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E-raamat: Hybrid Soft Computing Models Applied to Graph Theory

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This book describes a set of hybrid fuzzy models showing how to use them to deal with incomplete and/or vague information in different kind of decision-making problems. Based on the authors’ research, it offers a concise introduction to important models, ranging from rough fuzzy digraphs and intuitionistic fuzzy rough models to bipolar fuzzy soft graphs and neutrosophic graphs, explaining how to construct them. For each method, applications to different multi-attribute, multi-criteria decision-making problems, are presented and discussed. The book, which addresses computer scientists, mathematicians, and social scientists, is intended as concise yet complete guide to basic tools for constructing hybrid intelligent models for dealing with some interesting real-world problems. It is also expected to stimulate readers’ creativity thus offering a source of inspiration for future research.

1 Rough Fuzzy Graphs
1(78)
1.1 Introduction
1(4)
1.2 Rough Fuzzy Digraphs
5(3)
1.3 Some Algebraic Operations on Rough Fuzzy Digraphs
8(28)
1.4 Automorphic Rough Fuzzy Digraphs
36(4)
1.5 Irregular Rough Fuzzy Digraphs
40(6)
1.6 Connectivity Index of Rough Fuzzy Digraph
46(15)
1.6.1 Types of Arcs and Vertices in Rough Fuzzy Digraphs
48(13)
1.7 Applications
61(18)
1.7.1 Applications to Decision-Making
61(10)
1.7.2 Application to Human Trafficking
71(8)
2 Fuzzy Rough Graphs
79(50)
2.1 Introduction
79(2)
2.2 Application of Fuzzy Rough Sets to Graphs
81(25)
2.3 Automorphic Fuzzy Rough Digraphs
106(5)
2.4 Applications
111(13)
2.4.1 Simulating City-Level Infectious Diseases
111(3)
2.4.2 Identification of Best Location
114(4)
2.4.3 Blockage Path Problem
118(3)
2.4.4 Selection of Best Vehicle
121(3)
2.5 Comparison of Rough Fuzzy Model with Existing Models
124(5)
2.5.1 Fuzzy Rough Digraphs Versus Rough Fuzzy Digraphs
124(3)
2.5.2 Fuzzy Rough Digraphs Versus Fuzzy Graphs
127(2)
3 Intuitionistic Fuzzy Rough Graphs
129(82)
3.1 Introduction
129(2)
3.2 Intuitionistic Fuzzy Rough Relation
131(2)
3.3 Intuitionistic Fuzzy Rough Graphs
133(2)
3.4 Certain Operations on Intuitionistic Fuzzy Rough Graphs
135(12)
3.5 Certain Products of Intuitionistic Fuzzy Rough Graphs
147(21)
3.6 Strong and Complete Intuitionistic Fuzzy Rough Graphs
168(3)
3.7 Isomorphism Between Intuitionistic Fuzzy Rough Graphs
171(6)
3.8 Regular Intuitionistic Fuzzy Rough Graphs
177(7)
3.9 Irregular Intuitionistic Fuzzy Rough Graphs
184(3)
3.10 Applications of Hybrids Models to Decision-Making
187(24)
3.10.1 Selection of Suitable Embroidery
187(7)
3.10.2 Selection of a Suitable Network Connection
194(11)
3.10.3 Selection of a Suitable Candidate
205(6)
4 Fuzzy Soft Graphs
211(50)
4.1 Introduction
211(1)
4.2 Fuzzy Soft Graphs
212(8)
4.3 Some Operations on Fuzzy Soft Graphs
220(10)
4.4 Regular Fuzzy Soft Graphs
230(6)
4.5 Irregular Fuzzy Soft Graphs
236(2)
4.6 Fuzzy Soft Trees
238(16)
4.7 Applications of Fuzzy Soft Graphs to Decision-Making
254(7)
4.7.1 Social Networking
254(3)
4.7.2 Road Networking
257(4)
5 Intuitionistic Fuzzy Soft Graphs
261(62)
5.1 Introduction
261(1)
5.2 Intuitionistic Fuzzy Soft Graphs
262(17)
5.2.1 Operations on Intuitionistic Fuzzy Soft Graphs
265(10)
5.2.2 Strong Intuitionistic Fuzzy Soft Graphs
275(4)
5.3 Possibility Intuitionistic Fuzzy Soft Graphs
279(3)
5.4 Regular Intuitionistic Fuzzy Soft Graphs
282(3)
5.5 Edge Regular Intuitionistic Fuzzy Soft Graphs
285(6)
5.6 Irregular Intuitionistic Fuzzy Soft Graphs
291(5)
5.7 Edge Irregular Intuitionistic Fuzzy Soft Graphs
296(6)
5.8 Strongly Edge Irregular Intuitionistic Fuzzy Soft Graphs
302(5)
5.9 Applications
307(16)
5.9.1 Suitable Career Selection Problem
307(2)
5.9.2 Weapon Selection Problem
309(2)
5.9.3 Communication Network
311(3)
5.9.4 Suitable Machine Selection
314(2)
5.9.5 Object Recognition Problem
316(3)
5.9.6 Best Investment Project Selection
319(4)
6 Soft Rough Fuzzy Graphs
323(30)
6.1 Introduction
323(1)
6.2 Soft Rough Digraphs
324(2)
6.3 Soft Rough Fuzzy Digraphs
326(6)
6.4 Methods of Construction of Soft Rough Fuzzy Digraphs
332(13)
6.5 Applications
345(8)
7 Bipolar Fuzzy Soft Graphs
353(18)
7.1 Introduction
353(1)
7.2 Bipolar Fuzzy Soft Graphs
354(9)
7.3 Multiple Criteria Decision-Making Problems
363(8)
8 Soft Rough Neutrosophic Influence Graphs
371(60)
8.1 Introduction
371(1)
8.2 Soft Rough Neutrosophic Graphs
372(16)
8.3 Soft Rough Neutrosophic Influence Graphs
388(25)
8.4 Application
413(18)
8.4.1 Selection of Suitable Path
413(8)
References
421(10)
Index 431
Dr. Muhammad Akram received MSc degrees in Mathematics and Computer Science, MPhil in Computational Mathematics and PhD in Fuzzy Mathematics. He is currently a Professor in the Department of Mathematics at the University of the Punjab, Lahore, Pakistan, where he has been serving as a PhD supervisor of more than 10 students. Dr. Akrams research interests include numerical solutions of parabolic PDEs, fuzzy graphs, fuzzy algebras, and fuzzy decision support systems. He has published 7 monographs and 300 research articles in international peer-reviewed journals. He has served as editorial board member of 10 international academic journals and as reviewer of 122 International journals, including Mathematical Reviews and Zentralblatt MATH. Dr. Fariha Zafar received her PhD degree in Mathematics and MPhil degree in Mathematics from the University of the Punjab, Lahore. She has introduced the notions of Soft Trees and Fuzzy Soft Trees during her MPhil research work. She has published 10 research articles in top-ranked international journals. Her research interests include fuzzy graphs, soft set theory, rough set theory and decision-making.
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