Some Studies in Rough Set Theory Based on Soft Relations and Their Applications

Abstract

Traditional tools for reasoning, computing and formal modeling are crisp, precise and deterministic in character. However, many practical problems under di¤erent elds have uncertainties. Traditional mathematical tools can never be used due to many uncertainties existing in these problems. Traditionally, Probability theory is considered as a useful tool to handle uncertainty. A very basic requirement for its application is that a system must be stochastically stable. To establish it, a large number of trials is required. So, a lot of time will be spent on it. In today s fast pace life, humans have scarcity of time. This means some non-traditional ways must be sought to tackle this problem linked with uncertainty. For extraction of helpful information, specialists are dedicated step by step. They have pulled in light of a legitimate concern for specialists and experts in di¤erent elds of science and innovation. In this regard, Zadeh made a very nice attempt and introduced the theory of fuzzy sets [99]. Fuzzy sets not only cope with uncertainty but also have ability to translate human linguistic terms mathematically. Actually it was a great leap, and paced development many times. Now there are many generalizations of fuzzy sets and they are perceived and useful to manage uncertainty but every one of these speculations inherents certain challenges as Molodtsov have demonstrated