Search

The exponential increase in the number of diabetics around the world has led to an equally large increase in the number of diabetic retinopathy (DR) cases which is one of the major complications caused by diabetes. Left unattended, DR worsens the vision and would lead to partial or complete blindness. As the number of diabetics continue to increase exponentially in the coming years, the number of qualified ophthalmologists need to increase in tandem in order to meet the demand for screening of the growing number of diabetic patients. This makes it pertinent to develop ways to automate the detection process of DR. A computer aided diagnosis system has the potential to significantly reduce the burden currently placed on the ophthalmologists. Hence, this review paper is presented with the aim of summarizing, classifying, and analyzing all the recent development on automated DR detection using fundus images from 2015 up to this date. Such work offers an unprecedentedly thorough review of all the recent works on DR, which will potentially increase the understanding of all the recent studies on automated DR detection, particularly on those that deploys machine learning algorithms. Firstly, in this paper, a comprehensive state-of-the-art review of the methods that have been introduced in the detection of DR is presented, with a focus on machine learning models such as convolutional neural networks (CNN) and artificial neural networks (ANN) and various hybrid models. Each AI will then be classified according to its type (e.g. CNN, ANN, SVM), its specific task(s) in performing DR detection. In particular, the models that deploy CNN will be further analyzed and classified according to some important properties of the respective CNN architectures of each model. A total of 150 research articles related to the aforementioned areas that were published in the recent 5 years have been utilized in this review to provide a comprehensive overview of the latest developments in the detection of DR.The online version contains supplementary material available at 10.1007/s10462-022-10185-6.

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 article proposes the Mamdani complex fuzzy inference system (Mamdani CFIS) to improve performance of the classical FIS and complex FIS. The applicability of the proposed CFIS is demonstrated by applying it to six commonly available datasets from UCI Machine Learning under the comparison with Mamdani FIS and the Adaptive Neuro Complex Fuzzy Inference System (ANCFIS). It is successfully proven that the proposed Mamdani CFIS is computationally less expensive and presents a more efficient method to handle time-series data and time-periodic phenomena, among all the fuzzy IS found thus far in the literature. Furthermore, the novelty of CFIS mainly lies in its implementation of the complex number throughout the entire procedures of computation. This gives much greater flexibility of implementing unexpected, nonlinear fluctuations.

The single-valued neutrosophic set (SVNS) is a well-known model for handling uncertain and indeterminate information. Information measures such as distance measures, similarity measures and entropy measures are very useful tools to be used in many applications such as multi-criteria decision making (MCDM), medical diagnosis, pattern recognition and clustering problems. A lot of such information measures have been proposed for the SVNS model. However, many of these measures have inherent problems that prevent them from producing reasonable or consistent results to the decision makers. In this paper, we propose several new distance and similarity measures for the SVNS model. The proposed measures have been verified and proven to comply with the axiomatic definition of the distance and similarity measure for the SVNS model. A detailed and comprehensive comparative analysis between the proposed similarity measures and other well-known existing similarity measures has been done. Based on the comparison results, it is clearly proven that the proposed similarity measures are able to overcome the shortcomings that are inherent in existing similarity measures. Finally, an extensive set of numerical examples, related to pattern recognition and medical diagnosis, is given to demonstrate the practical applicability of the proposed similarity measures. In all numerical examples, it is proven that the proposed similarity measures are able to produce accurate and reasonable results. To further verify the superiority of the suggested similarity measures, the Spearman’s rank correlation coefficient test is performed on the ranking results that were obtained from the numerical examples, and it was again proven that the proposed similarity measures produced the most consistent ranking results compared to other existing similarity measures.

Inaccurate prediction would cause the insurance company encounter catastrophic losses and may lead to overpriced premiums where low-earning consumers cannot afford to insure themselves. The ability to forecast mortality rates accurately can allow the insurance company to take preventive measures to introduce new policies with reasonable prices. In this paper, several Lee–Carter (LC) based models are used to forecast the mortality rates in a case study of the Malaysian population. The LC-ARIMA model and also a combination of the LC model with two machine learning (ML) methods, namely the random forest (RF) and artificial neural network (ANN) methods are utilized on the prediction of mortality rates for males and females in Malaysia, whereby the LC-Random Forest (LC-RF) hybrid model is a new model that is introduced in this paper. Seventeen years of mortality data in Malaysia are selected as the dataset for this research. To analyze how the forecasting models perform for other countries, we have determined the model that has the best fit and produced the best forecasted mortality rates for all the other countries that are studied. This research has showed that LC-ANN and LC-ARIMA are the best model in predicting the mortality rates of males and females in Malaysia, respectively. This study has also found that the LC-ARIMA model is the best performing model in forecasting the mortality rates in countries that have longer life expectancy and a good healthcare system such as Sweden, Ireland, Japan, Hong Kong, Norway, Switzerland and Czechia. In contrast, the LC-ANN model is the best performing model in forecasting the mortality rates in countries that have a less efficiency, less accessibility healthcare system, and bad personal behavior such as Malaysia, Canada and Latvia.

