Naeem Jan

• Ph.D Mathematics
• Researcher at National University of Transportation

The aim of this study is to develop new and efficient theories for handling complex and unreliable data in real-world scenarios. The proposed approach integrates two distinct theories: the Bipolar Complex Fuzzy Set (BCFS) and the Soft Set (SS), resulting in a novel and superior method compared to existing solutions. Furthermore, the value of big da...

This study introduces the Complex T-Spherical Fuzzy Soft Set (CTSFSS), a novel and practical model for representing two-dimensional ambiguous information. This is achieved by integrating the Complex T-Spherical Fuzzy Set (CTSFS) with the Soft Set (SS). The development of the CTSFSS theory is motivated by the absence of neutral membership in complex...

The goal of this study is to provide a framework for a novel concept, which is highly effective at expressing ambiguous information in two dimensions. As a result, of the absence of a neutral degree in interval-valued complex Pythagorean fuzzy sets, we developed the theory of interval-valued complex spherical fuzzy sets. Moreover, a network securit...

The major objective of this study is to create innovative and useful concepts to address challenging real-world decision-making issues. The assessment of the importance of a specific element in a process could be always important, but regarding the importance of the operating system (OS), in a computer system, is critical due to its pivotal role in...

The goal of this paper is to present novel concepts and effective theories for the ability to accurately represent difficult and ambiguous information in real-life problems. In order to accomplish this goal, this paper investigated the original idea of bipolar complex picture fuzzy soft set (BCPFSS), which combination of two distinct theories known...

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 o...

Generative adversarial networks Uncertainty Deep learning Machine learning Complex picture fuzzy soft set Complex picture fuzzy soft relations a b s t r a c t Generative Adversarial Networks (GANs) are the models that generate data samples from the statistical distribution of the data. It is one of the most well-known branches of machine learning a...

Today robotics technology will increase economic growth and productivity and create new career opportunities for many people worldwide. Robotics is a branch of study concerned with the creation of robots and automation, and robotics is a programmable machine that can fulfill a task. In this paper, we want to evaluate the novel concept of bipolar co...

Dear Colleagues, We are delighted to inform you of the release of a new Special Issue in the open-access journal Mathematics (IF 2.592). The issue is entitled "Recent Advances in Fuzzy Deep Learning for Uncertain Medicine Data" and is currently accepting submissions for publication. Prof. Dr. Jeonghwan Gwak and Dr. Naeem Jan have been appointed as...

In the last few years, intelligent industrial systems and consumer electronics are being developed extensively and broadly. Fuzzy logic and fuzzy techniques that integrate these approaches are recognized as effective ways to realize such intelligent functions. These intelligent systems rely on fuzzy control techniques i.e., common sense rules to de...

The utilization of energy (EU) encompasses technologies aimed at discovering more effective methods for using electricity across various sectors, including residential, commercial, industrial, and transportation. Energy is an integral aspect of modern society and a driving force behind many processes in the universe. This paper aims to introduce a...

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 reach large quantities of renewable energy on the grid. There are several methods to store energy such as mechanical, electrical, chemical, electrochemical, and thermal energy....

Artificial neural network is revolutionizing business and everyday life, bringing us to the next level in artificial intelligence. It has a unique ability to extract meaning from complex data to find patterns and detect trends that are too convoluted for the human brain. This paper analyzes the artificial neural network impact on different computat...

Artificial neural network is revolutionizing business and everyday life, bringing us to the next level in artificial intelligence. It has a unique ability to extract meaning from complex data to find patterns and detect trends that are too convoluted for the human brain. This paper analyzes the artificial neural network impact on different computat...

The word sustainable or green supply chain refers to the concept of incorporating sustainable environmental procedures into the traditional supply chain. Green supply chain management gives a chance to revise procedures, materials, and operational ideas. Choosing the fuzziness of assessing data and the spiritual situations of experts in the decisio...

Data clustering is an instrumental tool in the area of energy management resources, marketing, and business. Clustering helps to increase productivity, facilitate decision-making, and generate new business opportunities. They have faced many difficulties while dealing with imprecise and vague information, such as decision-making issues. The soft se...

A blockchain is a valuable and proficient type of digital ledger technology that involves of expanding list of records, called blocks, that are strongly connected simultaneously using cryptography. Further, complex Pythagorean fuzzy sets (CPFSs) are the generalized form of the intuitionistic fuzzy sets (IFSs), Pythagorean fuzzy sets (PyFSs), and co...

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...

Oil is a highly demanded worldwide product as oil prices can have a major economic and social impact. There are many factors affecting oil prices, but little is known about which factor mostly influenced oil prices. To understand what caused the fluctuation of oil prices, the investigation leading up to the identification of the factors must be con...

The prosperity of a country is defined by its economic structure. The exports play an important role in the economy of a country and its development. Thus, this research mainly focuses on the said subjects. Furthermore, some innovative structures are developed as the generalizations of fuzzy set theory which were successfully applied to explain the...

