Muhammad Akram

• MSc degrees in Math and CS, PhD in Fuzzy Mathematics
• Professor (Full) at University of the Punjab

We introduce the notion of fuzzy ideals in nearrings with respect to a t-norm T and investigate some of their properties. Using T-fuzzy ideals, characterizations of Artinian and Noetherian nearrings are established. Some properties of T-fuzzy ideals of the quotient nearrings are also considered.

We define the Cartesian product, composition, union and join on interval-valued fuzzy graphs and investigate some of their properties. We also introduce the notion of interval-valued fuzzy complete graphs and present some properties of self-complementary and self-weak complementary interval-valued fuzzy complete graphs.

Humanitarian supply chain management plays a crucial role in effectively delivering aid and allocating resources during crises. It involves coordinated logistics, inventory control, and collaboration among stakeholders to ensure timely and ethical support. The integration of artificial intelligence with human judgment enhances logistics efficiency,...

In two-sided matching decision problems, the matching objects with different knowledge, experiences, and cultures provide linguistic assessments using diverse or multi-granular sets with a factor that the information provided is hesitant in nature due to different opinions given by experts. In the proposed approach, the hesitant 2-tuple linguistic...

Soft set theory builds on the idea of a parameterized family of subsets of a universal set, where for each pertinent characteristic, any specific member of the universe either satisfies it or not. The concept of an N-soft set sharpens this model with the aid of multinary parameterized descriptions; that is, N-soft sets categorize the options in ter...

Granulation of a network is crucial for the structural analysis of a network. One of the efficient granulation methodology is provided by rough set theory (RST) whereas graph theory provides different metrics for network analysis. Symmetry and symmetry-breaking in a network provides information about the network dynamics. In this paper, we provide...

Multi-polar fuzzy sets are crucial for capturing and representing diverse opinions or conflicting criteria in decision-making processes with greater flexibility and precision. While, Z-numbers are important for effectively modeling uncertainty by incorporating both the reliability of information and its degree of fuzziness, enhancing decision-makin...

Water is the essence of life, sustaining ecosystems, agriculture, industries, and human well-being. The water waste or contaminated by human activity, such as domestic, industrial or agricultural use make it unsafe for consumption, threatens human health, disrupts ecosystems and can lead to the depletion of clean water resources. It contains harmfu...

Useful decisions are made based on reliable information. The concept of -number involves the issue of reliability of information. Multipolar information is particularly important in scenarios involving multiple attributes in a decision making process. There does not exist a study in the literature that conveys multipolar information with reliabili...

This study pioneers an innovative decision-making framework, integrating interval rough numbers with the elimination and choice translating reality method, enhanced by the level-based weight assessment approach, specifically designed to assess sustainable mining technologies. The proposed model overcomes the limitations of traditional multi-criteri...

The Chinese economy is one of the largest and most dynamic economies in the world. Over the past few decades, China has experienced rapid economic growth from agrarian to industrial powerhouse fueled by manufacturing, exports, and services. However, this rapid growth has also brought about challenges, including environmental issues like water conta...

One significant component of the sharing economy, which is expanding globally, is car sharing. In order to broaden their potential and marketing shares, service suppliers want to build more car sharing stations. In order to address the location selection challenge of car sharing stations, a new model is presented in this study that offers a conveni...

Advanced manufacturing stands as an essential component of the fourth industrial era, where innovative machinery can sense and act autonomously in the production process to give higher and more convenient efficiency. However, there could be certain manufacturing-related possible failures. Identifying the possible failures and assessing their risk a...

Occupational noise is one of the most significant disadvantages of industrialization. The impact of noise pollution on workers results in hearing loss and a variety of other problems. Precautions should be taken to protect workers from the harmful effects of occupational noise. In this study, we propose a multi-criteria group decision-making (MCGDM...

Fuel cells offer a clean energy alternative across various sectors, including transportation and power storage. Hydrogen fuel cells emit only water and heat, eliminating carbon dioxide and other harmful emissions. This makes them a sustainable choice, free from the costs and hazards associated with traditional fuels like diesel or battery acid. Ove...

