Browsing by Author "Dr. Atiq ur Rehman"

Now showing 1 - 9 of 9

A Multi-person Decision Model for Low-Carbon Supplier Selection using Intuitionistic Preference Relations
(Library Information Services, COMSATS University Islamabad, Lahore Campus, 2022) Zurwa Abrar; SP20-RMT-041; LHR TP 7909; Dr. Atiq ur Rehman
In this thesis we presented a group decision framework to solve the low carbon supplier issue by employing intuitionistic preference relations, (IOWA) intuitionistic ordered weighted averaging operators and induced intuitionistic ordered weighted averaging operator (IIOWA) We use rectification and obtain weight vector and we then rank them and get the best decision out of it.
Consensus-Based Group Decision Making Using Hesitant Fuzzy Preference Relations
(Library Information Services, COMSATS University Islamabad, Lahore Campus, 2021) Syeda Mifzalah Bukhari; CIIT/SP20-RMT-019/LHR; Dr. Atiq ur Rehman; LHR TP 7650
In this thesis we presented a consensus-based technique for dealing with multi-person decision making (MPDM) employing hesitant fuzzy preference relations (HFPRs) that aren't in the standard format. At the most basic level, we suggested a Lukasiewicz transitivity (TL-transitivity)-based technique for obtaining normalized hesitant fuzzy preference relations (NHFPRs), after which a consensus-based model is built. Then, in order to build TL-consistent HFPRs and symmetrical matrices, a transitive closure formula is established.
Multi-Criteria Group Decision Making with Incomplete Fuzzy Preference Relations Using TL-Transitivity
(Library Information Services, COMSATS University Islamabad, Lahore Campus, 2021) Sidra Riaz; CIIT/FA19-RMT-046/LHR; Dr. Atiq ur Rehman; LHR TP 7380
In this thesis, we first present the concept of a consensus-based technique for selecting and evaluating suppliers in an incomplete fuzzy preference relations (IFPRs) environment utilizing TL-transitivity (Lukasiewicz transitivity). The suggested method is developed based on the criteria of the Analytical Hierarchy Process (AHP) Framework, and constructs the decision matrix is consistent fuzzy preference relations (FPRs). A variety of numerical explanations and an analysis of quantitative results illustrate the logic and effectiveness of the suggested methodology.
Multi-person Decision Making Based on Triangular Fuzzy Preference Relations
(Library Information Services, COMSATS University Islamabad, Lahore Campus, 2022) Ghulam Mohyudin; CIIT/SP20-RMT-015/LHR; Dr. Atiq ur Rehman; LHR TP 7629
A multi-person decision making (MPDM) model is proposed when the experts evaluate their opinions through triangular fuzzy numbers. First, it is pointed out that the preference relations with triangular fuzzy numbers are inconsistent in nature. In order to distinguish the typical consistency, the concept of Lukasiewicz Transitivity consistency is proposed for triangular fuzzy matrices. The properties of triangular fuzzy numbers are studied in detail. Second, using preference values, a triangular fuzzy preference relation with Lukasiewicz Transitivity consistency is constructed. Third, a novel compatibility degree among triangular fuzzy preference relations is defined. There is a selection phase to rank all the alternatives for choosing the best of them. Finally, a new algorithm for the multi-person decision making problem with triangular fuzzy preference relations using Lukasiewicz Transitivity is presented. A numerical example is carried out to illustrate the proposed definitions and algorithm.
On Connectivity Indices in the Realm of Intuitionistic Fuzzy Graphs with Applications
(Library Information Services COMSATS University Lahore Campus, 2024-03-14) Ahmed Hassan; FA22-RMT-051; Dr. Atiq ur Rehman; LHR TP 9350
In this thesis we study a numbers of various concept relating to intuitionistic fuzzy graph structures, such as complete intuitionistic fuzzy graph strong and weak cycle connectivity, and examined several relating attributes. The membership and non memebership values of nodes in intuitionistic fuzzy graph structures were also described with the help of an examples. Furthermore, we suggested execution of intuitionistic fuzzy graph framework to compare strong and weak connections between different nodes of Internet Routing and Network Transport Flow.
On the Consistency Model for GDM Using Incomplete Interval-Valued Fuzzy Preference Relations
(Library Information Services, COMSATS University Islamabad, Lahore Campus, 2021) Javaria Sarwar; CIIT/SP20-RMT-026/LHR; Dr. Atiq ur Rehman; LHR TP 7654
In this thesis work we provided a process grounded on consistency for multi- person decision making when suggestions of experts are presented in the shape of incomplete interval-valued fuzzy preference relations. The presented methodology utilizes Lukasiewicz's triangular norm in conjunction with scaling conditions to obtain the complete interval-valued fuzzy preference relations (IVFPRs) against every expert, the transitive closure formula satisfies Lukasiewicz's consistency. Consistency analysis makes us capable to find the consistency weights of decision makers. Final priority weights are allocated to the decision makers by accumulating consistency weights and predefined weights. The weighted sum of matrices of preference is then contrived as a combined consistency matrix. Procedure of normalization is then utilized to establish complementary matrices after manipulating the degrees of likelihood and the final ranking values of options or alternative(s) are also acquired. Some numerical illustrations verify the effectiveness of the presumed consistency model given in the methodology.
Some Notions of Interval Valued Fuzzy Graph Structures
(Library Information Services, CUI Lahore, 2023) CIIT/FA21-RMT-011/LHR; Muhammad Shoaib Azhar; Dr. Atiq ur Rehman
This work aims to study the notions of interval valued fuzzy sets (IVFSs) and fuzzy graph structures (FGSs) to build the interval valued fuzzy graph structures (IVFGSs) and develop some interesting results. An FGS G = (V; E), (1 i n), is an algebraic framework of the collection of vertices and disjoint subsets of edges along with two fuzzy mappings, h : V ! [0; 1] and x
Some Notions of Picture Fuzzy Graphs
(Library Information Services, COMSATS University Islamabad, Lahore Campus, 2021) Muhammad Rashid; SP19-RMT-034; LHR TP 7349; Dr. Atiq ur Rehman
In this thesis, we first present the concept of Picture Fuzzy Graphs (PFGs), which is the generalization of the intuitionistic fuzzy graphs (IFGs). Then we discuss some operations on of Picture Fuzzy Graphs (PFGs), including cartesian product of Picture Fuzzy Graphs (PFGs), composition of Picture Fuzzy Graphs (PFGs), union and join of Picture Fuzzy Graphs (PFGs), direct product of Picture Fuzzy Graphs (PFGs), and lexicographic product of Picture Fuzzy Graphs (PFGs). Finally, we discussed application of Picture Fuzzy social network (PFSN).
Weighted Mean Product of Fuzzy Graph Structures
(Library Information Services COMSATS University Islamabad Lahore Campus, 2021) Ali Raza; SP19-RMT-004; LHR TP 7352; Dr. Atiq ur Rehman
In this thesis we presented a numbers of various concepts relating to fuzzygraphic structures, such as the weighted mean product of two fuzzy-graphic structures and regular fuzzy-graphic structures, and examined several relating attributes. The degree and total degree of vertex in weighted mean product of fuzzy-graphic structures were also described with the help of examples. Furthermore, we have suggested execution of fuzzy-graphic frameworks to compare the five major cities of Pakistan on the basis of four criteria, such as Hospitals, Education, Industry and Roads