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Digital technology is so broad today as to encompass almost everything. It eases the difficulties of day-to day life with internet. E-commerce plays an important role in digital age of technology. Instead of many benefits of online system, it faces many types of threats. Sometime, choosing the best e-commerce security has a lot of uncertainties and ambiguities to reduce the effect of threats. To reduce these uncertainties, this article developed a new concept of complex cubic picture fuzzy set (CoCPFS) of fuzzy algebra that explains the positive effect, neutral effect, and negative effect of any object and additionally discussed the Cartesian product between two CoCPFSs, CoCPF relations, and their types. The relationship among the e-commerce securities and threats is investigated for the first time in the history of fuzzy algebra. These relations show the ways of disabling the effects of a threat by an effective security technique. Furthermore, the advantages and benefits of CoCPFS are explained through comparison tests with preexisting frameworks of fuzzy sets. [ABSTRACT FROM AUTHOR]

In today's world, the countries that have easy access to energy resources are economically strong, and thus, maintaining a better geopolitical position is important. Petroleum products such as gas and oil are currently the leading energy resources. Due to their excessive worth, the petroleum industries face many risks and security threats. Observing the nature of such problems, it is asserted that the complex bipolar fuzzy information is a better choice for modeling them. Keeping the said problem in mind, this article introduces the novel structure of complex bipolar fuzzy relation (CBFR), which is basically used to find out the relationships between complex bipolar fuzzy sets (CBFSs). Similarly, the types of CBFRs are also defined, which is helpful during the process of analyzing and interpreting the problem. Moreover, some useful results and interesting properties of the proposed structures are deliberated. Further, a new modeling technique based on the proposed structures is initiated, which is used to investigate the security risks to petroleum industries. Furthermore, a detailed comparative analysis proves the advantages and supremacy of CBFRs over other structures. Therefore, the results achieved by the proposed methods are substantially reliable, practical and complete. [ABSTRACT FROM AUTHOR]

Many industries are developing robust models, capable of analyzing huge and complex data by using machine learning (ML) while delivering faster and more accurate results on vast scales. ML is a subfield of artificial intelligence, which is broadly defined as the capability of a machine to imitate intelligent human behavior. ML tools enable organizations to swiftly identify profitable opportunities and potential risks. Besides these uses, ML also has a wide range of applications in our daily lives. So, the development in ML is most important in this age of digital system to solve more complex problems. In order to further develop ML and diminish the uncertainties to improve accuracy, an innovative concept of complex bipolar intuitionistic fuzzy sets (CBIFSs) is introduced in this article. Further, the Cartesian product of two CBIFSs is defined. Moreover, the complex bipolar intuitionistic fuzzy relations (CBIFRs) and their types with suitable examples are defined. In addition, some important results and properties are also presented. The proposed modeling techniques are used to study different ML factors and their interrelationship, so that the functionality of ML might be enhanced. Furthermore, the advantages and benefits of proposed methods are described by their side to side comparison with preexisting frameworks in the literature. [ABSTRACT FROM AUTHOR]

In our lives, we cannot avoid the uncertainty. Randomness, rough knowledge, and vagueness lead us to uncertainty. In mathematics, the fuzzy set (FS) theory and logics are used to model uncertain events. This article defines a new concept of complex picture fuzzy relation (CPFR) in the field of FS theory. In addition, the types of CPFRs are also discussed to make the paper more fruitful. Today's complex network architecture faces the ever-changing threats. The cyber-attackers are always trying to discover, catch, and exploit the weaknesses in the networks. So, the security measures are essential to avoid and dismantle such threats. The CPFR has a vast structure composed of levels of membership, abstinence, and nonmembership which models uncertainty better than any other structures in the theory. Moreover, a CPFR has the ability to cope with multivariable problems. Therefore, this article proposes modeling techniques based on the complex picture fuzzy information which are used to study the effectiveness and ineffectiveness of different network securities against several threats and cyber-attack practices. Moreover, the strength and preeminence of the proposed methods are verified by studying their comparison with the existing methods. [ABSTRACT FROM AUTHOR]