The priority of all organizations is to provide the best security setup to create awareness among the nation protection and safety. To solve this problem, a variety of multi-criteria decision-making methods are used. Individual expert assessment is a prerequisite for multi-criteria decision-making. The accuracy of the results is affected by the sub...

Decision making approaches depending on the assessments of individual decision makers produce inaccurate results due to the existence of multiple uncertainties. To model intrapersonal uncertainty, interpersonal uncertainty and randomness in decision making assessments, this research study proposes a novel approach by integrating various fuzzy numbe...

One of the most commonly used reliability analysis methods is failure mode and effects analysis, which is very effective at finding, assessing, and addressing potential failure modes in a variety of commercial applications. Its wide-ranging viewpoint facilitates the investigation of potential failures, causes, and effects in designs, products, and...

Group decision making in third-party logistics service selection plays an essential role for improving service quality, increasing efficiency and reducing the net cost. Fuzzy and uncertain linguistic variables are commonly used to represent experts‘rankings in optimization problems. To recognize the limits of human cognition and subjectivity of hum...

Vietnam, a country in Southeast Asia, is anticipated to experience an increase in energy consumption due to the growth of its manufacturing and industrial sectors, which aims to establish Vietnam as the world’s new production hub. Fossil fuels, which are ecologically unfriendly and quickly running out, are now Vietnam’s primary energy source. Due t...

The fourth industrial revolution, in which mechanical appliances can be precisely and automatically handled, depends extensively on intelligent manufacturing. It has the potential to create more productive manufacturing facilities. Still, defects and possible mishaps in the production process affect the workflow, deplete resources, and worsen envir...

This article presents the exact solution of a bipolar fuzzy heat equation based on bipolar fuzzy Fourier transform under generalized Hukuhara partial (gH-p) differentiability. A bipolar fuzzy Fourier transform is defined, and the related key propositions and fundamental characteristics are discussed. Further, a bipolar fuzzy heat equation model is...

The main purpose of this research work is to develop a novel approach for multi-objective optimization within the framework of hesitant Fermatean fuzzy methodology incorporating both, the ratio analysis and the complete multiplicative form techniques, to effectively tackle multi-criteria group decision-making (MCGDM) challenges arising from uncerta...

Shared mobility initiatives offer real possibilities to overcome problems such as traffic congestion, air pollution, and natural resource depletion while uniting city residents in a more connected and vibrant atmosphere. This study outlines four innovative and sustainable urban mobility sharing models: electric vehicle (EV),\documentclass[12pt]{min...

The purpose of this article is to present the Laplacian energy of cubic graphs and cubic directed graphs by analyzing the eigenvalues of the adjacency matrix and the Laplacian matrix. The proposed energy concept is discussed through mathematical and graphical models. Some useful properties related to cubic graph energies are studied, including thei...

The fractional generalized Bagley-Torvik equation (FGB-TE) is a mathematical description of the motion of an immersed plate in a Newtonian fluid. The analytical study of the FGB-TE with uncertain initial conditions and two independent fractional orders is usually complex and difficult. Therefore, it is necessary to develop a proper and effective te...

Incidence graphs are an effective to model interconnected networks with additional vertex-edge interactions. They are widely used to establish modes of operation and controllers to illustrate the influence of one factor on another. The purpose of this paper is to present the concept of directed Pythagorean fuzzy incidence graphs. Physical problems...

In this research article, the credibility distribution is defined as a Pythagorean fuzzy restriction, which serves as an elastic constraint on the possible input states of a variable. This definition relates the credibility theory to the theory of Pythagorean fuzzy sets. The current study first defines Cauchy Pythagorean fuzzy numbers and offers a...

The interactive group decision-making method with dual probabilistic linguistic term sets (DPLTSs) is talked about in this paper. The benefit of choosing DPLTSs is that they take into account both random and stochastic uncertainties at the same time. The DPLTSs are superior to hesitant fuzzy sets (HFSs), probabilistic HFSs, and probabilistic dual H...

Soft set theory, initially introduced through the seminal article “Soft set theory—First results” in 1999, has gained considerable attention in the field of mathematical modeling and decision-making. Despite its growing prominence, a comprehensive survey of soft set theory, encompassing its foundational concepts, developments, and applications, is...