Over the past 20 years, the emergence of social media and its developments have rapidly changed communication and information technology. Social media plays a necessary part in accessing information and communication. In spite of its many advantages, users have also been facing many threats on social media platforms. This research aims to analyze a...

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. Observin...

Artificial intelligence (AI) has made the life more efficient and powered many programs and services. AI is progressing rapidly, and the future is arriving faster than the predictions. Soon, AI will be more proficient as compared to humans in all aspects. Many industries are using AI for the analysis of data to find the best methods for investments...

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 organiza...

Transportation is among the more vital economic activities for a business and our daily life actions. At present, transport is one of the key branches playing a crucial role in the development of the economy. Transportation decision-making looks for ways to solve current and anticipated transportation problems while avoiding future problems. An int...

Picture fuzzy graph (PFG) is a useful tool in fuzzy graph theory that can be used to model a variety of real-world problems involving uncertainty caused by unknown, changing, and indeterminate data. PFG might be more fruitful at solving confusing problems than fuzzy graph (FG) and intuitionistic fuzzy graph (IFG). In this study, some interesting pr...

The involution of complex numbers in the theory of fuzzy sets (FSs) opened the gates for many new ideas. In a complex fuzzy set (CFS), the level of membership attains values from the unit circle in a complex plane. Since the level of membership is a complex number, it is expressed in a form consisting of two parts called the amplitude term and the...

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 dis...

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 validati...

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 theore...

The paper aims to present the concept of power aggregation operators for the T-spherical fuzzy sets (T-SFSs). T-SFS is a powerful concept, with four membership functions denoting membership, abstinence, non-membership and refusal degree, to deal with the uncertain information as compared to other existing fuzzy sets. On the other hand, the relation...

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 re...

Technology is rapidly advancing and every aspect of life is being digitalized. Since technology has made life much better and easier, so organizations, such as businesses, industries, companies and educational institutes, etc., are using it. Despite the many benefits of technology, several risks and serious threats, called cyberattacks, are associa...

In this paper, we establish the new concept of rational coupled fuzzy cone contraction mapping in fuzzy cone metric spaces and prove some unique rational-type coupled fixed-point theorems in the framework of fuzzy cone metric spaces by using “the triangular property of fuzzy cone metric.” To ensure the existence of our results, we present some illu...

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...

The concept of fuzzy graph (FG) and its generalized forms have been developed to cope with several real-life problems having some sort of imprecision like networking problems, decision making, shortest path problems etc. This paper is based on some developments in generalization of FG theory to deal with situations where imprecision is characterize...

In this paper, we introduce the new concept of coupled fixed point (FP) results depending on another function in fuzzy cone metric spaces (FCM-spaces) and prove some unique coupled FP theorems under the modified contractive type conditions by using “the triangular property of fuzzy cone metric”. Another function is a self-mapping continuous, one-on...

Neutrosophic set (NS) is a framework used when the imprecision and uncertainty of an event are described based on three possible aspects, ie, 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 co...

Fuzzy set theory and fuzzy logics are the powerful mathematical tools to model the imprecision and vagueness. In this research, the novel concept of complex Pythagorean fuzzy relation (CPFR) is introduced. Furthermore, the types of CPFRs are explained with appropriate examples such as CPF composite relation, CPF equivalence relation, CPF order rela...

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 Ur...

The theory developed in this article is based on graphs of cubic intuitionistic fuzzy sets (CIFS) called cubic intuitionistic fuzzy graphs (CIFGs). This graph generalizes the structures of fuzzy graph (FG), intuitionistic fuzzy graph (IFG), and interval-valued fuzzy graph (IVFG). Moreover, several associated concepts are established for CIFG, such...

Fuzzy set theory resolved the crux of modeling uncertainty, vagueness, and imprecision. Many researchers have contributed to the development of the theory. This paper intends to define the innovative concept of the interval valued complex fuzzy relations (IVCFRs) using the proposed Cartesian product of two interval valued complex fuzzy sets (IVCFSs...

Fuzzy sets and fuzzy logics are used to model events with imprecise, incomplete, and uncertain information. Researchers have developed numerous methods and techniques to cope with fuzziness or uncertainty. This research intends to introduce the novel concepts of complex neutrosophic relations (CNRs) and its types based on the idea of complex neutro...

Uncertainty is the unavoidable part of the life. In almost all circumstances, we regularly find ourselves in a state of uncertainty. Several reasons can lead to uncertainty, such as randomness, vagueness and rough knowledge. Fuzzy set (FS) theory deals with these kinds of information. Many generalizations had been made in the theory of FSs, such as...

