Dr. Wajid Ali is a Lecturer (VFM) at Air University Islamabad and completed his Ph.D. in Mathematics in March 2024. His doctoral research focused on generalizations of fuzzy sets, rough sets, and three-way decision models, with strong applications in medical diagnosis, investment decision-making, sustainable systems, and data classification. He has authored 25+ publications in reputable SCI/Scopus-indexed journals, reflecting deep expertise in fuzzy algebra, rough set theory, and advanced decision-making algorithms. He also contributed to an HEC-funded project on developing Urdu Sign Language gloves for speech conversion to support mute individuals. His research interests include Fuzzy Sets and Their Extensions, Rough Sets and Decision-Theoretic Rough Sets, Three-Way and Multi-Granulation Decision Models, Artificial Intelligence and Machine Learning, Deep Learning and Computer Vision, Reinforcement Learning & Autonomous Navigation, and Graph Theory and Intelligent Systems. He has strong practical experience with Python, MATLAB, Neo4j, and Excel, and is passionate about building intelligent, application-oriented solutions for complex, uncertain environments.
He can be contacted at email: wajidali00258@gmail.com
His research interests include Fuzzy Sets and Their Extensions Rough Sets and Decision-Theoretic Rough Sets Three-Way and Multi-Granulation Decision Models Artificial Intelligence and Machine Learning Deep Learning and Computer Vision Reinforcement Learning & Autonomous Navigation and Graph Theory and Intelligent Systems. He has strong practical experience with Python MATLAB Neo4j and Excel and is passionate about building intelligent application-oriented solutions for complex uncertain environments.
Intuitionistic hesitant fuzzy set (IHFS) is a mixture of two separated notions called intuitionistic fuzzy set (IFS) and hesitant fuzzy set (HFS), as an important technique to cope with uncertain and awkward information in realistic decision issues. IHFS contains the grades of truth and falsity in the form of the subset of the unit interval. The notion of IHFS was defined by many scholars with different conditions, which contain several weaknesses. Here, keeping in view the problems of already defined IHFSs, we will define IHFS in another way so that it becomes compatible with other existing notions. To examine the interrelationship between any numbers of IHFSs, we combined the notions of power averaging (PA) operators and power geometric (PG) operators with IHFSs to present the idea of intuitionistic hesitant fuzzy PA (IHFPA) operators, intuitionistic hesitant fuzzy PG (IHFPG) operators, intuitionistic hesitant fuzzy power weighted average (IHFPWA) operators, intuitionistic hesitant fuzzy power ordered weighted average (IHFPOWA) operators, intuitionistic hesitant fuzzy power ordered weighted geometric (IHFPOWG) operators, intuitionistic hesitant fuzzy power hybrid average (IHFPHA) operators, intuitionistic hesitant fuzzy power hybrid geometric (IHFPHG) operators and examined as well their fundamental properties. Some special cases of the explored work are also discovered. Additionally, the similarity measures based on IHFSs are presented and their advantages are discussed along examples. Furthermore, we initiated a new approach to multiple attribute decision making (MADM) problem applying suggested operators and a mathematical model is solved to develop an approach and to establish its common sense and adequacy. Advantages, comparative analysis, and graphical representation of the presented work are elaborated to show the reliability and effectiveness of the presented works.
The intuitionistic hesitant fuzzy set (IHFS) is an enriched version of hesitant fuzzy sets (HFSs) that can cover both fuzzy sets (FSs) and intuitionistic fuzzy sets (IFSs). By assigning membership and non-membership grades as subsets of [0, 1], the IHFS can model and handle situations more proficiently. Another related theory is the theory of set pair analysis (SPA), which considers both certainties and uncertainties as a cohesive system and represents them from three aspects: identity, discrepancy, and contrary. In this article, we explore the suitability of combining the IHFS and SPA theories in multi-attribute decision making (MADM) and present the hybrid model named intuitionistic hesitant fuzzy connection number set (IHCS). To facilitate the design of a novel MADM algorithm, we first develop several averaging and geometric aggregation operators on IHCS. Finally, we highlight the benefits of our proposed work, including a comparative examination of the recommended models with a few current models to demonstrate the practicality of an ideal decision in practice. Additionally, we provide a graphical interpretation of the devised attempt to exhibit the consistency and efficiency of our approach.
