In this paper, we investigate the probabilistic decision making problems with hesitant fuzzy information, some new probabilistic decision making analysis methods are developed. Then, we have developed some new probability aggregation operators with hesitant fuzzy information: probability hesitant fuzzy Hamacher weighted average(P-HFHWA) operator, immediate probability hesitant fuzzy Hamacher or...

With respect to decision making problems by using probabilities, immediate probabilities and information that can be represented with hesitant fuzzy information, some new decision analysis are proposed. Then, we have developed some new probability aggregation operators with hesitant fuzzy information: probability hesitant fuzzy weighted average (P-HFWA) operator, immediate probability hesitant ...

Dual hesitant fuzzy sets (DHFSs), originally introduced by Zhu et al. [23], are a new tool to handle fuzziness considering the membership and nonmembership degrees by a set of possible values respectively. As a more comprehensive set, DHFSs have close relationship with the existing fuzzy sets, including the Zadeh’s fuzzy set, Atanassov’s intuitionistic fuzzy set, and hesitant fuzzy set, etc. An...

Fuzzy best simultaneous approximation of a finite number of functions is considered. For this purpose, a fuzzy norm on $Cleft (X, Y right )$ and its fuzzy dual space and also the  set of subgradients of a fuzzy norm are introduced. Necessary case of a proved theorem about characterization of simultaneous approximation will be extended to the fuzzy case.

In this paper, a hesitant fuzzy multiple attribute group decision making problem where there exists prioritization relationships over the attributes and decision makers is studied. First, some Einstein operations on hesitant fuzzy elements and their properties are presented. Then, several generalized hesitant fuzzy prioritized Einstein aggregation operators, including the generalized hesitant f...

On the basis of the combination of single-valued neutrosophic sets and hesitant fuzzy sets, this article proposes a single-valued neutrosophic hesitant fuzzy set (SVNHFS) as a further generalization of the concepts of fuzzy set, intuitionistic fuzzy set, single-valued neutrosophic set, hesitant fuzzy set, and dual hesitant fuzzy set. Then, we introduce the basic operational relations and cosine...

In hesitant fuzzy sets (HFSs), which are generalized from fuzzy sets, the membership degree of an element to a set, for which decision-makers hesitate while considering several values before expressing their preferences concerning weights and data, can be assigned one or more possible precise values between zero and one. If two or more decision-makers assign an equivalent value, that value is o...

In this paper, we defined some aggregation operators to aggregate generalized hesitant fuzzy elements and the relationship between our proposed operators and the existing ones are discussed in detail. Furthermore, the procedure of multicriteria decision making based on the proposed operators is given under generalized hesitant fuzzy environment. Finally, a practical example is provided to illus...

the purpose of the present work is to establish a one-to-one correspondence between the family of interval type-2 fuzzy reflexive/tolerance approximation spaces and the family of interval type-2 fuzzy closure spaces.

In this article we define some aggregation operators for bipolar-valued hesitant fuzzy sets. These operations include bipolar-valued hesitant fuzzy ordered weighted averaging (BPVHFOWA) operator, bipolar-valued hesitant fuzzy ordered weighted geometric (BPVHFOWG) operator and their generalized forms. We also define hybrid aggregation operators and their generalized forms and solved a decision-m...