Research On Theories And Applications Of Extension Models Of Interval-valued Fuzzy Soft Set

In real life, we often deal with vague or imprecise information. The obtainedinformation is sometimes blurred, sometimes inaccurate, and sometimes not sufficient. Itcan be seen that uncertainty is a major feature of information, many areas like economics,engineering, environmental and so there are many uncertain, imprecise, vague question.Classical mathematical methods can’t successfully deal with the uncertainty of thesecomplex issues. In order to solve this problem, probability theory, fuzzy set, rough settheory have been produced. However, these theories can only deal with part of theuncertainty, they all have the same deficiencies that parameter tool theory is not sufficient.To solve this problem, in1999, Molodtsov proposed the concept of soft set to overcomethese deficiencies. Today the soft set theory has been successfully applied to many fieldsand has widely attention in academia.In2011, S. Alkhazaleh and AR Salleh proposed the concept of possibility fuzzy softsets, which have a possibility for each parameter of each element, we can also call thispossibility as the degree of importance. This paper aims to extend the possibility fuzzysoft set and gives two extended models, the first one is the possibility interval-valuedfuzzy soft sets, which is combined the possibility fuzzy soft set and the interval-valuedfuzzy set. In other words, the membership and possibility in possibility fuzzy soft set aredescribed with the interval-valued instead of a single number. This description is closer toreality; the second one is the bipolar possibility interval-valued fuzzy soft set, which iscombined the possibility interval-valued fuzzy soft set and bipolar fuzzy set. This modeldescribes information from positive and negative aspects so that we can decide moreaccurately when we make decisions in a more comprehensive. This paper give thedefinition of the two models respectively, and analyzes the properties they have.Finally, this paper gives two cases. The first one is the teaching evaluation whichthere are six teachers to take part in. We will choose the best performing teacher. We usethe possibility interval-valued fuzzy soft sets to describe different aspects of eachteacher’s performance. Then, we give an appropriate algorithm and obtain the bestperforming teacher by calculating the relevant data. The second case is the competition ofseveral candidates for a company’s post. We will have candidates’ professional standards in all aspects by the bipolar possibility interval-valued fuzzy soft sets. We use appropriatealgorithm to calculate and get the most suitable candidate for this post.