The bi-directional flow of energy and information in the smart grid makes it possible to record and analyze the electricity consumption profiles of consumers. Because of the increasing rate of inflation over the past few years, people started looking for means to use electricity illegally, termed as electricity theft. Many data analytics techniques are proposed in the literature for electricity theft detection (ETD). These techniques help in the detection of suspected illegal consumers. However, the existing approaches have a low ETD rate either due to improper handling of the imbalanced class problem in a dataset or the selection of inappropriate classifier. In this paper, a robust big data analytics technique is proposed to resolve the aforementioned concerns. Firstly, adaptive synthesis (ADASYN) is applied to handle the imbalanced class problem of data. Secondly convolutional neural network (CNN) and long-short term memory (LSTM) integrated deep siamese network (DSN) are proposed to discriminate the features of both honest and fraudulent consumers. Specifically, the task of feature extraction from weekly energy consumption profiles is handed over to the CNN module while the LSTM module performs the sequence learning. Finally, the DSN contemplates on the shared features provided by the CNN-LSTM and applies final judgment. The data analytics is performed on different train–test ratios of the real-time smart meters' data. The simulation results validate the proposed model's effectiveness in terms of high area under the curve, F 1 -Score, precision and recall. • A robust big data analytic technique for electricity theft detection in smart grid is proposed. • We propose an adaptive synthesis to handle imbalanced class problem. • A deep siamese network with underpinned integrated networks of convolution neural network and long-short term memory is proposed to discriminate both features of fair and fraud consumers. • Simulation results validate the proposed model in terms of high area under the curve, low false positive rate and low false negative rate. [ABSTRACT FROM AUTHOR]

Soft set theory initiated by Molodtsov in 1999 has been emerging as a generic mathematical tool for dealing with uncertainty. A noticeable progress is found concerning the practical use of soft set in decision-making problems. The purpose of this manuscript is to explore the novel of multi-valued picture fuzzy set (MPFS) and multi-valued picture fuzzy soft set (MPFSS) which are the generalizations of the notions of picture fuzzy soft set (PFSS) and multi-fuzzy soft set (MFSS). This notion can be used to express fuzzy information in more general and effective way. In particular, some basic operations such as union, intersection, complement and product of the proposed MPFSS are developed, and their properties are investigated. Furthermore, some aggregation operators corresponding to the proposed MPFSSs are called multi-picture fuzzy soft weighted averaging, multi-picture fuzzy soft ordered weighted averaging and multi-picture soft hybrid weighted averaging operators for a collections of MPFSSs are also developed. Moreover, based on these operators, we presented a new method to deal with the multi‐attribute group decision-making problems under the multi-valued picture fuzzy soft environment. Finally, we used some practical examples to illustrate the validity and superiority of the proposed method by comparing with other existing methods. The graphical interpretation of the explored approaches is also utilized with future directions. [ABSTRACT FROM AUTHOR]

Atanassov's intuitionistic fuzzy set described the uncertainty of real-life events with the help of a membership and a non-membership degree. However, human opinion cannot be restricted to yes or no, but there is some abstinence and refusal degree as well. In such cases, picture fuzzy set is a suitable solution which described the abstinence and refusal grade of human opinion along with membership and non-membership grades. The aim of this paper is to analyse a social network and a wife network using the concept of picture fuzzy graph (PFG). For this purpose, the concept of PFG is proposed and some basic terms are demonstrated including complement, degree and bridges. The main advantage of the proposed PFG is that it describes the uncertainty in any real-life event with the help of four membership degrees where the traditional FG and IFG fail to be applied. The viability of PFG is shown by utilizing the concept in demonstrating two real-life problems including a social network and a Wi-Fi-network. A comparison of PFG with existing notions is established showing its superiority over the existing frameworks. [ABSTRACT FROM AUTHOR]

