scholarly journals Some aggregation operators of neutrosophic Z-numbers and their multicriteria decision making method

2020 ◽  
Author(s):  
Shigui Du ◽  
Jun Ye ◽  
Rui Yong ◽  
Fangwei Zhang
Keyword(s):  
Decision Making ◽  
Fuzzy Numbers ◽  
Score Function ◽  
Multicriteria Decision Making ◽  
Neutrosophic Set ◽  
Human Knowledge ◽  
Multicriteria Decision ◽  
Business Partners ◽  
Weighted Arithmetic ◽  
New Framework

Abstract As the generalization of the classical fuzzy number, the concept of Z-number introduced by Zadeh indicates more ability to depict the human knowledge and judgments of both restraint and reliability as an order pair of fuzzy numbers. In indeterminacy and inconsistent environment, a neutrosophic set is described by the truth, falsity, and indeterminacy degrees, but they lack measures related to reliability. To describe the hybrid information of combining the truth, falsity and indeterminacy degrees with their corresponding reliability degrees, this paper first proposes the concept of a neutrosophic Z-number (NZN) set, which is a new framework of neutrosophic values combined with the neutrosophic measures of reliability, as the generalization of the Z-number and the neutrosophic set. Then, we define the operations of neutrosophic Z-numbers (NZNs) and a score function for ranking NZNs. Next, we present NZN weighted arithmetic averaging (NZNWAA) and NZN weighted geometric averaging (NZNWGA) operators to aggregate NZN information and investigate their properties. Regarding the NZNWAA and NZNWGA operators and the score function, a multicriteria decision making (MDM) approach is developed in the NZN environment. Finally, an illustrative example about the selection problem of business partners is given to demonstrate the applicability and effectiveness of the developed MDM approach in NZN setting.

scholarly journals An Extended EDAS Method for Multicriteria Decision-Making Based on Multivalued Neutrosophic Sets

Complexity ◽  
2020 ◽  
Vol 2020 ◽  
pp. 1-9
Author(s):  
Lili Han ◽  
Cuiping Wei
Keyword(s):  
Decision Making ◽  
Belief Systems ◽  
Intuitionistic Fuzzy Set ◽  
Weighted Average ◽  
Multicriteria Decision Making ◽  
Parameter Analysis ◽  
Neutrosophic Set ◽  
Neutrosophic Sets ◽  
Multicriteria Decision ◽  
Comprehensive Evaluations

Neutrosophic set (NS) is a generalization of intuitionistic fuzzy set (IFS). It depicts not only the incomplete information but also the indeterminate information and inconsistent information which exist commonly in belief systems. In this paper, the evaluation based on distance from average solution (EDAS) method is extended to handle multicriteria decision-making problems with multivalued neutrosophic numbers (MVNNs). The average solution under all the criteria is calculated by the proposed convex weighted average operator of MVNNs. Then, the positive distance and the negative distance from each solution to the average solution are calculated, and the comprehensive evaluations of alternatives are obtained by integrating two kinds of distance values to get the ranking result. Finally, the rationality and efficiency of the proposed method are shown by the parameter analysis and comparisons with some existing methods.

Introducing a new type of HFSs and its application in solving MAGDM problems

2021 ◽  
pp. 1-12
Author(s):  
Abazar Keikha
Keyword(s):  
Decision Making ◽  
Fuzzy Sets ◽  
Fuzzy Numbers ◽  
Score Function ◽  
Hesitant Fuzzy Sets ◽  
Vague Sets ◽  
Weighted Arithmetic ◽  
New Concepts ◽  
New Type ◽  
Magdm Problems

Uncertainty has long been explored as an objective and inalienable reality, and then modeled via different theories such as probability theory, fuzzy sets (FSs) theory, vague sets, etc. Hesitant fuzzy sets (HFSs) as a generalization of FSs, because of their flexibility and capability, extended and applied in many practical problems very soon. However, the above theories cannot meet all the scientific needs of researchers. For example, in some decision-making problems we encounter predetermined definite data, which have inductive uncertainties. In other words, the numbers themselves are crisp in nature, but are associated with varying degrees of satisfaction or fairness from the perspective of each decision-maker/judge. To this end, in this article, hesitant fuzzy numbers as a generalization of hesitant fuzzy sets will be introduced. Some concepts such as the operation laws, the arithmetic operations, the score function, the variance of hesitant fuzzy numbers, and a way to compare hesitant fuzzy numbers will be proposed. Mean-based aggregation operators of hesitant fuzzy numbers, i.e. hesitant fuzzy weighted arithmetic averaging (HWAA), hesitant fuzzy weighted geometric averaging (HWGA), hesitant fuzzy ordered weighted arithmetic averaging (HOWAA), and hesitant fuzzy ordered weighted geometric averaging (HOWGA) operators have been discussed in this paper, too. These new concepts will be used to model, and solve an uncertain multi-attribute group decision making (MAGDM) problem. The proposed method will be illustrated by a numerical example and the validity of the obtained solution will be checked by test criteria.

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