scholarly journals SIMPLIFIED NEUTROSOPHIC INDETERMINATE DECISION MAKING METHOD WITH DECISION MAKERS’ INDETERMINATE RANGES

2020 ◽  
Vol 26 (6) ◽  
pp. 590-598 ◽  
Author(s):  
Shigui Du ◽  
Jun Ye ◽  
Rui Yong ◽  
Fangwei Zhang
Keyword(s):  
Decision Making ◽  
Decision Makers ◽  
Neutrosophic Set ◽  
Design Scheme ◽  
Weighted Arithmetic ◽  
Simplified Neutrosophic Set ◽  
Slope Design ◽  
Neutrosophic Number

There exists the indeterminate situations of truth, falsity, indeterminacy degrees due to the uncertainty and inconsistency of decision makers’ arguments in a complicated decision making (DM) problem. Then, existing neutrosophic set cannot describe the indeterminate information of truth, falsity, indeterminacy degrees. It is noted that the simplified neutrosophic set (SNS) is depicted by truth, falsity, indeterminacy degrees, while a neutrosophic number (NN) can be flexibly depicted by its determinate part and its indeterminate part. Regarding the indeterminate situations of truth, falsity, indeterminacy degrees in indeterminate DM problems, this study first presents a simplified neutrosophic indeterminate set (SNIS) to express the hybrid information of SNS and NN and defines the score, accuracy, and certainty functions of simplified neutrosophic indeterminate elements (SNIEs) with indeterminate ranges to compare SNIEs. Then, we introduce a SNIE weighted arithmetic averaging (SNIEWAA) operator and a SNIE weighted geometric averaging (SNIEWGA) operator to aggregate simplified neutrosophic indeterminate information. Next, a multi-attribute DM approach with decision makers’ indeterminate ranges is established regarding the SNIEWAA and SNIEWGA operators in SNIS setting. Finally, the proposed DM approach is applied in a DM example on choosing a suitable slope design scheme to indicate the applicability and suitability of the proposed approach.

scholarly journals Q-INDETERMINATE CORRELATION COEFFICIENT BETWEEN SIMPLIFIED NEUTROSOPHIC INDETERMINATE SETS AND ITS MULTICRITERIA DECISION-MAKING METHOD

2021 ◽  
Vol 27 (6) ◽  
pp. 404-411
Author(s):  
Shigui Du ◽  
Jun Ye ◽  
Rui Yong ◽  
Fangwei Zhang
Keyword(s):  
Decision Making ◽  
Correlation Coefficients ◽  
Multicriteria Decision Making ◽  
Decision Makers ◽  
Open Pit ◽  
Neutrosophic Set ◽  
Multicriteria Decision ◽  
Simplified Neutrosophic Set ◽  
Uncertainty Information ◽  
Slope Design

Owing to the indeterminacy, incompleteness, and inconsistency of decision makers’ arguments/cognitions regarding complicated decision-making problems, the truth, falsity, and indeterminacy degrees given by decision makers may imply the partial certainty and partial uncertainty information. In this case, a simplified neutrosophic set (SNS) cannot express the uncertainty degrees of the truth, falsity, indeterminacy arguments. To depict the hybrid information of SNS and neutrosophic (indeterminate) numbers (NNs) together, this study presents a simplified neutrosophic indeterminate set (SNIS) to describe the uncertainty degrees of the truth, falsity, indeterminacy, and then based on the de-neutrosophication technology using the parameterized SNSs of SNISs we introduce the q-indeterminate correlation coefficients of SNISs with a parameter q ∈ [0, 1]. Next, a simplified neutrosophic indeterminate multicriteria decision-making method using the qindeterminate correlation coefficients of SNISs is established along with decision makers’ risk attitudes, such as the small risk for q = 0, the moderate risk for q = 0.5, and the large risk for q = 1, to carry out multicriteria decision-making problems in SNIS setting. Eventually, the proposed decision-making approach is applied in an example of selecting a satisfactory slope design scheme for an open pit mine to indicate the practicality and flexibility in SNIS setting.

scholarly journals Operations and Aggregation Methods of Single-Valued Linguistic Neutrosophic Interval Linguistic Numbers and Their Decision Making Method

Information ◽  
2018 ◽  
Vol 9 (8) ◽  
pp. 196 ◽  
Author(s):  
Jun Ye ◽  
Wenhua Cui
Keyword(s):  
Decision Making ◽  
Score Function ◽  
Decision Makers ◽  
Decision Making Process ◽  
Aggregation Methods ◽  
Weighted Arithmetic ◽  
Multi Attribute Decision Making ◽  
Linguistic Argument ◽  
Degree Level ◽  
Neutrosophic Number