Plant‐derived natural products are of great interest due to their diversity in modern drug discovery. Sarcococca saligna has been used for the treatment of different diseases. The present study was aimed at isolating phytochemical constituents including Alkaloid‐C (a), Dictyophlebine (b), Sarcovagine‐D (c) and Saracodine (d) Holaphylline (e) from Sarcococca saligna to investigate the anticancer effect of these compounds. These compounds were evaluated for inhibition of aromatase enzyme of breast cancer in assistance by molecular docking simulations to understand molecular interaction between the enzyme and ligands. The IC50 values of compound 1 and 5 were found 138.27 ± 0.01 µl and 12.91 ± 0.01 µl, respectively, and both were found active due to their bulky structures in comparison to the active site of aromatase enzyme. The standard drug exemestane showed potent activity in comparison with the test compounds, having IC50 values of 0.052 ± 0.01 µl. Both compounds showed favorable electrostatic interactions with the active site of aromatase enzyme but the shape and steric bulk of the compounds was the limiting factor in their inhibitory effects. New lead compounds could be generated after extensive modifications guided by computational and experimental tools as a possible anticancer agents by targeting aromatase enzyme. [ABSTRACT FROM AUTHOR]

Recently, Jun et al. have introduced the concept of cubic set as a generalization of the concept of fuzzy set and that of the interval valued fuzzy set. This concept has been widely applied in many circumstances like pattern recognition, decision making etc. So far, no attention has been paid towards graph of cubic set therefore leads us in this manuscript to study the concepts of interval valued bipolar fuzzy graph (IVBFG) and cubic bipolar fuzzy graph (CBFG). Some graph theoretic terms for CBFGs are defined along with the several operations. Illustrative examples are provided to explain the defined terms and several results are discussed. As application, a cubic bipolar fuzzy influence graph in a social group is elaborated. [ABSTRACT FROM AUTHOR]

In this article, a new concept of intuitionistic fuzzy graph of nth type (IFGNT) is proposed as a generalization of intuitionistic fuzzy graphs (IFGs) and intuitionistic fuzzy graphs of second type (IFGST). Some light has also been shed upon the concepts of constant intuitionistic fuzzy graphs of second type (CIFGST) and constant intuitionistic fuzzy graphs of nth type (CIFGNT). Moreover, some basic definitions of and results from IFGNT have been developed, supported with examples. Besides, the advantages of proposed new concept over the existing concepts have been highlighted and a comparative study of new and existing works made. Further, an application of IFGNT has been demonstrated in social networks context. [ABSTRACT FROM AUTHOR]

Our Larson-type microemulsion model for surfactant chains in oil–water solvents leads to long relaxation times as well as, for essential modifications, to a stable peak in the chain-cluster size distribution. Transfer energies for surfactant chains moving to the oil–water interface, and characteristic micelle concentrations (CMC) as a function of chain length are compared with experiment. [ABSTRACT FROM AUTHOR]

In this paper, the concept of linguistic cubic number (LCN) is introduced which further extends the concept of linguistic intuitionistic fuzzy number (LIFN). More specifically, the notions of internal (external) developed and (P-)R-order for LCN are studied. For a given LCN, some basic operational laws, score and accuracy function are proposed. Also, some generalized aggregation operators based on the operational rules are developed and their related properties are investigated. As application, a multi-attribute decision-making (MADM) method is established based in the environment of LCNs and with the help of defined aggregation operators. Finally, an illustrative example is provided to show the effectiveness of the proposed MADM method. [ABSTRACT FROM AUTHOR]

In this paper, we introduced a new concept of single valued neutrosophic graph (SVNG) known as constant single valued neutrosophic graph (CSVNG). Basically, SVNG is a generalization of intuitionistic fuzzy graph (IFG). More specifically, we described and explored somegraph theoretic ideas related to the introduced concepts of CSVNG. An application of CSVNG in a Wi-Fi network system is discussed and a comparison of CSVNG with constant IFG is established showing the worth of the proposed work. Further, several terms like constant function and totally constant function are investigated in the frame-work of CSVNG and their characteristics are studied. [ABSTRACT FROM AUTHOR]

