ترجيحات الشيخ ثناء الله بانی بتی في تفسير سورة الفاتحة: دراسة تطبيقية نموذجية

The topic of this research is “Preferences of Qazi Sana Ullah Pani patti in Tafseer of Surah al Fatiha, and these preferences are taken from his famous book of tafseer, named: “Tafseer al Mazhari.  Qazi Sana Ullah Pani Patti is one of the most eminent scholars of Tafseer in sub-continent. He belongs to the progeny of Usman R.A. He was born in PaniPat and got his early education there. Then he travelled to Dehli for higher education of that time. His teachers include: Abdul Raheem al Umari al Dehlvi, Muhammad Abid al Sinami, Sheikh janjan al Dehlvi. Among his famous books are followings: Al Tafseer al Mazhari, Mabsoot, Al saif al Maslool, Irshad ul Talibeen, Tazkira tul Mota, Haqeeqa tul Islam, and many other books. In this research I will discuss preferences of Qazi Sana Ullah with reference to two major types of Tafeer i.e Tafseer bil riwayyah (narration) and Tafseer bil dirayyah (sound reasoning).  

Novel Hybrid Models Based on Hesitant Fuzzy Sets

Hesitant fuzzy set theory is an impressive tool, to express the vagueness and ambiguity derive from experts, to analyze the characteristics of objects, and to determine the membership functions for each criterion domain. Due to the unpredictability of real world problems, and the limitation of human’s observations, it is very challenging to apply only a particular or specific uncertainty method to deal with complex problems. One can approach to more impressive and effective models to handle decision-making problems, by relating or associating the advantages of several other distinct theories of uncertainty. Hesitant fuzzy sets and soft sets are considered more efficient to deal the uncertain conditions. By combining these theories with several other useful models, novel hybrid models can be developed for decision-making problems. The aim of this research is to construct novel hybrid models based on hesitant fuzzy sets, because the use of hesitant fuzzy computations makes the decision-makers assessments more feasible and significant in decision-making. The proposed hybrid models are named as, hesitant N-soft sets, hesitant fuzzy N-soft sets, interval-valued hesitant fuzzy N-soft sets, m−polar hesitant fuzzy sets and hesitant m−polar fuzzy sets. These models are obtained by the hybridization of hesitant fuzzy sets with N-soft sets and m−polar fuzzy sets, which are more flexible and expressive for modeling and processing of vague information under hesitancy. These models provide us information about the occurrence of ratings or grades and enable us to tackle multi-polar information with hesitancy. Various properties of hybrid models are investigated with different methods of their construction. Intrinsic operations are highlighted and explored with several new concepts including weak, top weak and bottom weak complements. The concept of decision-making methods named as choice value, L-choice value, TOPSIS and ELECTRE-I, is explored by applying them on proposed models. Potential applications related to real life situations are presented, that illustrate the procedure of the proposed decision-making methods. Efficient algorithms are developed to solve the decision-making problems based on hybrid models.