Digitization represents the ultimate expression of globalization that has revolutionized every facet of global existence, enhancing connectivity, financial terms, trade opportunities, and public services. To further broaden or fortify this digital realm and advance global progress, various strategies for multi-criteria group decision-making (MCGDM)...

This research study is dedicated to enhancing the ELECTRE(ELimination and Choice Translating REality methodology), a robust and efficient approach for multi-criteria group decision-making (MCGDM). The basic premise is to inaugurate an upgraded version of the ELECTRE-III technique by integrating 2-tuple linguistic -polar fuzzy data. This integration...

Average edge connectivity is a fundamental metric in classical and fuzzy graph theory. It is a key parameter in evaluating the reliability of a network. Fuzzy average edge connectivity more accurately describes the overall stability of links in the network by providing a more precise measure of the connectivity of the fuzzy graphs. It is particular...

In a universe full of fuzziness and uncertainty, it is an absolute blessing if some information is reliable to some degree. Considering the amount of uncertainty, Zadeh proposed the idea of Z-number, which carries both uncertainty information and the reliability of the information. Uncertain information can be reliably conveyed using Z numbers. On...

The traveling salesman problem is a well-known combinatorial optimization problem. Solving the traveling salesman problem efficiently becomes more challenging when considering uncertainties in the problem parameters, which are prevalent in real-world scenarios. Pythagorean fuzzy uncertain variables combine the strengths of fuzzy logic with the prin...

Pythagorean fuzzy fractional calculus provides a strong framework for modeling and analyzing complicated systems with uncertainty and indeterminacy. The primary focus of this article is to investigate the analytical solution of the Pythagorean fuzzy fractional wave equation using multivariate Pythagorean fuzzy Fourier transform under generalized Hu...

This study presents a new fuzzy fractional epidemiological model to investigate the Middle East respiratory syndrome coronavirus on a complex heterogeneous network using fuzzy Caputo gH-differentiability. The model configuration follows a susceptible-infectious-susceptible (SIS) structure for human and camel populations. The equations for the camel...

The traveling salesman problem is a classic combinatorial optimization challenge with profound implications for various industries. While significant progress has been made in solving traveling salesman problem instances, real-world applications often involve uncertainties that challenge the accuracy and robustness of traditional approaches. Pythag...

This research study keenly employs the ground-breaking theory of ELECTRE method in order to advance the literature with a more competent technique for the frequently implemented and incredibly practical model of spherical fuzzy sets. The eminent characteristics, broader approach and adaptable model of spherical fuzzy set empowers the proposed strat...

Rough set theory is an efficient and flexible tool for the removal of unnecessary or irrelevant attributes present in the evaluation process and interval rough numbers (IRNs) are designed to effectively treat the inherited uncertainty in human assessments in the multi-criteria decision making (MCDM) problems. In the ELECTRE (ELimination and Choice...

Rough set theory has revolutionized data analysis by exploring and extracting valuable insights from imprecise data. The concept of Pythagorean fuzzy sets is a relatively novel mathematical framework in the fuzzy family with a higher ability to deal with imprecision embedded in decision making. Both theories can be combined to develop a broader Pyt...

In this paper, Gaussian Pythagorean fuzzy numbers along with their credibility distribution are defined. The current approach offers a novel method for precise and analytic determination of the inverse credibility distribution based on the credibility measure. To assess uncertainty in project activity time, the Pythagorean fuzzy reasoning might be...

Energy production from the waste is an innovative idea to be implemented that can significantly raise one's energy production capacity via some adaptable waste-to-energy technology. This study ponders over the municipal solid waste management problem to dispose off the waste in a sanitary, beneficial and environmental friendly manner to reduce the...

Fuzzy fractional models have attracted considerable attention because of their comprehensive and broader understanding of real-world problems. Analytical studies of these models are often complex and difficult. Therefore, it is beneficial to develop a suitable and comprehensive technique to solve these models analytically. In this paper, an explici...

Multi-criteria group decision-making (MCGDM) relies heavily on the individual assessments of decision-makers, which can introduce subjectivity and uncertainty that can significantly affect the accuracy of results. Although a great deal of research has been done on managing subjectivity and uncertainty, it is still an uphill battle. Although fuzzy s...