The demand for natural medicines has increased because of their limited adverse effects. The aim of study is to explore the antidiabetic potential of isolated steroidal alkaloid from Sarcococca saligna in streptozotocin induced diabetic rats. To determine the antidiabetic activity of steroidal alkaloids, diabetes was induced in rats by injecting streptozotocin intraperitoneally at a dose of 40 mg/Kg. After a week of STZ injection the treatment were started and the 8th day was considered as the 1st day of treatment and up to four weeks the rats were treated with steroidal alkaloids. Animals were divided into five groups, group 1 considered as a control group by receiving normal saline (1 ml/Kg) twice daily and group 2, 3, 4 were treated with active compound sarcovagine-D, saracodine and holaphylline at the dose of 5 mg/Kg subcutaneously twice a day while group 5 was treated with a standard drug glibenclamide at a dose of 1 mg/Kg/day. The result showed that treated group 2 and 4 reduced the glucose level in blood significantly while group 3 showed moderate glucose reduction. The fructosamine level reduced significantly in treating group 4 from the 2nd week of treatment while group 2 and 3 decreased the level significantly in week 4 in diabetic rats. The treated groups showed gradual decreases the glucose level in 1st and 2nd week of oral glucose tolerance test compared to control group. The group receiving holaphylline (4) and sarcovagine-D (2) showed good improvements in blood lipids while the effect of compound on body weight showed less significant improvement. The present study concluded that steroid alkaloids from isolated Sarcococca saligna possess hypoglycemic effect and improve others diabetes associated complications. Together these finding further research is needed using a range of doses to explore the other possible beneficial effects in diabetes mellitus and its molecular mechanism. [ABSTRACT FROM AUTHOR]

• Novel concepts of interval-valued complex q-rung orthopair fuzzy relations have been defined. • A Hasse diagram for IVCqROFR is introduced with its properties. • The investigation of cybercrime and cybersecurity in the industry of FinTech has been conducted. • The effects of different cybersecurity techniques on different threats in FinTech are analyzed. Modeling the uncertainty has long been a crux for mathematicians which was resolved by the theory of fuzzy sets and logic initiated by Zadeh. Since its introduction, many developments and improvements have been made in the field. This research defines several innovative theories such as the Cartesian product (CP) of interval-valued complex q-rung orthopair fuzzy sets (IVCqROFSs), IVCqROF relations (IVCqROFRs), and their types. After deep analysis, related results and worthwhile properties have been stated. Moreover, a Hasse diagram for IVCqROFR is introduced with its properties. The proposed concepts are capable of modeling a wide range of problems of uncertain nature. The involvement of complex numbers enables these structures to cope with phase-altering problems and multidimensional problems, ultimately making them extremely powerful tools for handling ambiguity. An application has been proposed as an illustration. Since, in modern days, every business and industry is being digitalized, the business and finance departments are no exception. Digital systems have numerous risks and threats. Henceforth, for the first time in the theory of fuzzy logic, cybercrimes and cyber security in the industry of FinTech have been modeled and analyzed through fuzzy mathematics. The effects of different cybersecurity techniques on different threats in FinTech are analyzed by using the proposed methods. Finally, the selection and use of the proposed theories in the analysis of Fintech cybersecurity is justified and explained in contrast to other available competing fuzzy structures in the literature. [ABSTRACT FROM AUTHOR]

Recent work has shown that the distribution of steady state mutations for an asexual "bacteria" model has features similar to that seen in Self-Organized Critical (SOC) sandpile model of Baket al. We investigate this coincidence further and search for "selforganized critical" state for bacteria but instead find that the SOC sandpile critical behavior is very sensitive; critical behavior is destroyed with small perturbations effectively when the absorption of sand is introduced. It is only in the limit when the length of the genome of the bacteria tends to infinity that SOC properties are recovered for the asexual model. [ABSTRACT FROM AUTHOR]

The health organizations around the world are currently facing one of the greatest challenges, to overcome the current global pandemic, COVID-19. It erupted in December 2019, in Wuhan City, China. It spreads rapidly throughout the world within couple of months. In this paper, the data of the COVID-19 have been collected, organized, analyzed and interpreted using the discrete-time model of SIR epidemic model. Moreover, results for several countries from different regions of the world have been obtained. Furthermore, comparative study has been carried out for the countries under consideration. The comparison was performed for the data of different countries on same dates of each month. However, the calculations are carried out for thirteen consecutive weeks, to investigate the rate of spread and the control of the disease in these countries. This guides us to some important concepts like factors favoring the spread of virus and those resisting the spread. Different regions are studied and their data have been evaluated to know which regions are the most effected. This study helps to know the important factors about the behavior of the coronavirus in different environments, such as lockdowns, temperatures, humidity and other restrictions. The proposed concepts and equations can be used to project the upcoming behavior of the pandemic. [ABSTRACT FROM AUTHOR]

