Linguistic Interval-Valued Spherical Fuzzy Sets and Related Properties

Although traditional spherical fuzzy sets can handle the fuzzy information in the quantitative environment well, it cannot deal with the more realistic qualitative information. The linguistic term set attracts attention due to their ability to handle the qualitative information. Therefore, to provide the more freedom to the decision-makers, in this paper, we propose the linguistic interval-valued spherical fuzzy set and the linguistic interval-valued spherical fuzzy number, whose the membership, non-membership, hesitancy and waiver degree are represented by the interval-valued linguistic terms, for better dealing with the imprecise and uncertain information during the decision-making process. In this paper, we give the concept of the linguistic interval-valued spherical fuzzy set; then we discuss the basic operational laws, some important properties and their related proofs. Subsequently, we give the concept of the linguistic interval-valued spherical fuzzy number, and various operational laws, then the measure formula, score and accuracy functions of the linguistic interval-valued spherical fuzzy number are defined with a brief study of their related properties. At last, an admissible order between the linguistic interval-valued spherical fuzzy numbers using score and accuracy functions is introduced.