For choosing the optimal option for multiple issues, the multiattribute decision-making (MADM) technique within a Fermatean fuzzy environment is a well-known and significant method. This paper presents a novel superiority inferiority ranking (SIR) approach for Fermatean fuzzy sets in group decision-making using multicriteria to reduce investment risk. This approach aims to evaluate the strategies for selecting the optimal investment company. The SIR method is depicted, and its effectiveness in decision-making is explored. In this manuscript, we develop new types of Aczel–Alsina operations on the Fermatean fuzzy environment and Fermatean Fuzzy Aczel–Alsina (FF-AA) average aggregation operators, including their properties such as idempotency, monotonicity, and boundedness. Further, we introduce a Fermatean fuzzy Aczel–Alsina weighted average closeness coefficient (FF-AA-WA-CC) aggregation operator (AO) based on the closeness coefficient for MAGDM issues. By utilizing the proposed technique, we solve a numerical example of an MAGDM problem. The results show that this approach is accurate and practical, and consistent with a realistic investment circumstance. A demonstration was created to emphasize the significance and credibility of this approach and assess its validity by comparing its outcomes with the established methods.
Intuitionistic fuzzy information is a potent tool for medical diagnosis applications as it can represent imprecise and uncertain data. However, making decisions based on this information can be challenging due to its inherent ambiguity. To overcome this, power aggregation operators can effectively combine various sources of information, including expert opinions and patient data, to arrive at a more accurate diagnosis. The timely and accurate diagnosis of medical conditions is crucial for determining the appropriate treatment plans and improving patient outcomes. In this paper, we developed a novel approach for the three-way decision model by utilizing decision-theoretic rough sets and power aggregation operators. The decision-theoretic rough set approach is essential in medical diagnosis as it can manage vague and uncertain data. The redesign of the model using interval-valued classes for intuitionistic fuzzy information further improved the accuracy of the diagnoses. The intuitionistic fuzzy power weighted average (IFPWA) and intuitionistic fuzzy power weighted geometric (IFPWG) aggregation operators are used to aggregate the attribute values of the information system. The established operators are used to combine information within the intuitionistic fuzzy information system. The outcomes of various alternatives are then transformed into interval-valued classes through discretization. Bayesian decision rules, incorporating expected loss factors, are subsequently generated based on this foundation. This approach helps in effectively combining various sources of information to arrive at more accurate diagnoses. The proposed approach is validated through a medical case study where the participants are classified into three different regions based on their symptoms. In conclusion, the decision-theoretic rough set approach, along with power aggregation operators, can effectively manage vague and uncertain information in medical diagnosis applications. The proposed approach can lead to timely and accurate diagnoses, thereby improving patient outcomes.
In this study, a novel Pythagorean fuzzy aggregation operator is presented by combining the concepts of Aczel–Alsina () T‐norm and T‐conorm operations for multiple attribute group decision‐making (MAGDM) challenge for the superiority and inferiority ranking (SIR) approach. This approach has many advantages in solving real‐life problems. In this study, the superiority and inferiority ranking method is illustrated and showed the effectiveness for decision makers by using multicriteria. The Aczel–Alsina aggregation operators on interval‐valued IFSs, hesitant fuzzy sets (HFSs), Pythagorean fuzzy sets (PFSs), and T‐spherical fuzzy sets (TSFSs) for multiple attribute decision‐making (MADM) issues have been proposed in the literature. In addition, we propose a Pythagorean fuzzy Aczel–Alsina weighted average closeness coefficient () aggregation operator on the basis of the closeness coefficient for MAGDM challenges. To highlight the relevancy and authenticity of this approach and measure its validity, we conducted a comparative analysis with the method already in vogue.
