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Some Studies in L Fuzzy Soft Semirings

Thesis Info

Author

Samina

Department

Department of Mathematics, QAU

Program

Mphil

Institute

Quaid-i-Azam University

Institute Type

Public

City

Islamabad

Province

Islamabad

Country

Pakistan

Thesis Completing Year

2013

Thesis Completion Status

Completed

Page

73

Subject

Mathematics

Language

English

Other

Call No: Diss/ M. Phil . MAT/ 967

Added

2021-02-17 19:49:13

Modified

2023-02-19 12:33:56

ARI ID

1676718441222

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A Study of Pakistan’s Various Reform Policies Regarding Islamic Seminaries

ABSTRACT: Pakistan is an Islamic country based on Islamic ideology where society has an emotional attachment with religion, hence an expanded network of Dini Modaris [traditional institutions of Islamic learning] is prevailing in urban as well as in rural areas of the country; where the teaching- learning process remains continue in a traditional way. While on other hand, at the same time, modern education system is followed by government and non-government run institutions. These two different systems with different ideologies and pedagogical techniques have produced two different social classes with different world views about the way Pakistan should be managed. This situation of education system is worrying. In an Islamic welfare state, ideally speaking, serious efforts are required to be done in order to eliminate the gulf between the two systems entirely having antagonistic approaches. In such perspective, this paper is aimed to study the efforts and practical steps, taken for the reforms and development of Dini Modaris by various governments of Pakistan as per their policies.

Multi-Criteria Decision Making Techniques Based on Some Extensions of Fuzzy Set

Multi-criteriadecisionmaking(MCDM)isacommonactivityineverydaylifeandtheobjectiveistoselectthe most feasible alternative from a set of given alternatives with the highest level of satisfaction in the presence of multiple, usually conflicting, criteria. Similarly, there are many real-life complex problems, where we need involve wide domain of knowledge which are beyond a single expert. Therefore, it is usually necessary to allocate more than one expert to decision process from different fields, including the education backgrounds, work experience and knowledge structure. Consequently, the multi-criteria group decision making (MCGDM) is also an important tool to deal with human activities and their problems of daily lives. In this thesis, different MCDM/MCGDM techniques are discussed based on some important extensions of fuzzy set. This thesis is comprised of three stages. In the first stage, the MCDM method called the Characteristic Objects Method (COMET) is extended to solve problems for MCGDM with hesitant fuzzy sets (HFSs) and intuitionistic fuzzy sets (IFSs). It is a completely new idea for solving problems of group decision making (GDM) under uncertainty. In this approach, we use L-R-type generalized fuzzy numbers (GFNs) and triangular intuitionistic fuzzy numbers (TIFNs) to get the degree of hesitancy in the form of hesitant fuzzy elements (HFEs) and the degree of membership and non-membership in the form of intuitionistic fuzzy numbers (IFNs) respectively for an alternative under a certain criterion. Therefore, the classical COMET methodwasadaptedtoworkwithGFNsandTIFNsinGDMproblems. Theproposedextensionsarepresented in detail, along with the necessary background information. The second stage of the thesis is comprised of three parts. In the first part, an outranking method is constructed using hesitant intuitionitic fuzzy linguistic term sets (HIFLTSs) for ranking alternatives in MCGDM problems based on intuitionistic fuzzy support function (IFSF), intuitionistic fuzzy risk function (IFRF),intuitionisticfuzzycredibilityfunction(IFCF)andthenetoutrankingflowindex(NOFI).Inthesecond part, the notion of directional Hausdorff distance between two HIFLTSs has been proposed and used it to formulate ELECTRE-based outranking method in hesitant intuitionistic fuzzy linguistic (HIFL) environment. The linguistic scale functions (LSFs) are used in two methodologies as mentioned above to conduct the transformation mechanism between qualitative information and quantitative data. In the third part, the notions of some distance measures between two HIFLTSs and weighted distance measures between two collections xiv xv of HIFLTSs are proposed and analyzed for discrete and continuous cases, and then used them to rank the alternatives in MCGDM problem. The third stage of the thesis is also comprised of two parts. In the first part, two outranking methods are developed with intuitionistic 2-tuple fuzzy linguistic (I2FL) information and a comparative discussion is conductedtodeterminetheadvantagesoftheproposedmethodovertheother. Inthesecondpart, afuzzyAHP (analytic hierarchy process) methodology for intuitionistic 2-tuple fuzzy linguistic sets (I2FLSs) is proposed and applied to solve MCDM problems. Finally, illustrative numerical examples are provided to elaborate the proposed methods with respect to the support of decision processes. This thesis closes with the conclusion along with some future research directions in this area.