To comprehensively describe uncertain/interval linguistic arguments and confident linguistic arguments in the decision making process by a linguistic form, this study first presents the concept of a single-valued linguistic neutrosophic interval linguistic number (SVLN-ILN), which is comprehensively composed of its uncertain/interval linguistic number (determinate linguistic argument part) and its single-valued linguistic neutrosophic number (confident linguistic argument part), and its basic operations. Then, the score function of SVLN-ILN based on the attitude index and confident degree/level is presented for ranking SVLN-ILNs. After that, SVLN-ILN weighted arithmetic averaging (SVLN-ILNWAA) and SVLN-ILN weighted geometric averaging (SVLN-ILNWGA) operators are proposed to aggregate SVLN-ILN information and their properties are investigated. Further, a multi-attribute decision-making (MADM) method based on the proposed SVLN-ILNWAA or SVLN-ILNWGA operator and the score function is established under consideration of decision makers’ preference attitudes (pessimist, moderate, and optimist). Lastly, an actual example is given to show the applicability of the established MADM approach with decision makers’ attitudes.

scholarly journals Dombi Aggregation Operators of Linguistic Cubic Variables for Multiple Attribute Decision Making

Information ◽  
2018 ◽  
Vol 9 (8) ◽  
pp. 188 ◽  
Author(s):  
Xueping Lu ◽  
Jun Ye
Keyword(s):  
Decision Making ◽  
Multiple Attribute Decision Making ◽  
Optimal Choice ◽  
Decision Makers ◽  
Linguistic Variable ◽  
Operational Parameter ◽  
Arithmetic Average ◽  
Weighted Arithmetic ◽  
Multiple Attribute ◽  
Dombi Operations

A linguistic cubic variable (LCV) is comprised of interval linguistic variable and single-valued linguistic variable. An LCV contains decision-makers’ uncertain and certain linguistic judgments simultaneously. The advantage of the Dombi operators contains flexibility due to its changeable operational parameter. Although the Dombi operations have been extended to many studies to solve decision-making problems; the Dombi operations are not used for linguistic cubic variables (LCVs) so far. Hence, the Dombi operations of LCVs are firstly presented in this paper. A linguistic cubic variable Dombi weighted arithmetic average (LCVDWAA) operator and a linguistic cubic variable Dombi weighted geometric average (LCVDWGA) operator are proposed to aggregate LCVs. Then a multiple attribute decision making (MADM) method is developed in LCV setting on the basis of LCVDWAA and LCVDWGA operators. Finally, two illustrative examples about the optimal choice problems demonstrate the validity and the application of this method.

scholarly journals A Novel Dynamic Multi-Criteria Decision Making Method Based on Generalized Dynamic Interval-Valued Neutrosophic Set

Symmetry ◽  
2020 ◽  
Vol 12 (4) ◽  
pp. 618 ◽  
Author(s):  
Nguyen Tho Thong ◽  
Florentin Smarandache ◽  
Nguyen Dinh Hoa ◽  
Le Hoang Son ◽  
Luong Thi Hong Lan ◽  
...  
Keyword(s):  
Decision Making ◽  
Evaluation Model ◽  
Real Life ◽  
Decision Makers ◽  
Neutrosophic Set ◽  
Multi Criteria Decision Making ◽  
Neutrosophic Sets ◽  
Proposed Model ◽  
Interval Valued ◽  
Knowledge Evaluation

Dynamic multi-criteria decision-making (DMCDM) models have many meaningful applications in real life in which solving indeterminacy of information in DMCDMs strengthens the potential application of DMCDM. This study introduces an extension of dynamic internal-valued neutrosophic sets namely generalized dynamic internal-valued neutrosophic sets. Based on this extension, we develop some operators and a TOPSIS method to deal with the change of both criteria, alternatives, and decision-makers by time. In addition, this study also applies the proposal model to a real application that facilitates ranking students according to attitude-skill-knowledge evaluation model. This application not only illustrates the correctness of the proposed model but also introduces its high potential appliance in the education domain.

Weighted aggregation operators of fuzzy credibility cubic numbers and their decision making strategy for slope design schemes

2020 ◽  
Vol 01 ◽  
Author(s):  
Jun Ye ◽  
Shigui Du ◽  
Rui Yong ◽  
Fangwei Zhang
Keyword(s):  
Decision Making ◽  
Fuzzy Set ◽  
Real World ◽  
Fuzzy Numbers ◽  
Aggregation Operators ◽  
Open Pit Mine ◽  
Open Pit ◽  
Weighted Arithmetic ◽  
Ranking Of Alternatives ◽  
Slope Design