<abstract> <p>An intuitionistic hesitant fuzzy set is an extension of the fuzzy set which deals with uncertain information and vague environments. Multiple-attribute decision-making problems (MADM) are one of the emerging topics and an aggregation operator plays a vital role in the aggregate of different preferences to a single number. The Aczel-Alsina norm operations are significant terms that handle the impreciseness and undetermined data. In this paper, we build some novel aggregation operators for the different pairs of the intuitionistic hesitant fuzzy sets (IHFSs), namely as Aczel-Alsina average and geometric operators. Several characteristics of the proposed operators are also described in detail. Based on these operators, a multi-attribute decision-making algorithm is stated to solve the decision-making problems. A numerical example has been taken to display and validate the approach. A feasibility and comparative analysis with existing studies are performed to show its superiority.</p> </abstract>
In today’s fast-paced and dynamic business environment, investment decision making is becoming increasingly complex due to the inherent uncertainty and ambiguity of the financial data. Traditional decision-making models that rely on crisp and precise data are no longer sufficient to address these challenges. Fuzzy logic-based models that can handle uncertain and imprecise data have become popular in recent years. However, they still face limitations when dealing with complex, multi-criteria decision-making problems. To overcome these limitations, in this paper, we propose a novel three-way group decision model that incorporates decision-theoretic rough sets and intuitionistic hesitant fuzzy sets to provide a more robust and accurate decision-making approach for selecting an investment policy. The decision-theoretic rough set theory is used to reduce the information redundancy and inconsistency in the group decision-making process. The intuitionistic hesitant fuzzy sets allow the decision makers to express their degrees of hesitancy in making a decision, which is not possible in traditional fuzzy sets. To combine the group opinions, we introduce novel aggregation operators under intuitionistic hesitant fuzzy sets (IHFSs), including the IHF Aczel-Alsina average (IHFAAA) operator, the IHF Aczel-Alsina weighted average (IHFAAWAϣ) operator, the IHF Aczel-Alsina ordered weighted average (IHFAAOWAϣ) operator, and the IHF Aczel-Alsina hybrid average (IHFAAHAϣ) operator. These operators have desirable properties such as idempotency, boundedness, and monotonicity, which are essential for a reliable decision-making process. A mathematical model is presented as a case study to evaluate the effectiveness of the proposed model in selecting an investment policy. The results show that the proposed model is effective and provides more accurate investment policy recommendations compared to existing methods. This research can help investors and financial analysts in making better decisions and achieving their investment goals.
In the realm of medical diagnosis, intuitionistic fuzzy data serves as a valuable tool for representing information that is uncertain and imprecise. Nevertheless, decision-making based on this kind of knowledge can be quite challenging due to the inherent vagueness of the data. To address this issue, we employ power aggregation operators, which prove effective in combining several sources of data, such as expert thoughts and patient information. This allows for a more correct diagnosis; a particularly crucial aspect of medical practice where precise and timely diagnoses can significantly impact medication policy and patient results. In our research, we introduce a novel methodology to the three-way decision idea. Initially, we revamp the three-way decision model using rough set theory and incorporate interval-valued classes to handle intuitionistic fuzzy data. Secondly, we explore the use of intuitionistic fuzzy power weighted and intuitionistic fuzzy power weighted geometric aggregation operators to consolidate attribute values within the data system. Furthermore, we present a case study in the medical field to exhibit the validity and efficiency of our offered technique. This innovative method enables us to classify participants into three distinct zones based on their symptoms. The manuscript concludes with a summary of key points provided by the authors.
The intuitionistic hesitant fuzzy set is a significant extension of the intuitionistic fuzzy set, specifically designed to address uncertain information in decision-making challenges. Aggregation operators play a fundamental role in combining intuitionistic hesitant fuzzy numbers into a unified component. This study aims to introduce two novel approaches. Firstly, we propose a three-way model for investors in the business domain, which utilizes interval-valued equivalence classes under the framework of intuitionistic hesitant fuzzy information. Secondly, we present a multiple-attribute decision-making (MADM) method using various aggregation operators for intuitionistic hesitant fuzzy sets (IHFSs). These operators include the IHF Aczel–Alsina average (IHFAAA) operator, the IHF Aczel–Alsina weighted average (IHFAAWAϣ) operator, and the IHF Aczel–Alsina ordered weighted average (IHFAAOWAϣ) operator and the IHF Aczel–Alsina hybrid average (IHFAAHAϣ) operators. We demonstrate the properties of idempotency, boundedness, and monotonicity for these newly established aggregation operators. Additionally, we provide a detailed technique for three-way decision-making using intuitionistic hesitant fuzzy Aczel–Alsina aggregation operators. Furthermore, we present a numerical case analysis to illustrate the pertinency and authority of the esteblished model for investment in business. In conclusion, we highlight that the developed approach is highly suitable for investment selection policies, and we anticipate its extension to other fuzzy information domains.