Transportation systems are a key part of sustainable development, and they need to be carefully evaluated to show that they have a strong impact on the target area’s social, environmental, and economic sustainability. For this reason, involving the developed decision support systems helps to shed light on the users’ demand and provide unblemished p...

The homotopy perturbation method is a semi-analytical method for solving linear and nonlinear ordinary/partial differential equations. Since it is extremely difficult to find exact solutions to bipolar fuzzy fractional partial differential equations, any perturbation strategy that satisfies the conditions is acceptable. It is important to emphasize...

Fuzzy differential equations (FDEs) are the general concept of ordinary differential equations. FDE seems to be a natural way to model the propagation of cognitive uncertainty in dynamic environments. This article establishes the characteristics of the strongly generalized Hukuhara differentiability (SGHD)-based fifth-order derivative of the fuzzy-...

Linear programming is a technique widely used in decision-making nowadays. Linear programming in a fuzzy environment makes it even more interesting due to the vagueness and uncertainty of the available resources and variables. Since the market price and profit of certain goods are not known exactly, considering fuzzy variables and parameters in the...

The choice of an optimal airport for local businesses for any traveling purpose due to the complexity of the access to the global market could be considered a group decision-making problem. To cope with this type of problem, the goal of this research is to introduce the power Muirhead mean operators into the environment of a 2-tuple linguistic q-ru...

A mathematical technique called data envelope analysis is used to determine the relative efficiency of decision-making units (DMU) with numerous inputs and outputs. Compared to other DMUs, it determines how efficient the DMU is at delivering a specific level of output based on the amount of input it uses. The transportation problem is a linear prog...

The main objective of this research article is to study the analytical solution of the Pythagorean fuzzy wave equation under the generalized Hukuhara partial differentiability using the Pythagorean fuzzy Fourier sine transform. Some concepts of multivariate Pythagorean fuzzy-valued functions and their gH-partial differentiability along with integra...

An efficient river crossing project (RCP) requires careful planning, front-end design, installation and maintenance. It is important to evaluate different influencing factors and crossing techniques, such as horizontal directional drilling, microtunneling, direct pipe, guided auger boring, open cut, trenchless, trenched, semi-trenched, airborne, an...

A rough set is important for the reduction of attributes of an information system, since it approximates a subset of a universal set based on some binary connection. A Pythagorean fuzzy set, on the other hand, provides specific information about the extent to which a statement is true or false. Both of these theories address various types of uncert...

The integration of rough sets with other algebraic structures is a key approach to study different types of uncertainties simultaneously with a single mathematical approach. The main focus of this research article is to integrate the notions of rough approximations, type-2 soft sets and fuzzy sets in different ways. By computing rough approximation...

Multi-criteria decision analysis with multiple agents provides tools for the research and development of intelligent applications. The solution strategy depends largely on the structure of the data. In this paper we propose a decide-then-merge approach to the problem of multi-agent multi-criteria decision-making when each individual data comes in t...

Interesting insights into uncertain multi‐attribute decision‐making systems have come from the theory of hesitant fuzzy sets. Outputs become more reliable when a decision‐maker is not forced to produce one single assessment in the presence of hesitation. Hesitancy in fuzzy environments grants more flexibility to the decision‐maker, therefore enhanc...

This chapter presents 2-tuple linguistic bipolar fuzzy sets, a new strategy for the modelization uncertainty that incorporates a 2-tuple linguistic term into bipolar fuzzy sets. This model will enable us to provide new insights in decision making. Their operational rules will be used to define the 2-tuple linguistic bipolar fuzzy weighted averaging...

In this chapter, we consider bipolar fuzzy numbers for the expression of bipolar, non-exact data. In order to impose some structure on them, we focus our attention on trapezoidal bipolar fuzzy numbers and the particular case of triangular bipolar fuzzy numbers. However some experts opt for submitting linguistic expressions of their assessments in s...

The previous chapters have been dedicated to extend the scope of two known Multi-criteria decision making (MCDM) techniques, namely, TOPSIS and ELECTRE methods. This chapter deeply explores another well-known technique for solving the same problem, namely, the VIKOR method. In order to analyze the bipolar model from a different viewpoint in this mo...