Air pollutants can cause multifaceted harm to the human body. Respiratory diseases and immunology dysfunction are some of its main manifestations. Forecasting the air quality of a country is important to allow the government to take preventive measure. In this research, the artificial neural network (ANN), autoregressive integrated moving average (ARIMA), trigonometric regressors, Box-Cox transformation, ARMA errors, trend and seasonality (TBATS) and several fuzzy time series (FTS) models are utilized in the forecasting of air pollution index (API) of Kuala Lumpur, Malaysia, for the year 2017. Six years of daily API data for Kuala Lumpur from the year 2012 to the year 2017 for the Cheras observation station in Kuala Lumpur has been selected as the dataset of this research. The mean absolute percentage error (MAPE), root mean square error (RMSE) and computational time have been used as the performance evaluation metrics for the models and these values were calculated for each of the chosen forecasting models. A brief but comprehensive comparative study of the results obtained from each of the chosen model is presented in order to identify the most effective model to forecast API values. It was found that the fuzzy time series models outperformed the other models in terms of accuracy of forecasted values and computation time. Specifically, the Singh fuzzy time series model was found to be the most accurate and efficient forecasting model with RMSE of 1.4704 and MAPE of 4.364%.

In this paper, inspired by the concept of generalized single-valued neutrosophic graphs(GSVNG) of the first type, we define yet another generalization of neutrosophic graph called the generalized i...

COVID-19 is a highly contagious disease that has infected over 136 million people worldwide with over 2.9 million deaths as of 11 April 2021. In March 2020, the WHO declared COVID-19 as a pandemic and countries began to implement measures to control the spread of the virus. The spread and the death rates of the virus displayed dramatic differences among countries globally, showing that there are several factors affecting its spread and mortality. By utilizing the cumulative number of cases from John Hopkins University, the recovery rate, death rate, and the number of active, recovered, and death cases were simulated to analyse the trends and patterns within the chosen countries. 10 countries from 3 different case severity categories (high cases, medium cases, and low cases) and 5 continents (Asia, North America, South America, Europe, and Oceania) were studied. A generalized SEIR model which considers control measures such as isolation, and preventive measures such as vaccination is applied in this study. This model is able to capture not only the dynamics between the states, but also the time evolution of the states by using the fourth-order-Runge-Kutta process. This study found no significant patterns in the countries under the same case severity category, suggesting that there are other factors contributing to the pattern in these countries. One of the factors influencing the pattern in each country is the population's age. COVID-19 related deaths were found to be notably higher among older people, indicating that countries comprising of a larger proportion of older age groups have an increased risk of experiencing higher death rates. Tighter governmental control measures led to fewer infections and eventually reduced the number of death cases, while increasing the recovery rate, and early implementations were found to be far more effective in controlling the spread of the virus and produced better outcomes.

In this paper, the authors propose the concept of expert complex fuzzy soft sets as an extension to the classical complex fuzzy set model. Instead of being concerned with the study of the basic set theoretic operations for this model, which are essentially generalizations of the corresponding operations of the complex fuzzy set model, we extend the study of this model through the establishment of the mappings on classes of expert complex fuzzy soft sets. Through these mappings, we introduce the image and inverse image of an expert complex fuzzy soft set, which have immense applications in real-life applications. In addition to presenting the properties of the images and inverse images of this model, we present two numerical examples to demonstrate the utility of these concepts.

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.

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.

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.

