Probabilistic Single-Valued (Interval) Neutrosophic Hesitant Fuzzy Set and Its Application in Multi-Attribute Decision Making

The uncertainty and concurrence of randomness are considered when many practical problems are dealt with. To describe the aleatory uncertainty and imprecision in a neutrosophic environment and prevent the obliteration of more data, the concept of the probabilistic single-valued (interval) neutrosophic hesitant fuzzy set is introduced

Aggregation functions for typical hesitant fuzzy elements and the action of automorphisms

This work studies the aggregation operators on the set of all possible membership degrees of typical hesitant fuzzy sets, which we refer to as H, as well as the action of H-automorphisms which are defined over the set of all finite non-empty subsets of the unitary interval. In order to do so, the partial order ≤H, based on α-normalization, is introduced, leading to a comparison based on selecting the greatest membership degrees of the related fuzzy sets. Additionally, the idea of interval representation is extended to the context of typical hesitant aggregation functions named as the H-representation. As main contribution, we consider the class of finite hesitant triangular norms, studying their properties and analyzing the H-conjugate functions over such operators. © 2013 Elsevier Inc. All rights reserved.Peer Reviewe

Some Aggregation Operators Based on Einstein Operations under Interval-Valued Dual Hesitant Fuzzy Setting and Their Application

We investigate the multiple attribute decision making (MADM) problems in which attribute values take the form of interval-valued dual hesitant fuzzy information. Firstly, some operational laws for interval-valued dual hesitation fuzzy elements (IVDHFEs) based on Einstein operations are developed. Then we develop some aggregation operators based on Einstein operations: the interval-valued dual hesitant fuzzy Einstein weighted averaging (IVDHFEWA) operator, interval-valued dual hesitant fuzzy Einstein ordered weighted averaging (IVDHFEOWA) operator, interval-valued dual hesitant fuzzy Einstein hybrid averaging (IVDHFEHA) operator, interval-valued dual hesitant fuzzy Einstein weighted geometric (IVDHFEWG) operator, interval-valued dual hesitant fuzzy Einstein ordered weighted geometric (IVDHFEOWG) operator, and interval-valued dual hesitant fuzzy Einstein hybrid geometric (IVDHFEHG) operator. Furthermore, we discuss some desirable properties of these operators, and investigate the relationship between the developed operators and the existing ones. Based on the IVDHFEWA operator, an approach to MADM problems is proposed under the interval-valued dual hesitant fuzzy environment. Finally, a numerical example is given to show the application of the developed method, and a comparison analysis is conducted to demonstrate the effectiveness of the proposed approach

Interval Entropy of Fuzzy Sets and the Application to Fuzzy Multiple Attribute Decision Making

A series of new concepts including interval entropy, interval similarity measure, interval distance measure, and interval inclusion measure of fuzzy sets are introduced. Meanwhile, some theorems and corollaries are proposed to show how these definitions can be deduced from each other. And then, based on interval entropy, a fuzzy multiple attribute decision making (FMADM) model is set up. In this model, interval entropy is used as the weight, by which the evaluation values of all alternatives can be obtained. Then all alternatives with respect to each criterion can be ranked as the order of the evaluation values. At last, a practical example is given to illustrate an application of the developed model and a comparative analysis is made

Evaluate Public-Private-Partnership’s advancement using double hierarchy hesitant fuzzy linguistic PROMETHEE with subjective and objective information from stakeholder perspective

Public-Private-Partnership (PPP) as an efficient mode to provide public services through the government and social capital’s cooperation has been in China for more than 30 years. In this paper, we propose an approach to evaluate PPP’s advancement in different areas based on the subjective and objective information fusion. At first, we establish an index system from the perspective of the stakeholder. Then, considering that double hierarchy hesitant fuzzy linguistic term set (DHHFLTS) that has two hierarchies of linguistic term sets can describe the subjective linguistic information more accurately, it is applied in the paper to depict the subjective information. By applying the entropy of the DHHFLTS, a programming model is proposed to derive the attribute weight through combining subjective evaluation with objective data. In addition, we develop the double hierarchy hesitant fuzzy linguistic PROMETHEE combining the subjective and objective information (DHHFL-PROMETHEE-S&O) method. At last, we illustrate the index system and the method with the PPP’s advancement evaluation problem, and we can find the best choice based on the ranking result. Meanwhile, we also find that the objective information and the subjective information are complementary in the evaluation process. First published online 20 March 201

Interval-Valued Hesitant Fuzzy Hamacher Synergetic Weighted Aggregation Operators and Their Application to Shale Gas Areas Selection

We investigate the multiple criteria decision making (MCDM) problem concerns on the selection of shale gas areas with interval-valued hesitant fuzzy information. First, some Hamacher operations of interval-valued hesitant fuzzy information are introduced, which generalize and extend the existing ones. Then some interval-valued hesitant fuzzy Hamacher weighted aggregation operators, especially, the interval-valued hesitant fuzzy Hamacher synergetic weighted averaging (IVHFHSWA) operators and their geometric version (IVHFHSWG) operators that weight simultaneously the argument variables themselves and their position orders and thus generalize the ideas of the weighted averaging and the ordered weighted averaging, are proposed. The distinct advantages of these operators are that they can provide more choices for the decision makers and considerably enhance or deteriorate the performance of aggregation. The essential properties of these operators are studied and their specific cases are discussed. Based on the IVHFHSWA operator, we propose a practical approach to shale gas areas selection with interval-valued hesitant fuzzy information. Finally, an illustrative example for selecting the shale gas areas is used to demonstrate the practicality and effectiveness of the proposed approach and a comparative analysis is performed with other approaches to highlight the distinctive advantages of the proposed operators