Possibility Interval-Valued Vague Soft Expert Sets and Its Similarity Measure

Preliminaries

In this section, we provide the definitions of some important concepts.

• Definition 2.1: (Xu et al., 2010). A pair is called a vague soft set over U where is a mapping given by and is the power set of vague sets over U. Every set for all , from this family may be considered as the set of e-approximate elements of the vague soft set . Hence the vague soft set s can be viewed as consisting of a collection of approximations of the following form for all and for all :

  

• Definition 2.2: (Alhazaymeh & Hassan, 2012). A pair is called an interval-valued vague soft set over U, where is a mapping given by , where is the power set of interval-valued vague sets on U. In other words, an interval-valued vague soft set over U is a parameterized family of interval-valued vague sets of U.

• Definition 2.3: (Alhazaymeh & Hassan, 2012). The union (intersection) of two interval-valued vague soft sets and over a universe U, denoted by is an interval-valued vague soft set , where and for all :