The precise representation and analysis of complex data sets have become an increasingly important concern in areas such as medical diagnosis, economics, stock market analysis and pattern recognition. The advent of digital technology has resulted in the ubiquity of digitalized images and patterns. Unlike analog images and patterns, digital images and patterns are defined multi-dimensional data that consists of information pertaining to the physical and non-physical attributes of the images. This calls for a suitable complex fuzzy-based model that has the ability to represent multi-dimensional data in a succinct and concise manner. This paper achieves this goal using the complex vague soft set (CVSS) model to represent the multi-dimensional information for digital images. The information measures of CVSSs pertaining to the measures of distance and similarity are then established with the aim of solving pattern recognition problems involving digital images. The axiomatic definition of the distance-based similarity measure of CVSSs is introduced and the relations between this similarity measure and the distance measure of CVSSs are proposed and verified. The utility of this measure is demonstrated by applying it in a pattern recognition problem involving digitalized images that are defined by multi-dimensional data pertaining to the physical features and non-physical features such as the geographical data and timestamp of the images.

Analyzing the relations and patterns that exist in complex data sets is an integral part of the research in complex fuzzy set theory. The main object of study in this paper is the interval-valued complex fuzzy set (IV-CFS) model. This adaptation of complex fuzzy sets can handle datasets with a time-periodic feature, and the partial ignorance that exists in the data as well as the process of assigning values for the membership functions, in addition to modeling multi-dimensional data. This paper focuses on finding the patterns and relations between complex data sets using the properties of interval-valued complex fuzzy sets (IV-CFSs). To achieve this objective, this paper establishes the concept of relations and the composition operation for IV-CFSs using the extensive properties of the Cartesian product. Some of the algebraic properties of the relations and compositions are also introduced to define the equivalence relation between IV-CFSs. The proposed method is then applied to an MCDM problem related to customers’ online shopping preferences and behavior. A detailed case study of this MCDM problem is then presented through the interpretation of the results that were obtained. A brief comparison is then presented between our proposed method and other methods in literature used to analyze patterns between complex data sets.

In this paper, we propose an intuitively straightforward extension of the vague soft set model called the vague parameterized vague soft set (vp-VSS). This model generalizes the vague soft set by including the opinions of an expert or a moderator regarding the values of the membership function for the parameters that are considered, in the form of a vague set. The values provided by the experts indicate the threshold values for the membership functions of the elements, i.e., the minimum values that must be ideally satisfied by all the elements for each parameter. This provides a clear indication to the users of these information, and forms a pertinent component of the model, particularly in the decision-making process. Subsequently, we define some operations for this model and examine its properties. Subsequently, we introduce two algorithms based on a modified TOPSIS approach and a weighted aggregation operator approach, both of which are based on our proposed vp-VSS model. These algorithms are then applied in two multi-attribute decision-making problems involving supplier selection and the evaluation of supplier performance. The performance and utility of these algorithms are compared and contrasted in terms of the computational complexity and discriminative power of the algorithms.

Pythagorean fuzzy set, generalized by Yager, is a new tool to deal with vagueness considering the membership grade $$\mu $$ and non-membership $$\nu $$ satisfying the condition $$\mu ^2+\nu ^2\le 1$$ . It can be used to characterize the uncertain information more sufficiently and accurately than intuitionistic fuzzy set. Pythagorean fuzzy set has attracted great attention of many scholars that have been extended to new types and these extensions have been used in many areas such as decision making, aggregation operators, and information measures. Because of such a growth, we present an overview on Pythagorean fuzzy set with aim of offering a clear perspective on the different concepts, tools and trends related to their extension. In particular, we provide two novel algorithms in decision making problems under Pythagorean fuzzy environment. It may be served as a foundation for developing more algorithms in decision making.

In this chapter, the authors study a kind of network where the edge weights are characterized by single-valued triangular neutrosophic numbers. First, rigorous definitions of nodes, edges, paths, and cycles of such a network were proposed, which are then defined in algebraic terms. Then, characterization on the length of paths in such a network were presented. This is followed by the presentation of an algorithm for finding the shortest path length between two given nodes on the network. The proposed algorithm gives the shortest path length from source node to destination node based on a ranking method that takes both the length of edges and the number of nodes into account. Finally, a numerical example based on a real-life scenario is also presented to illustrate the efficiency and usefulness of the proposed approach.

A country's inflation rate and exchange rate forms a two-way relationship, whereby the former can affect the latter and vice versa. However, past researches have proven that the exchange rate affects inflation to a lesser extent. Thus, we choose to study the behaviour of exchange rate in response to inflation. While Malaysia has a relatively constant inflation rate for the past 35 years, without exceeding 10 percent, Vietnam's inflation rate is significantly higher with great fluctuations in the same duration. With this large difference in inflation rates, it would be interesting to study the affect onto the movement of the VND/MYR exchange rate. Besides observing the relationship, we are predicting the 2015 exchange rate based on historical data. This is done by fitting the data to two prediction models, the Purchasing Power Parity model and the Autoregressive model, and evaluating the most appropriate and accurate model. We found that the best prediction model is the Autoregressive model and proceeded to generate the forecasted exchange rate.