This chapter aims to deliver a new multiple-criteria decision making model, namely, the bipolar fuzzy ELECTRE II method, by combining the traits of bipolar fuzzy sets with the ELECTRE II technique. The proposed approach can successfully address the imprecision of bipolar fuzzy information. This method examines the strong and weak outranking relatio...

The theory presented in this chapter, incredibly provides a multi-skilled framework for the bipolar fuzzy modeling of inconsistent human interpretations. This remarkable model addresses the bipolar abstruseness of two-dimensional inexact data. Moreover, some fundamental and elementary concepts relevant to the presented theory are introduced. The pr...

A new version of the PROMETHEE method using bipolar fuzzy information is presented in this chapter. Consequently, it is named as the bipolar fuzzy PROMETHEE method. The proposed method accepts the initial assessments via bipolar fuzzy linguistic terms expressed by trapezoidal bipolar fuzzy numbers.

In this chapter, we present various methods for solving multi-criteria decision making problems involving bipolar measurements with positive and negative values. They are attractive because we focus on two fundamental methods in the broad field of multi-criteria decision making, namely, Technique for Order of Preference by Similarity to Ideal Solut...

This monograph examines some theoretical and practical advancements in multicriteria decision making. The primary objective of multicriteria decision making is to establish organized approaches for optimizing feasible options and to provide rationale for designating certain alternatives as "optimal". However, decision-making often occurs in uncerta...

The use of Pythagorean fuzzy N-soft sets (PFNSs) enables the examination of belongingness and non-belongingness of membership degrees, as well as their combinations with N-grading, in the unpredictable nature of individuals. This research aims to enhance our understanding of a popular multi-criteria group decision making (MCGDM) technique, Preferen...

The primary objective of this research article is to present two novel tactical approaches, 2-tuple linguistic Fermatean fuzzy TOPSIS (2TLFF-TOPSIS) and 2-tuple linguistic Fermatean fuzzy ELECTRE I (2TLFF-ELECTRE I), for multi-attribute group decision-making based on 2-tuple linguistic Fermatean fuzzy data. The proposed algorithm exploits the benef...

This study elevates the potential of ELECTRE IV method using the logical backgrounds of fuzzy sets in the proposed fuzzy ELECTRE IV method to capture the water supply problem of Iran. ELECTRE IV method, being an advanced variant of ELECTRE family, operates on the outranking principle to achieve the results using three types of preferences and five...

Fermatean fuzzy sets are a more efficient, flexible, and general model for dealing with uncertainty as compared to Pythagorean fuzzy sets. The multi-objective transportation problem in a Fermatean fuzzy setting is examined in this study. Due to the volatility of competitive marketplaces, transportation costs, supply and demand factors are not alway...

Our aim is to study the adjacency matrix, the Laplacian matrix, the spectra and energy of fuzzy graphs where the diagonal entries are the weights of vertices on these fuzzy graphs. We also characterize these matrices for certain operations on fuzzy graphs and we obtain new results about the spectra on these operations.

Rough soft knowledge is a key approach to understand and model uncertain, vague and not clearly defined situations in a parametric manner. Graphs, hypergraphs and other algebraic structures can be discussed more precisely when upper and lower approximate relations of objects are to be dealt with soft set theory. In this article, the notion of rough...

The current study proposes the concept of 2-tuple linguistic complex q-rung orthopair fuzzy sets (2TLCq-ROFSs) to address the uncertainty of the multi-attribute group decision making (MAGDM) challenge. A 2TLCq-ROFS, characterized by 2-tuple linguistic complex-valued membership and non-membership degrees, is a useful technique for dealing with ineff...

Pythagorean fuzzy set theory is one of the significant tools to deal with real-life problems which are prone to imprecision, partial truth or uncertainty. A Pythagorean fuzzy set reports the degree of truthness as well as falsity of a statement in order to illustrate the imprecision of that statement. Motivated by the resourcefulness of this theory...

The Floyd-Warshall algorithm is frequently used to determine the shortest path between any pair of nodes. It works well for crisp weights, but the problem arises when weights are vague and uncertain. Let us take an example of computer networks, where the chosen path might no longer be appropriate due to rapid changes in network conditions. The opti...