Recently, there has been enormous development due to advancements in technology. Industries and enterprises are moving towards a digital system, and the oil and gas industries are no exception. There are several threats and risks in digital systems, which are controlled through cyber-security. For the first time in the theory of fuzzy sets, this research analyzes the relationships between cyber-security and cyber-crimes in the oil and gas sectors. The novel concepts of complex intuitionistic fuzzy relations (CIFRs) are introduced. Moreover, the types of CIFRs are defined and their properties are discussed. In addition, an application is presented that uses the Hasse diagram to make a decision regarding the most suitable cyber-security techniques to implement in an industry. Furthermore, the omnipotence of the proposed methods is explained by a comparative study. [ABSTRACT FROM AUTHOR]

The article "Mathematical analysis of COVID-19 pandemic by using the concept of SIR model" has been retracted by the publisher due to concerns about compromised editorial handling and peer review processes, inappropriate references, and being out of scope for the journal. Authors Harish Garg and Abdul Nasir have not responded to the retraction, while the publisher has been unable to contact authors Naeem Jan and Sami Ullah Khan. Springer Nature, the publisher, remains neutral in this matter. [Extracted from the article]

In this paper, we study some coincidence point and common fixed point theorems in fuzzy metric spaces by using three-self-mappings. We prove the uniqueness of some coincidence point and common fixed point results by using the weak compatibility of three-self-mappings. In support of our results, we present some illustrative examples for the validation of our work. Our results extend and improve many results given in the literature. In addition, we present an application of fuzzy differential equations to support our work. [ABSTRACT FROM AUTHOR]

The key objective of this research article includes the study of some rational type coincidence point and deriving common fixed point (CFP) results for rational type weakly-compatible three self-mappings in fuzzy metric (FM) space. The "triangular property of FM" is used as a fundamental tool. Moreover, some unique coincidence points and CFP theorems were presented for three self-mappings in an FM space under the conditions of rational type weakly-compatible fuzzy-contraction. In addition, some suitable examples are also given. Furthermore, an application of fuzzy differential equations is provided in the aid of the proposed work. Hence, the innovative direction of rational type weakly-compatible fuzzy-contraction with the application of fuzzy differential equations in FM space will certainly play a vital role in the related fields. It has the potential to be extended in any direction with different types of weakly-compatible fuzzy-contraction conditions for self-mappings with different types of differential equations. [ABSTRACT FROM AUTHOR]

In the theory of fuzzy fixed point, many authors have been proved different contractive type fixed point results with different types of applications. In this paper, we establish some new fuzzy cone contractive type unique coupled fixed point theorems (FP-theorems) in fuzzy cone metric spaces (FCM-spaces) by using "the triangular property of fuzzy cone metric" and present illustrative examples to support our main work. In addition, we present a Lebesgue integral type mapping application to get the existence result of a unique coupled FP in FCM-spaces to validate our work. [ABSTRACT FROM AUTHOR]

Fuzzy graphs (FGs) and their generalizations have played an essential role in dealing with real-life problems involving uncertainties. The goal of this article is to show some serious flaws in the existing definitions of several root-level generalized FG structures with the help of some counterexamples. To achieve this, first, we aim to improve the existing definition for interval-valued FG, interval-valued intuitionistic FG and their complements, as these existing definitions are not well-defined; i.e., one can obtain some senseless intervals using the existing definitions. The limitations of the existing definitions and the validity of the new definitions are supported with some examples. It is also observed that the notion of a single-valued neutrosophic graph (SVNG) is not well-defined either. The consequences of the existing definition of SVNG are discussed with the help of examples. A new definition of SVNG is developed, and its improvement is demonstrated with some examples. The definition of an interval-valued neutrosophic graph is also modified due to the shortcomings in the current definition, and the validity of the new definition is proved. An application of proposed work is illustrated through a decision-making problem under the framework of SVNG, and its performance is compared with existing work. [ABSTRACT FROM AUTHOR]