A country's exchange rate and commodity price forms a two-way relationship. However, past researches showed that the exchange rate has weaker effects towards commodity price. Hence, This study focuses on the behaviour of exchange rate in response to commodity price. This work will analyzed the behaviour of Malaysia and Australia in response to commodity price is to forecast future exchange rate. This study will determine if there exists a trend in the historical commodity price and exchange rate of Australia and Malaysia over the period of 2005 to 2015. Other than observing the relationship, the exchange rate for the 2016 was also forecast by using the historical data. Historical data of price of petroleum in Malaysia and price of iron ore in Australia will be used to predict the following year's price Historical data are fitted into two prediction models which are Purchasing Power Parity (PPP) model and Autoregressive models. The most appropriate and accurate model was evaluated. Result showed that autoregressive models was found to be the best prediction model and is used to predict the future exchange rate. Using the autoregressive model, forecasted the exchange rate in 2016 was 3.417 AUD/MYR.

Oil, being a major commercial energy source in the world, its fluctuation is often interrelated with the global economy. Generally, people would perceived that earning power of transportation sectors which include airline companies, courier companies and shipping companies are heavily relied on oil price fluctuation. Apparently, oil seems to be the major operating expense for those companies. As oil price goes down, it is naturally assumed that transportation industry is doing well as their operating expense is low and vice versa. This study has focused on the issue of whether the profitability of courier companies are wholly dependent on oil price. Comparison was done between four courier companies, namely Pos Malaysia, TNT Express, United Parcel Service and Deutsche Post. The data analyzed were the oil price and the net profit of each courier company from year 2006 to 2014. Simple linear regression and t-test analysis was done. The results showed that only linear relationship between oil price and net profit was exhibited by TNT Express. This means that the net profit of other three companies including Pos Malaysia, United Parcel Service and Deutsche Post are not mainly affected by oil price.

Fuzzy graph theory plays an important role in the study of the symmetry and asymmetryproperties of fuzzy graphs. With this in mind, in this paper, we introduce new neutrosophic graphs called complex neutrosophic graphs of type 1 (abbr. CNG1). We then present a matrix representation for it and study some properties of this new concept. The concept of CNG1 is an extension of the generalized fuzzy graphs of type 1 (GFG1) and generalized single-valued neutrosophic graphs of type 1 (GSVNG1). The utility of the CNG1 introduced here are applied to a multi-attribute decision making problem related to Internet server selection.

This paper examines the generalized intuitionistic fuzzy soft set (GIFSS) model which is an intuitively straightforward extension of the intuitionistic fuzzy soft set (IFSS) model. This concept which arises from IFSSs, is generalized by including a moderator’s opinion regarding the validity of the information at hand, thus making it highly suitable for use in decision-making problems that involve uncertain, vague and/or unreliable data. In this paper, we introduce the tools that measure the distance, similarity and the degree of fuzziness of GIFSSs. The axiomatic definitions of the distance measure is introduced and subsequently used to define the similarity measure and intuitionistic entropy induced by this distance measure. Some of the algebraic properties of these measures are also verified. The well-known Hamming, normalized Hamming, Euclidean and normalized Euclidean distances are generalized to make them compatible with the concept of GIFSSs. Subsequently, some relations among these information measures are proposed and verified. These results indicate how these measures are related and how they can be deduced from one another. Finally, we demonstrate the application of the information measure between GIFSSs by applying it to a case study related to the moderation of school-based assessment components of students in externally accredited academic programs.

In this paper, the authors aim to extend the notion of interval-valued vague soft sets to establish the concept of possibility interval-valued vague soft expert sets. The set theoretic operations of this concept and other related concepts are introduced. The algebraic properties of this notion such as the laws of commutativity, associativity and De Morgan are established and verified. Lastly, the similarity measure between this set is introduced and illustrated using a hypothetical example related to texture synthesis.

