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Soft Rough Fuzzy Graphs With Applications

Thesis Info

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Author

Zafar, Fariha

Program

PhD

Institute

University of the Punjab

City

Lahore

Province

Punjab

Country

Pakistan

Thesis Completing Year

2019

Thesis Completion Status

Completed

Subject

Physical Sciences

Language

English

Link

http://prr.hec.gov.pk/jspui/bitstream/123456789/11167/1/Fariha%20Zafar_Maths_2019_UoP_Punjab_26.03.2019.pdf

Added

2021-02-17 19:49:13

Modified

2024-03-24 20:25:49

ARI ID

1676725034659

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Vagueness arises in several complex issues of engineering, science and many other fields. These issues cannot be resolved using crisp mathematical methods. Rough set theory is an approach for dealing with the inaccurate and ambiguous knowledge. Because of the confinement of human’s learning to comprehend the perplexing issues, it is exceptionally hard to apply one kind of uncertainty technique to address such issues. Consequently, it is important to build hybrid models by combining the benefits of numerous other diverse mathematical models dealing with uncertainty. In this dissertation, the concepts and methods of fuzzy sets, rough sets and soft sets are applied to construct rough fuzzy digraphs and soft rough fuzzy digraphs. Several new concepts, concerning these digraphs are introduced. Also various properties of these two models are discussed in detail. Some real world problems are also presented and solved through these graphical models. Furthermore, efficient algorithms are designed to solve these problems and the time complexity of these algorithms are also computed.
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Terrorism and its Elimination an Islamic Perspective

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Some Studies on Reproductive Biology of Sol Channa Marulius in the Punjab, Pakistan

Sol (Channa marulius) is a good target species for introduction into the aquaculture system of Pakistan, being indigenous and having potential to survive under variety of stressful freshwater conditions. The present study has been undertaken to study the growth and reproductive biology of the species under the conditions of Punjab (Pakistan). The analysis of morphometric and meristic characters suggested a significant correlation between the morphometric characters and a non-significant correlation between meristic characters, suggesting that meristic characters have a higher taxonomic value. Principal Component analysis suggested that fishes of different sizes have different patterns of growth of recorded variables. The fish with an average size of 7.37 cm (2.88g) increased to 53.8 cm (1165.7 g) from the age of 2 months to the age of 16 months. The fish at different ages suggested an isometric growth of weight in relation to length, with an average regression coefficient value of 3.05. Analysis of different reproductive biology variables conducted on fish captured from wild conditions suggested that the condition factor, gonadosomatic index (GSI), levels of progesterone and testosterone started gradually increasing after December, reaching peak values in April and a sudden decline in May. However, estrdiol peaked in March and showed minimum level in June. Hepatosomatic index (HSI) showed an inverse pattern, showing a decline in December with minimum values in May, when it started increasing to maximum values in the later part of the year. The pattern of histological changes in gonads followed the pattern of other variables of reproductive biology indicating that these variables truly represent the reproductive state of the individual. The studies suggest that the species is a long day species, where the reproductive activities commence after December and spawning takes place between late march and early May, under the environmental conditions of the Punjab (Pakistan).