Neutrosophic graph (NG) is a powerful tool in graph theory, which is capable of modeling many real-life problems with uncertainty due to unclear, varying, and indeterminate information. Meanwhile, the fuzzy graphs (FGs) and intuitionistic fuzzy graphs (IFGs) may not handle these problems as efficiently as NGs. It is difficult to model uncertainty d...

Soft set theory was 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 pictur...

The recent emerging advancements in the domain of the fuzzy sets are the framework of the T-spherical fuzzy set (TSFS) and interval valued T-spherical fuzzy set (IVTSFS). Keeping in view the promising significance of the latest research trend in the fuzzy sets and the enabling impact of IVTSFS, we proposed a novel framework for decision assembly us...

Atanassov’s intuitionistic fuzzy set (IFS) 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 (PFS) is a suitable solutioin which described the absti...

In this paper, we propose some developments in fuzzy graph theory. An original notion of a T-spherical fuzzy graph is presented as a commonality of fuzzy graph, an intuitionistic fuzzy graph and a picture fuzzy graph. The originality, the imperativeness and the importance of this notion is discussed by showing some results, giving examples and grap...

Recently, Yager has established that the notion of q-rung orthopair fuzzy set (q-ROFS) is more accomplished than pythagorean fuzzy set (PyFS) and intuitionistic fuzzy set (IFS) to cope with awkward and complicated information in real decision theory. This notion works with yes-, no- and refusal-type fuzzy information. The constraint of q-ROFS is th...

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 inter...

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...

Pythagorean fuzzy set (PyFS) is a generalized fuzzy structure that copes with imprecisions of real life accurately and with a larger domain. The aim of this manuscript is to develop the notion of graph for newly established concept of interval-valued PyFS (IVPyFS). We introduced the concept of interval-valued Pythagorean fuzzy graphs (IVPyFGs) and...

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 ma...

The concept of complex fuzzy set (CFS) and complex intuitionistic fuzzy set (CIFS) is two recent developments in the field of fuzzy set (FS) theory. The significance of these concepts lies in the fact that these concepts assigned membership grades from unit circle in plane, i.e., in the form of a complex number instead from [0, 1] interval. CFS can...

The ideas of q-rung ortho pair fuzzy set (q-ROPFS) and interval valued q-rung ortho pair fuzzy set (IVq-ROPFS) are two major recent developments in the field of fuzzy set theory. A q-ROPFS and IVq-ROPFS improved the limited structures of Pythagorean fuzzy set (PyFS), intuitionistic fuzzy set (IFS) as well as fuzzy set (FS) by improving the conditio...

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...

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. Als...

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 some graph theoretic ideas related to the introduced concepts of CSVNG. An application...

In this work, we proposed the theory of picture hesitant fuzzy set (PHFS) as a generalization of picture fuzzy set (PFS) and hesitant fuzzy set (HFS). Some basic operations on PHFSs have been developed and their results are studied. These aggregation operators included picture hesitant fuzzy weighted averaging (PHFWA) operator, picture hesitant fuz...

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...

The aim of this article is to develop some distance measures for newly defined framework of picture hesitant fuzzy set (PHFS). A PHFS is a picture fuzzy set (PFS) having membership, abstinence and non-membership grades in the form of hesitant fuzzy numbers (HFNs). These distance measures include generalized picture hesitant distance measure, genera...

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...

T-spherical fuzzy sets (T-SFSs) and spherical fuzzy sets (SFSs) are the generalizations of fuzzy sets (FSs), intuitionistic fuzzy set (IFS) and picture fuzzy sets (PFSs). This manuscript is a contribution to the area of SFSs and T-SFSs. In this manuscript, some properties of aggregation operators for SFSs and T-SFSs are discussed and some ordered w...

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 n...

: The aim of this paper is to develop a novel clustering algorithm in the environment of picture fuzzy graph. The proposed clustering algorithm is an improved version of clustering algorithms of fuzzy (resp. intuitionistic fuzzy) graph. The paper thoroughly investigated the existing clustering algorithms proposed in the framework of intuitionistic...

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 propertie...

In this manuscript, a novel structure of bipolar-valued hesitant fuzzy set (BPVHFS) is proposed as a generalization of fuzzy set (FS). The basic set theoretic operations of BPVHFSs are defined and their related results are studied. Based on the basic operations, some aggregation operators for BPVHFSs are developed and their fitness is verified usin...

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 fuz...

In this article, we give some basic definitions related to picture fuzzy graphs and we explore several properties of these fuzzy graphs. Moreover, the operations union, join, Cartesian product and composition of picture fuzzy graphs and their properties are also studied.

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 th...

his article is based on Einstein operations for bipolar-valued hesitant fuzzy sets (BVHFSs). We extend the concept of Einstein operators for BVHFSs by defining bipolar-valued hesitant fuzzy Einstein weighted averaging (BPVHFEWA) operators and weighted geometric (BPVHFEWG) operators. Similarly, we define ordered weighted averaging operators and hybr...