Display Omitted Complex vague soft sets (CVSSs for short) are a hybrid model of complex fuzzy sets and vague soft sets and the study of CVSSs was initiated by Selvachandran et al. (2016).In this paper, the Cartesian product and the composition of CVSSs are defined and these are used to introduce the relations between CVSSs.This relations are then classified into symmetric, transitive, reflexive and equivalence relations and the algebraic properties and the relationships between these relations are then studied.The relations between CVSSs introduced here have the ability to: (i) Describe the degree of interaction and the phase between the elements in two sets by means of an interval-based membership structure. (ii) Capture the information pertaining to the time frame of the intersection between the elements in two sets, which cannot be accomplished by using other relations such as relations between fuzzy sets, soft sets or complex fuzzy sets.An application of the relations between CVSSs in the area of economics is then presented through the discussion of a real-life problem involving the influence of the financial indicators of the Chinese economy on the financial indicators of the Malaysian economy. Complex vague soft sets are essentially vague soft sets characterized by an additional parameter called the phase term which is defined over the set of complex numbers. In this study, we introduce and discuss the relations between complex vague soft sets. We present the definitions of the Cartesian product of complex vague soft sets and subsequently that of complex vague soft relations. The definition of the composition of complex vague soft sets is also provided. The notions of symmetric, transitive, reflexive and equivalence complex vague soft relations are then proposed and the algebraic properties of these concepts are verified. The relation between complex vague soft sets is then discussed in the context of a real-life problem: the relation between the financial indicators of the Chinese economy which are characterized by their degrees of influence on the financial indicators of the Malaysian economy, and the time required for the former to affect the latter. Interpretations of the results obtained from this example are then proposed by relating them to recent significant real-life events in the Chinese and Malaysian economies.

In this paper, we propose the concept of complex vague soft sets which are vague soft sets defined in a complex setting. Based on this new concept we define some concepts related to this notion as well as some basic operations namely the complement, union, intersection, AND and OR. The basic properties and relevant laws pertaining to this concept such as the De Morgan’s laws are also verified. We introduce the axiomatic definition of the distance function between two complex vague soft sets and subsequently define several distance measures between complex vague soft sets. Finally some of the algebraic properties of these distance measures are verified.

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.

This paper introduces a mathematical model for precise analysis of uncertainty and its fluctuation in the given interval-valued fuzzy attributes. In this regard, a method is introduced for drawing the interval-valued complex lattice and its navigation at user required complex granules with demonstration.

In recent years, the theory of complex fuzzy sets has captured the attention of many researchers, and research in this area has intensified in the past five years. However, almost all of the researchers in this area have focused on the development of various complex fuzzy based models as well as constructing decision making processes using current decision making approaches and tools. In this spirit, this paper focuses on developing the algebraic structures pertaining to groups and subgroups for the complex intuitionistic fuzzy soft set model. This paper was constructed based on the complex intuitionistic fuzzy soft set model which is characterized by a membership and a non-membership structure for both the amplitude and phase terms of the elements. This model was chosen due to its dual-membership structure that is better able to handle the uncertainties and partial ignorance that exists in most complex data, whilst retaining all the characteristics and advantages of complex fuzzy sets. Besides examining the properties and structural characteristics of the algebraic structures, the relationship between the algebraic structures introduced here and the corresponding algebraic structures in fuzzy group theory and classical group theory were also discussed and verified.

A single-valued neutrosophic set (SVNS) is a special case of a neutrosophic set which is characterized by a truth, indeterminacy, and falsity membership function, each of which lies in the standard interval of [0, 1]. This paper presents a modified Technique for Order Preference by Similarity to an Ideal Solution (TOPSIS) with maximizing deviation method based on the single-valued neutrosophic set (SVNS) model. An integrated weight measure approach that takes into consideration both the objective and subjective weights of the attributes is used. The maximizing deviation method is used to compute the objective weight of the attributes, and the non-linear weighted comprehensive method is used to determine the combined weights for each attributes. The use of the maximizing deviation method allows our proposed method to handle situations in which information pertaining to the weight coefficients of the attributes are completely unknown or only partially known. The proposed method is then applied to a multi-attribute decision-making (MADM) problem. Lastly, a comprehensive comparative studies is presented, in which the performance of our proposed algorithm is compared and contrasted with other recent approaches involving SVNSs in literature.

Fuzzy graph theory plays an important role in the study of the symmetry and asymmetry properties of fuzzy graphs. With this in mind, in this paper, we introduce new neutrosophic graphscalled complex neutrosophic graphs of type 1 (abbr. CNG1).