Q-rung orthopair fuzzy sets have been proven to be highly effective at handling uncertain data and have gained importance in decision-making processes. Torra's hesitant fuzzy model, on the other hand, offers a more generalized approach to fuzzy sets. Both of these frameworks have demonstrated their efficiency in decision algorithms, with numerous scholars contributing established theories to this research domain. In this paper, recognizing the significance of these frameworks, we amalgamated their principles to create a novel model known as Q-rung orthopair hesitant fuzzy sets. Additionally, we undertook an exploration of Aczel-Alsina aggregation operators within this innovative context. This exploration resulted in the development of a series of aggregation operators, including Q-rung orthopair hesitant fuzzy Aczel-Alsina weighted average, Q-rung orthopair hesitant fuzzy Aczel-Alsina ordered weighted average, and Q-rung orthopair hesitant fuzzy Aczel-Alsina hybrid weighted average operators. Our research also involved a detailed analysis of the effects of two crucial parameters: λ, associated with Aczel-Alsina aggregation operators, and N, related to Q-rung orthopair hesitant fuzzy sets. These parameter variations were shown to have a profound impact on the ranking of alternatives, as visually depicted in the paper. Furthermore, we delved into the realm of Wireless Sensor Networks (WSN), a prominent and emerging network technology. Our paper comprehensively explored how our proposed model could be applied in the context of WSNs, particularly in the context of selecting the optimal gateway node, which holds significant importance for companies operating in this domain. In conclusion, we wrapped up the paper with the authors' suggestions and a comprehensive summary of our findings.
The Decision-Theoretic Rough Set model stands as a compelling advancement in the realm of rough sets, offering a broader scope of applicability. This approach, deeply rooted in Bayesian theory, contributes significantly to delineating regions of minimal risk. Within the Decision-Theoretic Rough Set paradigm, the universal set undergoes a tripartite division, where distinct regions emerge and losses are intelligently distributed through the utilization of membership functions. This research endeavors to present an enhanced and more encompassing iteration of the Decision-Theoretic Rough Set framework. Our work culminates in the creation of the Generalized Intuitionistic Decision-Theoretic Rough Set (GI-DTRS), a fusion that melds the principles of Decision-Theoretic Rough Sets and intuitionistic fuzzy sets. Notably, this synthesis bridges the gaps that exist within the conventional approach. The innovation lies in the incorporation of an error function tailored to the hesitancy grade inherent in intuitionistic fuzzy sets. This integration harmonizes seamlessly with the contours of the membership function. Furthermore, our methodology deviates from established norms by constructing similarity classes based on similarity measures, as opposed to relying on equivalence classes. This shift holds particular relevance in the context of aggregating information systems, effectively circumventing the challenges associated with the process. To demonstrate the practical efficacy of our proposed approach, we delve into a concrete experiment within the information technology domain. Through this empirical exploration, the real-world utility of our approach becomes vividly apparent. Additionally, a comprehensive comparative analysis is undertaken, juxtaposing our approach against existing techniques for aggregation and decision modeling. The culmination of our efforts is a well-rounded article, punctuated by the insights, recommendations, and future directions delineated by the authors.
The intuitionistic fuzzy set (IFS), which has a membership and non-membership degree, is a controlling and effective device for dealing with fuzziness and uncertainty. Recently,the square root fuzzy set which is one of the efficient generalizations of an IFS for dealing with uncertainty and haziness in information has beenintroduced. In this study, a novel method for multiple attribute decision-making (MADM) based on SR-fuzzy information isinvestigated. Since aggregation operators are significant in the decision-making (DM) process, to achievethis goal, the current paper suggests a variety of novel Bonferroni mean and weighted Bonferroni mean operators to aggregate the SR-fuzzy values for the various decision-maker preferences. To achieve this goal, the current paper suggests a variety of novel Bonferroni mean and weighted Bonferroni mean operators to aggregate the SR-fuzzy values for the various decision-maker preferences. SR-fuzzyBonferroni mean operator and weighted SR-fuzzy Bonferroni mean operator are established and their properties are described. Then, we constructed a MADM approach using the proposed operators for the SR-fuzzyinformation and proved the approach with a mathematical example. Inthe end, a comparative study ofthe developed and existing approaches has been discussed to evaluate the pertinency and practicality of the proposed DM technique.
In recent years, the application of fuzzy sets has gained significant attraction in various fields, including medical diagnosis, due to their ability to manage uncertainties and imprecise information. This paper focuses on the comparative analysis of similarity measures within the realm of Generalized Interval-Valued Intuitionistic Fuzzy Soft Expert Sets (GIVIFSESs) and explores their application in the domain of medical diagnosis. Most of the important topics in fuzzy set theory are the similarity measures between the generalizations of fuzzy set theory. Similarity measures are a crucial tool which was used in data science. In this process, we measure how much the data sets are related and comparable. Measures of similarity give a numerical value that reveals the strength of associations between sets or sets of variables. In this paper, we initiate a new concept of generalized interval-valued intuitionistic fuzzy soft expert sets and their fundamental operations. This new concept is more flexible than existing concepts based on their algebraic definition. Unlike fuzzy sets, the concept of generalized interval-valued intuitionistic fuzzy soft expert sets is characterized by a degree of membership and degree of non-membership along with fuzzy set theory. The proposed methodology is validated through an empirical application in medical diagnosis, where (GIV-IFSESs) are employed to model the uncertainty and imprecision inherent in expert assessments. The selected similarity measures are then applied to quantify the degree of resemblance between different medical cases, facilitating a more informed decision-making process. We introduce several types of similarity measures on generalized interval-valued intuitionistic fuzzy soft expert sets. We also discuss a similarity measure of Type-I, Type-II, and Type-III for two (GIVIFSESs) and its application in medical diagnosis problems.