Rough set theory is a key approach to model and apprehend the situations involving uncertainty without additional information and suppositions. Complex fuzzy sets are useful in developing parsimonious models in various fields such as image processing, machine learning and data mining. To manipulate the subjectivity and fluctuation in decision makin...

In recent years, fossil fuel resources have become increasingly rare and caused a variety of problems, with a global impact on economy, society and environment. To tackle this challenge, we must promote the development and diffusion of alternative fuel technologies. The use of cleaner fuels can reduce not only economic cost but also the emission of...

Industrialization plays a significant role in the development and growth of a country. Pakistan is one of the developing countries which entirely depends upon their industrial steel sector to meet their economic growth. Pakistan Steel Mills Corporation (PSMC) is a Pakistan's largest steel industry producing tonnes of steel every year but this produ...

In this study, we aim to develop a method for solving multi-attribute group decision-making (MAGDM) problems with complex q-rung orthopair fuzzy 2-tuple linguistic sets. First, a complex q-rung orthopair fuzzy 2-tuple linguistic set (Cq-ROFTLS) is presented by combining the idea of 2-tuple linguistic set (2TLS) with complex q-rung orthopair fuzzy s...

This paper describes a computational method for solving the nonlinear equations with fuzzy input parameters that we encounter in engineering system analysis. In addition to discussing the existence of solutions, the definition and formalization of numerical solutions is based on a new fuzzy computation operation as a transmission average. Error ana...

Every real-world physical phenomena is inherently based on uncertainty and vagueness. There is a frequent need of a useful tool that can handle the uncertainty, solve and explain the results one encounters in the world of vagueness. Pythagorean fuzzy set introduced by Yager may model the uncertainty with its membership and non-membership grades, ef...

The 2-tuple linguistic Fermatean fuzzy set is an effective tool that combines the advantages of the reliable 2-tuple linguistic model with Fermatean fuzzy set. We aim to develop novel decision-making techniques based on 2TLFFS that can handle the situations in which linguistic labels are assigned to given data. The main objective of this study is t...

The digitalization of the traditional technologies have facilitated humans globally as these technologies are not only time saving, modern, environment friendly but are economic as well. This study is concerned with the digitalization of the public transportation system in Istanbul to reduce the environmental pollution that is a big cause of differ...

The current study is mainly devoted to explore and extend the measurement and ranking of alternatives according to the compromise solution under the background of 2-tuple linguistic-rung picture fuzzy sets. The capability of-rung picture fuzzy sets to accommodate a broad range of information, and the salient features of 2-tuple linguistic term sets...

Many scholars have been challenged by multi-attribute group decision-making problems that have stimulated the appearance of increasingly general models. Pythagorean fuzzy sets were a reaction by Yager who in 2013, suggested this model to improve the performance of intuitionistic fuzzy sets. Another hybrid model-soft expert sets-deals with uncertain...

A rough set approximates a subset of a universal set on the basis of some binary relation and is significant for the reduction of attributes of an information system. On the other hand, a Pythagorean fuzzy set provides information about the extent of truthness and falsity of a statement. Both these theories deal with different forms of uncertainty...

Some problems in science and technology are modeled using ambiguous, imprecise, or lacking contextual data. In the modeling of some real-world problems, differential equations often involve multi-agent, multi-index, multi-objective, multi-attribute, multi-polar information or uncertainty, rather than single bits. These types of differentials are no...

The preference ranking organization method for enrichment evaluation (PROMETHEE) technique is a comprehensive and efficient multi-criteria decision-making (MCDM) method. This research study is devoted to establishing an improved version of the PROMETHEE approach based on 2-tuple linguistic Fermatean fuzzy sets (2TLFFS) to address the MCDM problems...

The advent of Yager’s generalized orthopair fuzzy sets (also called q-rung orthopair fuzzy sets) has brought more possibilities to accomplish the challenging task of modelling uncertainties. Compared with Pythagorean fuzzy sets and intuitionist fuzzy sets, q-rung orthopair fuzzy sets are more general in theory and more powerful in practice. Neverth...

Connectivity is among the most essential concerns in graph theory and its applications. We consider this issue in a framework that stems from the combination of m-polar fuzzy set theory with graphs. We introduce two measurements of connectedness of m-polar fuzzy graphs that we call their connectivity and average connectivity indices. Examples are g...