In this paper, we establish some new generalized rational type common fixed point results for compatible three self-mappings in complex-valued b-metric space, in which a one self-map is continuous. In support of our results, we present some illustrative examples to verify the validity of our main work. Moreover, we present the application of two Urysohn integral type equations (UITEs) for the existence of a common solution to support our work. The UITEs are v 1 p = ∫ k 1 k 2 Q 1 p , r , v 1 r d r + ℏ 1 p and v 2 p = ∫ k 1 k 2 Q 2 p , r , v 2 r d r + ℏ 2 p , where p ∈ k 1 , k 2 , v 1 , v 2 , ℏ 1 , ℏ 2 ∈ V , where V = C k 1 , k 2 , ℝ n is the set of all real-valued continuous functions defined on k 1 , k 2 and Q 1 , Q 2 : k 1 , k 2 × k 1 , k 2 × ℝ n ⟶ ℝ n . [ABSTRACT FROM AUTHOR]

Energy storage is a way of storing energy to reduce imbalances between demand and energy production. The ability to store electricity and use it later is one of the keys to reaching large quantities of renewable energy on the grid. There are several methods to store energy such as mechanical, electrical, chemical, electrochemical, and thermal energy. Regarding their operation, storage, and cost, the choice of these energy storage techniques appears to be interesting. This issue becomes very serious when there involves uncertainty. To consider this kind of uncertain information, a picture fuzzy soft set is found to be a more appropriate parameterization tool to deal with imprecise data. Based on the advanced structure of picture fuzzy soft set, here in this article, firstly, we have developed the notions of basic operational laws for picture fuzzy soft numbers. Then based on these developed operational laws, we have established the notions of picture fuzzy soft power average PFS ft PA , weighted picture fuzzy soft power average WPFS ft PA and ordered weighted picture fuzzy soft power average OWPFS ft PA aggregation operators. Moreover, we have introduced the notions for picture fuzzy soft power geometric PFS ft PG , weighted picture fuzzy soft power geometric WPFS ft PG and ordered weighted picture fuzzy soft power geometric OWPFS ft PG aggregation operators. Furthermore, we have established the application of picture fuzzy soft power aggregation operators for the selection of thermal energy storage techniques. For this, we have developed a decision-making approach along with an explanatory example to show the effective use of the developed theory. Furthermore, a comparative analysis of the introduced work shows the advancement of developed notions. [ABSTRACT FROM AUTHOR]

We analyse the fossil data of Benton with and without interpolation schemes. By Fourier transform analysis, we find a frequency dependence of the amplitude of 1/f for the various interpolation schemes used in the past. We illustrate that shuffling the interpolated data changes the spectra only slightly. On the other hand, an identical analysis performed on the raw (uninterpolated) fossil data gives a flat frequency spectrum. We conclude that the 1/f behavior is an artifact of the interpolation schemes. We next introduce a simulation of extinctions driven only by interactions between two trophic levels. Fourier transform analysis of the simulation data shows a frequency dependence of 1/f. When the data are grouped into a form resembling the fossil record the frequency dependence vanishes, giving a flat spectrum. Our simulation produces a frequency spectrum that agrees with the observed fossil record. [ABSTRACT FROM AUTHOR]

Neutrosophic set (NS) is a framework used when the imprecision and uncertainty of an event are described based on three possible aspects, i.e., the membership degree, neutral membership degree and non-membership degree. On the other hand, neutrosophic graphs (NG) are applicable to deal with bulk information events. Furthermore, the incidence graph concept in neutrosophic sets contains a handful of problems like decision-making as well as, social and communication networks. This paper aims to propose the interval-valued neutrosophic sets to incidence graph and represent a new concept, namely interval-valued neutrosophic incidence graph (IVNIG). An IVNIG is a generalization of the concept of single-valued neutrosophic incidence graph (SVNIG). Moreover, some properties related to IVNIG, such as strong edge, strong pair, strong cut pair and neutrosophic incidence cut pair, are also discussed using suitable examples. The defined new concept of IVNIG is applied and investigated on a practical problem of safe root travelling. [ABSTRACT FROM AUTHOR]

Neutrosophic set (NS) is a framework used when the imprecision and uncertainty of an event are described based on three possible aspects, i.e., the membership degree, neutral membership degree and non-membership degree. On the other hand, neutrosophic graphs (NG) are applicable to deal with bulk information events. Furthermore, the incidence graph concept in neutrosophic sets contains a handful of problems like decision-making as well as, social and communication networks. This paper aims to propose the interval-valued neutrosophic sets to incidence graph and represent a new concept, namely interval-valued neutrosophic incidence graph (IVNIG). An IVNIG is a generalization of the concept of single-valued neutrosophic incidence graph (SVNIG). Moreover, some properties related to IVNIG, such as strong edge, strong pair, strong cut pair and neutrosophic incidence cut pair, are also discussed using suitable examples. The defined new concept of IVNIG is applied and investigated on a practical problem of safe root travelling. [ABSTRACT FROM AUTHOR]