This paper introduces a refined and broadened version of decision-theoretic rough sets (DTRSs) named Generalized Sequential Decision-Theoretic Rough Set (GSeq-DTRS), which integrates the three-way decision (3WD) methodology. Operating through multiple levels, this iterative approach aims to comprehensively explore the boundary region. It introduces the concept of generalized granulation, departing from conventional equivalence-relation-based structures to incorporate similarity/tolerance relations. GSeq-DTRS addresses the limitations encountered by its predecessor, Seq-DTRS, particularly in managing sequential procedures and integrating new attributes. A notable advancement is its seamless handling of continuous-scale datasets through a defined Generalized Granular Structure (GGS), enabling classification across multiple levels without necessitating reduction of attributes. A refined version of conditional probability (CP), aligned with tolerance classes, enhances the approach, supported by a meticulously designed algorithm. Extensive experimental analysis conducted on two datasets sourced from https://www.kaggle.com demonstrates the efficacy of the procedure for both continuous and discrete datasets, effectively classifying probable elements into POS or NEG regions based on their membership. Unlike traditional Seq-DTRS, it does not require reduction of attributes at each new level. Additionally, the algorithm exhibits lower sensitivity to parametric values and yields results in fewer iterations. Thus, its potential impact on decision-making processes is readily apparent.
The concept of q-rung orthopair hesitant fuzzy set represents an advancement and extension of hesitant fuzzy sets, encompassing both fuzzy sets and q-rung orthopair fuzzy sets. q-rung orthopair hesitant fuzzy set characterizes a set of membership and non-membership grades within the interval [0, 1], which enhances its adaptability compared to existing methods. This flexibility proves invaluable in providing more insightful data about various objects. The primary objective of this research is to introduce a decision-making technique in the context of q-RHF using the theory of set pair analysis (SPA). q-RHFS effectively handles ambiguous data by incorporating membership and non-membership grades, while the connection number (CN) based on SPA theory manages the intricacies of uncertainty and certainty structures by relying on "identity", "discrepancy" and "contrary" grades. Building on the relationship between q-RHFS and the connection number of set pair analysis, a comprehensive framework known as q-rung hesitant fuzzy connection number set (qHCNs) is developed. This model not only addresses uncertainty, but also offers valuable insights. Furthermore, this research introduces similarity measures derived from qHCN and examines their advantages through illustrative examples. Additionally, a novel approach to decision modeling utilizing these measures applied to medical diagnosis is also introduced. The application of this established model contributes to an effective approach and demonstrated its soundness and efficiency. In addition, a detailed comparative study is conducted with the existing models and advantages of proposed model. The research concludes with a summary of the authors' findings, highlighting the consistency and effectiveness of their work.
Rough set (RS) and generalized rough set theories utilize single relations to obtain approximations of sets on a given universe of discourse. In granular computation, this is called single granularity. This article first expands -fuzzified RSs established on fuzzy tolerance relation to -optimistic multi-granulation fuzzified RSs by using a set of tolerance fuzzy relations over a given universe. Moreover, several elementary measures are proposed in this framework. Its application in feature selection has been highlighted through experimental analysis.
To determine how often care is limited at the end of life and the factors that are associated with this decision, we reviewed the medical records of all patients that passed away in the intensive care units (ICU) of Aga Khan University. We found that a majority of patients had Do-Not-Resuscitate orders in place at the time of death. Our analysis yielded 6 variables that were associated with the decision to limit care. These are patient age, sex, duration of mechanical ventilation, Glasgow Coma Scale (GCS) ≤8 at any point during ICU stay, GCS ≤8 in the first 24 hours following ICU admission, and mean arterial pressure <65 mm of Hg while on vasopressors in the first 24 hours following ICU admission. These variables require further study and should be carefully considered during end of life discussions to allow for optimal management at the end of life.
