Browsing by Author "Dr. Madiha Qayyum"

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Comprehensive Ranking of Neutrosophic Data using Information Measures in AI-Based Multi Criteria Decision-Making Models
(Library Information Services, COMSATS University Islamabad, Lahore Campus, 2025) Rumaisa; SP23-RMT-026; Dr. Madiha Qayyum; LHR TP 9750
In this research, a novel and inclusive framework involving existential set theory is pro posed with regard to uncertainty of the single-valued neutrosophic environment where the existential set refers to an approach that emphasizes the most possible or dominant membership values, while the effects of non-membership and indeterminacy are indirectly handled through their complemented forms. This idea is motivated by the observation that traditional neutrosophic measures, such as distance and cardinality, directly use non membership and indeterminacy degrees, which often introduces ambiguity in accurate measurement. By focusing on what is most likely to exist rather than what is uncertain or absent, the existential approach improves the interpretability and realism of neutro sophic modeling. Fuzzy and other traditional models show a lot of difficulties in capturing the complexity of the uncertain or conflicting data. In order to have a solution to these constraints, a parametric family of cardinality measure which is referred to as Paramet ric Class of Existential Weighted Average Cardinality is derived. It can be applied to single-valued neutrosophic sets and generalized neutrosophic trapezoidal numbers, allow ing comparing the entire neutrosophic data of different shapes and forms, including exist ing degrees of membership through adding the existential levels of membership to enhance interpretability and realism. Toenhancethemodelingofhumanjudgmentandbehavior, aparametricfamilyoffuzzy distance measures named the Multivariate Neutro-Existential Minkowski Distance is proposed. Building on this, a new confidence-based metric, Confidence Existential De gree, is designed to reflect cognitive attitudes such as optimism, pessimism, and neutrality.
Intelligent Solution for Transportation Problems Using Complete Ordering of Single Valued Neutrosophic Numbers
(Library Information Services, COMSATS University Islamabad, Lahore Campus, 2025) Muhammad Anees (FA20-BSM-068) : Muhammad Waqar Khizer (FA20-BSM-069); Dr. Madiha Qayyum; LHR TP 9909
TheTransportation Problem (TP) is extensively studied in operations research due to its nu merous real-world applications. However, real-world scenarios often involve uncertainty, making it difficult to determine costs, supply, and demand accurately. Fuzzy Numbers are commonly used to address this uncertainty but have limitations. These limitations arise from the inherent uncertainties in human thought patterns, which vary due to different val ues assigned to the three basic degrees of human thought—membership, non-membership, and indeterminacy—termed by Florentin. To better describe uncertainty in real-life situa tions, modern science uses Single Valued Neutrosophic Numbers (SVNS), which assign all three degree functions to any value, providing a more comprehensive mathematical model. Despite their extensive applicability in many Multi-Criteria Decision Making (MCDM) sit uations, ranking SVNS’s remain a significant challenge. Therefore, in this thesis we have f irstly defined a comprehensive ranking model for Single Valued Trapezoidal Neutrosophic Numbers (Normalized/Non-Normalized/ Uniform and Non Uniform Spread) based on four ranking functions/measures involving three existential levels namely- the Basic member ship (involving only membership function)-the Possible membership (a simple compliment of non- membershipfunction)–the Biggest membership (a combination of membership and indeterminacy function) and last but most important a Parametric combination of Possible membership and the Biggest membership. Next, we have employed the last ranking func tion– the parametric combination of Possible membership and the Biggest membership to ix build a Generalized Single Valued Trapezoidal Transportation Problem. In particular, we have utilized generalized trapezoidal data (normailized,/non-normalized/ with Uniform and Non Uniform Spread) to study three different types of transportation problems involving Crip and Single Valued Neutrosophic (triangular and trapezoidal) data for supply, demand, and cell costs. The thesis extends the principles of Least Cost Method (LCM), the North West Corner Method (NWCM), Vogel’s Approximation Method (VAM), and the Modified Distribution Method (MODI) to solve the Transportation Problem within a Single valued Neutrosophic environment. In this thesis, all the above modified solution models for TP incorporates generalized single valued trapezoidal neutrosophic data in different scenarios. Thus they provides the decision maker a flexible intelligence based environment which is capable of accommodating all different types of human mind behaviors (including the three basic behaviors of being optimist, pessimist and neutral ) due to the presence of logical op erations of fuzzy conjunctions and disjunctions that can be modelled by any pair of fuzzy t-norms and their conforms.
New Dimensions in MCDM with Multi Phase Hyper Neutrosophic Sets
(Library Information Services, COMSATS University Islamabad, Lahore Campus, 2021) Sunny Raza Qureshi; CIIT/FA19-RMT-025/LHR; Dr. Madiha Qayyum; LHR TP 7386
This work introduces a new mathematical model of the human brain, the Multi-Phase Neutrosophic set, which is an extension of the Neutrosophic set: which deal with human mind uncertainties on a level-by-level basis, encountering sentimental and emotional activity in the human mind as well as presenting the mathematical expression of Neutrality - a distinct state of human psychology. Firstly, we have built a Neutrality degree for a Neutrosophic set and defined a new modified neutrosophic set called Neutro-intelligent set (NIS) which consist of membership, indeterminacy, neutrality and non-membership. We have built Neutro-Intelligent constructive and mathematical operators such as union, intersection, complement, cross product, and special product as well as two families of cardinality measure called Weighted Possible Cardinality and Weighted Neutral Cardinality. Using these measures we have defined relative sigma count and a Ranking Relation between Neutro-Intelligent Sets. Later, by utilizing the new introduced Neutrality Degree we have built a State/Phase Function –a function giving level wise classifications of human thought which then is employed in defining the initially mentioned Multi-Phase Neutrosophic set. A Neutro-Intelligent version of Multi- Phase Neutrosophic Set namely Final Phase Neutrosophic Set is also introduced in order to incorporate the basic building operations and measures in Multi-Phase Neutrosophic Set Theory and Logic. Moreover, we have worked on implementing a Multi-Phase Neutrosophic set in the MCDM environment, with a specific focus on developing an effective COVID -19 Medical Diagnosis approach.
Ranking of Fuzzy Numbers and their Extension via Measures with Applications
(Library Information Services COMSATS University Lahore Campus, 2023-03-13) Sana Hayat; SP22-RMT-021; Dr. Madiha Qayyum; LHR TP 8727
This study introduces advanced ranking techniques for extended fuzzy numbers, specifically in both an intuitionistic fuzzy environment and a neutrosophic environment. In the intuitionistic fuzzy setting, a novel ranking method is proposed using a similarity measure based on intuitionistic fuzzy bi-implicators. This approach is applied to rank extended fuzzy numbers and is further employed in the context of multicriteria decision-making problems. Additionally, in the neutrosophic environment, the work presents an artificial intelligence-based ranking methodology for extended fuzzy numbers (neutrosophic environment), utilizing cardinality-based similarity measures. This method involved the development of structures for Jaccard, Dice, and Sokal-Sneath-2 similarity measures. The research demonstrates the consistent ranking results across these measures for Single-Valued Neutrosophic Numbers (SVNNs), emphasizing the broad applicability of the proposed approach. The method's flexibility is highlighted by the incorporation of three distinct human mind states (optimistic, pessimistic, and neutral) through logical operators.