ trust on extension and promote social and performance expectation for CAPs. Besides, policy recommendations can be made for sustainable agriculture development in developing and developed countries.

Many effective tools in fuzzy soft set theory have been proposed to handle various complicated problems in different fields of our real life, especially in decision making. Molodtsov’s soft set theory has been regarded as a newly emerging mathematical tool to deal with uncertainty and vagueness. Lattice ordered multi-fuzzy soft set (LMFSS) has been applied in forecasting process. However, similarity measure is not used in this application. In our research, similarity measure of LMFSS is proposed to calculate the similarity between two LMFSSs. Moreover, some of its properties are introduced and proved. Finally, an application of LMFSS in decision making using similarity measure is analysed.

Plithogenic set is an extension of the crisp set, fuzzy set, intuitionistic fuzzy set, and neutrosophic sets, whose elements are characterized by one or more attributes, and each attribute can assume many values. Each attribute has a corresponding degree of appurtenance of the element to the set with respect to the given criteria. In order to obtain a better accuracy and for a more exact exclusion (partial order), a contradiction or dissimilarity degree is defined between each attribute value and the dominant attribute value. In this paper, entropy measures for plithogenic sets have been introduced. The requirements for any function to be an entropy measure of plithogenic sets are outlined in the axiomatic definition of the plithogenic entropy using the axiomatic requirements of neutrosophic entropy. Several new formulae for the entropy measure of plithogenic sets are also introduced. The newly introduced entropy measures are then applied to a multi-attribute decision making problem related to the selection of locations.

The concept of bipolar fuzziness is of relatively recent origin where in addition to the presence of a property, which is done in fuzzy theory, the presence of its counter-property is also taken into consideration. This seems to be much natural and realistic. In this paper, an attempt has been made to incorporate this bipolar fuzziness in topological perspective. This is done by introducing a notion of bipolar gradation of openness and to redefine the bipolar fuzzy topology. Furthermore, a notion of bipolar gradation preserving map is given. A concept of bipolar fuzzy closure operator is also introduced and its characteristic properties are studied. A decomposition theorem involving our bipolar gradation of openness and Chang type bipolar fuzzy topology is established. Finally, some categorical results of bipolar fuzzy topology (both Chang type and in our sense) are proved.

The framework of the T-spherical fuzzy set is a recent development in fuzzy set theory that can describe imprecise events using four types of membership grades with no restrictions. The purpose of this manuscript is to point out the limitations of the existing intuitionistic fuzzy Einstein averaging and geometric operators and to develop some improved Einstein aggregation operators. To do so, first some new operational laws were developed for T-spherical fuzzy sets and their properties were investigated. Based on these new operations, two types of Einstein aggregation operators are proposed namely the Einstein interactive averaging aggregation operators and the Einstein interactive geometric aggregation operators. The properties of the newly developed aggregation operators were then investigated and verified. The T-spherical fuzzy aggregation operators were then applied to a multi-attribute decision making (MADM) problem related to the degree of pollution of five major cities in China. Actual datasets sourced from the UCI Machine Learning Repository were used for this purpose. A detailed study was done to determine the most and least polluted city for different perceptions for different situations. Several compliance tests were then outlined to test and verify the accuracy of the results obtained via our proposed decision-making algorithm. It was proved that the results obtained via our proposed decision-making algorithm was fully compliant with all the tests that were outlined, thereby confirming the accuracy of the results obtained via our proposed method.

The complex vague soft set (CVSS) model is a hybrid of complex fuzzy sets and soft sets that have the ability to accurately represent and model two-dimensional information for real-life phenomena that are periodic in nature. In the existing studies of fuzzy and its extensions, the uncertainties which are present in the data are handled with the help of membership degree which is the subset of real numbers. However, in the present work, this condition has been relaxed with the degrees whose ranges are a subset of the complex subset with unit disc and hence handle the information in a better way. Under this environment, we developed some entropy measures of the CVSS model induced by the axiomatic definition of distance measure. Some desirable relations between them are also investigated. A numerical example related to detection of an image by the robot is given to illustrate the proposed entropy measure.

We further develop the theory of vague soft groups by establishing the concept of normalistic vague soft groups and normalistic vague soft group homomorphism as a continuation to the notion of vague soft groups and vague soft homomorphism. The properties and structural characteristics of these concepts as well as the structures that are preserved under the normalistic vague soft group homomorphism are studied and discussed.

We propose the theory of possibility intuitionistic fuzzy soft expert theory and define some related concepts pertaining to this notion as well as the basic operations on this concept, namely, the complement, union, intersection, AND, and OR. The basic properties and relevant laws pertaining to this concept such as De Morgan’s laws are proved. Lastly, a generalized algorithm is introduced and applied to the concept of possibility intuitionistic fuzzy soft expert sets in hypothetical decision making problem.

We apply the classical theory of hyperrings to vague soft sets to derive the concepts of vague soft hyperrings, vague soft hyperideals, and vague soft hyperring homomorphism. The properties and structural characteristics of these concepts are also studied and discussed. Furthermore, the relationship between the concepts introduced here and the corresponding concepts in classical hyperring theory and soft hyperring theory is studied and investigated.

We introduce and develop the initial theory of vague soft hyperalgebra by introducing the novel concept of vague soft hypergroups, vague soft subhypergroups, and vague soft hypergroup homomorphism. The properties and structural characteristics of these concepts are also studied and discussed.