جدید اور ہم عصر ریاستوں كے مقابلے میں خلافت راشدہ كی انفرادیت

During the Dark middle ages of Europe, The Holy Prophet Muhammad (PBUH) established the first ever Islamic state, in the Arab soil, at Medinah. The successors of the Prophet, known as Khulfa-i- Rashideen (the Glorious Caliphs) not only maintained it rather they extended with further development. The Caliphate was not only a model statefor the world but also a unique one with respect to its political appratus, principles and the governance. This paper discovers the same uniqueness of the Caliphate in past and modern perspective.

Soft Rough Fuzzy Graphs With Applications

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.