The framework of T-spherical fuzzy set is a generalization of fuzzy set, intuitionistic fuzzy set and picture fuzzy set having a great potential of dealing with uncertain events with no limitation. A T-spherical fuzzy framework can deal with phenomena of more than yes or no type; for example, consider the scenario of voting where one's voting interest is not limited to "in favor" or "against" rather there could be some sort of abstinence or refusal degree also. The objective of this paper is to develop some correlation coefficients for T-spherical fuzzy sets due to the non-applicability of correlations of intuitionistic fuzzy sets and picture fuzzy sets in some certain circumstances. The fitness of new correlation coefficients has been discussed, and their generalization is studied with the help of some results. Clustering and multi-attribute decision-making algorithms have been proposed in the environment of T-spherical fuzzy sets. To demonstrate the viability of proposed algorithms and correlation coefficients, two real-life problems including a clustering problem and a multi-attribute decision-making problem have been solved. A comparative study of the newly presented and pre-existing literature is established showing the superiority of proposed work over the existing theory. Some advantages of new correlation coefficients and drawbacks of the pre-existing work are demonstrated with the help of numerical examples. [ABSTRACT FROM AUTHOR]

Human opinion cannot be restricted to yes or no as depicted by conventional fuzzy set (FS) and intuitionistic fuzzy set (IFS) but it can be yes, abstain, no and refusal as explained by picture fuzzy set (PFS). In this article, the concept of spherical fuzzy set (SFS) and T-spherical fuzzy set (T-SFS) is introduced as a generalization of FS, IFS and PFS. The novelty of SFS and T-SFS is shown by examples and graphical comparison with early established concepts. Some operations of SFSs and T-SFSs along with spherical fuzzy relations are defined, and related results are conferred. Medical diagnostics and decision-making problem are discussed in the environment of SFSs and T-SFSs as practical applications. [ABSTRACT FROM AUTHOR]

In this manuscript, two generalizations of fuzzy sets, intuitionistic fuzzy sets and picture fuzzy sets, known as spherical fuzzy sets and T-spherical fuzzy sets, are discussed and a numerical and geometrical comparison among them is established. A T-spherical fuzzy set can model phenomena like voting using four characteristic functions denoting the degree of vote in favor, abstinence, vote in opposition, and refusal with an infinite domain, whereas an intuitionistic fuzzy set can model only phenomena of yes or no types. First, in this manuscript, some similarity measures in the frameworks of intuitionistic fuzzy sets and picture fuzzy sets are discussed. With the help of some numerical results, it is discussed that existing similarity measures have some limitations and could not be applied to problems where information is provided in T-spherical fuzzy environment. Therefore, some new similarity measures in the framework of spherical fuzzy sets and T-spherical fuzzy sets are proposed including cosine similarity measures, grey similarity measures, and set theoretic similarity measures. With the help of some results, it was proved that the proposed similarity measures are a generalization of existing similarity measures. The newly-defined similarity measures were subjected to a well-known problem of building material recognition and the results are discussed. A comparative study of new and existing similarity measures was established and some advantages of the proposed work are discussed. [ABSTRACT FROM AUTHOR]

In this study, we aim to consider a new kind of a set called by a double framed soft fuzzy set, which is convenient to handle the real world applications and to investigate the near rings in the view of this new set. We define some of the elementary set operations of double framed soft fuzzy sets. We propose the notion of double framed soft fuzzy near rings (ideals) with several properties and characteristics. Further, we illustrate the given notions with some examples. [ABSTRACT FROM AUTHOR]

The concept of picture hesitant fuzzy set (PHFS) is a general- ization of picture fuzzy set (PFS) and hesitant fuzzy set (HFS). Such kind of idea can be very helpful in problems where opinions are of more than two types i.e. yes, no, abstinence and refusal. The goal of this manuscript is to introduce the concept of similarity measures for PHFSs as a general- ization of the similarity measures for PFS. We studied the basic concepts of PFSs, HFSs and PHFSs. We proposed some similarity measures for PHFSs such as cosine similarity measure, set-theoretic similarity measure and grey similarity measure for PHFSs. Some weighted similarity mea- sures are also proposed where weight of the attributes is considered. Then these similarity measures for PHFSs are applied to a building material recognition problem. Finally, a comparative study of similarity measures of PHFSs is established with similarity measures of PFSs, HFSs, IFSs and IHFSs and the advantages of new work are studied. [ABSTRACT FROM AUTHOR]

In this work, miniaturised tunable two‐antenna multiple‐input–multiple‐output (MIMO) systems composed of printed F‐slot shaped are developed to operate in the global positioning system (GPS), personal communication system (PCS), distributed control system and Universal Mobile Telecommunications System bands. The two‐element MIMO antenna occupies a volume of 50 × 37.5 × 1.6 mm3, and is printed on an FR4 substrate. Initially, the frequency tunability of the MIMO antennas was verified by lumped capacitors with values between 0.75 to 2.75 pF to achieve a tuning range from 1.55 to 2.07 GHz while the low mutual coupling between the radiators was accomplished by adding an I‐shaped branch to a cut‐away ground plane. The two antennas are then loaded with varactors to simultaneously achieve miniaturisation and tunability. Simulation and measurement results demonstrate the successful implementation of a tunable MIMO with coupling reduction mechanism for a portable handheld wireless transceiver. The channel capacity of the proposed antenna is investigated and found to be close to that of a un‐correlated system with efficient diversity in which the mutual coupling across the full bandwidth was better than −13 dB. Owing to the compact size and ease of manufacture, the proposed antennas can be a promising solution for adaptive MIMO systems in handheld devices. [ABSTRACT FROM AUTHOR]

An asexual set of primitive bacteria is simulated with a bit-string Penna model with a Fermi function for survival. A recent hypothesis by Jan, Stauffer, and Moseley on the evolution of sex from asexual cells as a strategy for trying to escape the effects of deleterious mutations is checked. This strategy is found to provide a successful scenario for the evolution of a stable macroscopic sexual population. [ABSTRACT FROM AUTHOR]

Expressing the measure of uncertainty, in terms of an interval instead of a crisp number, provides improved results in fuzzy mathematics. Several such concepts are established, including the interval-valued fuzzy set, the interval-valued intuitionistic fuzzy set, and the interval-valued picture fuzzy set. The goal of this article is to enhance the T-spherical fuzzy set (TSFS) by introducing the interval-valued TSFS (IVTSFS), which describes the uncertainty measure in terms of the membership, abstinence, non-membership, and the refusal degree. The novelty of the IVTSFS over the pre-existing fuzzy structures is analyzed. The basic operations are proposed for IVTSFSs and their properties are investigated. Two aggregation operators for IVTSFSs are developed, including weighted averaging and weighted geometric operators, and their validity is examined using the induction method. Several consequences of new operators, along with their comparative studies, are elaborated. A multi-attribute decision-making method in the context of IVTSFSs is developed, followed by a brief numerical example where the selection of the best policy, among a list of investment policies of a multinational company, is to be evaluated. The advantages of using the framework of IVTSFSs are described theoretically and numerically, hence showing the limitations of pre-existing aggregation operators. [ABSTRACT FROM AUTHOR]

The objective of this manuscript is to present some new, improved aggregation operators for the T-spherical fuzzy sets, which is an extension of the several existing sets, such as intuitionistic fuzzy sets, picture fuzzy sets, neutrosophic sets, and Pythagorean fuzzy sets. In it, some new, improved operational laws and their corresponding properties are studied. Further, based on these laws, we propose some geometric aggregation operators and study their various relationships. Desirable properties, as well as some special cases of the proposed operators, are studied. Then, based on these proposed operators, we present a decision-making approach to solve the multi-attribute decision-making problems. The reliability of the presented decision-making method is explored with the help of a numerical example and the proposed results are compared with several prevailing studies' results. Finally, the superiority of the proposed approach is explained with a counter example to show the advantages of the proposed work. [ABSTRACT FROM AUTHOR]