Background: A fuzzy cubic set (FCS) is composed of a fuzzy set (FS) (certain fuzzy numbers) and an intervalvalued fuzzy set (IVFS) (uncertain fuzzy numbers) to describe the hybrid information of both. To enhance the credibility of both, they should be closely related to the measures/degrees of credibility owing to the vagueness and uncertainty of humans’ cognitions regarding the real world. Objective: This paper presents the notions of a fuzzy cubic credibility set (FCCS) and a fuzzy cubic credibility number (FCCN) as the new generalization of the FCS notion so as to enhance the credibility level of FCS by means of the credibility degrees of both FS and IVFS. Next, we define operations of FCCNs, an expected value of FCCN, and the FCCN weighted arithmetic averaging (FCCNWAA) and FCCN weighted geometric averaging (FCCNWGA) operators for decision making (DM) strategy. Method: A decision making (DM) strategy using the FCCNWAA or FCCNWGA operator is proposed to solve multicriteria DM problems in the environment of FCCNs. Then, the proposed DM strategy is applied to a DM example of slope design schemes for an open pit mine in the environment of FCCNs to reflect the feasibility of the proposed DM strategy. Result: By comparison with the fuzzy cubic DM strategy, the DM results with and without the degrees of credibility can impact on the ranking of alternatives in the DM example to reflect the effectiveness of the proposed DM strategy. Result: By comparison with the fuzzy cubic DM strategy, the DM results with and without the degrees of credibility can impact on the ranking of alternatives in the DM example to reflect the effectiveness of the proposed DM strategy. Conclusion: However, the highlighting advantage of this study is that the proposed DM strategy not only indicates the degrees of credibility regarding the assessed values of FCNs in the DM process but also enhances the DM reliability in the environment of FCCNs. Hence, the proposed DM strategy is superior to the fuzzy cubic DM strategy in the environment of FCCNs.

An Improved MABAC Group Decision-Making Method Using Regret Theory and Likelihood in Probability Multi-Valued Neutrosophic Sets

2020 ◽  
Vol 19 (05) ◽  
pp. 1353-1387
Author(s):  
Peide Liu ◽  
Shufeng Cheng
Keyword(s):  
Decision Making ◽  
Group Decision Making ◽  
Group Decision ◽  
Decision Makers ◽  
Neutrosophic Set ◽  
Regret Theory ◽  
Neutrosophic Sets ◽  
Three Phase ◽  
Distance Deviation

Probability multi-valued neutrosophic set (PMVNS) is a preferable tool to capture the preference and hesitancy of decision makers (DMs) and to depict inconsistent and ambiguous information. In this paper, we improve the multi-attributive border approximation area comparison (MABAC) method under the PMVNS environment and establish a three-phase multi-attribute group decision-making (MAGDM) method. Firstly, some concepts of PMVNS, traditional MABAC method and regret theory (RT) are reviewed. Then, the similarity measure for PMVNSs is defined and utilized to derive the important degree of DMs, and the likelihood of preference relations expressed by the probability multi-valued neutrosophic numbers (PMVNNs) is first presented and employed to replace the distance deviation in traditional MABAC method. Furthermore, a novel MAGDM method where the performance of alternatives is expressed by the PMVNN is established by combining the likelihood-based MABAC method and RT which considered given DMs’ behavior psychology. Finally, a case study is implemented to demonstrate the feasibility and applicability of our proposed approach.

A novel method for multi-attribute risk decision-making based on regret theory and hybird information

2020 ◽  
Vol 39 (5) ◽  
pp. 6955-6964
Author(s):  
Nian Zhang ◽  
Yunpeng Han ◽  
Quanshen Si ◽  
Guiwu Wei
Keyword(s):  
Decision Making ◽  
Transformation Method ◽  
Decision Makers ◽  
Regret Theory ◽  
Utility Values ◽  
Weighted Arithmetic ◽  
Relative Closeness ◽  
Decision Making Problem ◽  
Ranking Order ◽  
Risk Decision

To consider the decision makers’ regret behavior and describe the hybrid evolution information in the risk decision-making problem, a new approach is proposed based on regret theory in this paper. Firstly, the probable value of different states are calculated by Pignistic probability transformation method. Secondly, the relative closeness formula of hybrid information are established and the utility values of alternatives are computed. Then, decision makers’ utility values are obtained according to the regret theory. Moreover, the overall perceived utility values of alternatives are obtained by weighted arithmetic mean and got the optimal one by the ranking order. Finally, an numerical example is illustrated the method and comparative analysis are offered between the proposed approach and other existed methods to show that is feasible and usable.

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 Application of the Bipolar Neutrosophic Hamacher Averaging Aggregation Operators to Group Decision Making: An Illustrative Example

Symmetry ◽  
2019 ◽  
Vol 11 (5) ◽  
pp. 698 ◽  
Author(s):  
Muhammad Jamil ◽  
Saleem Abdullah ◽  
Muhammad Yaqub Khan ◽  
Florentin Smarandache ◽  
Fazal Ghani
Keyword(s):  
Decision Making ◽  
Group Decision Making ◽  
Group Decision ◽  
Real Life ◽  
Aggregation Operators ◽  
Decision Makers ◽  
Weighted Averaging ◽  
Neutrosophic Set ◽  
Ordered Weighted Averaging ◽  
New Methods

The present study aims to introduce the notion of bipolar neutrosophic Hamacher aggregation operators and to also provide its application in real life. Then neutrosophic set (NS) can elaborate the incomplete, inconsistent, and indeterminate information, Hamacher aggregation operators, and extended Einstein aggregation operators to the arithmetic and geometric aggregation operators. First, we give the fundamental definition and operations of the neutrosophic set and the bipolar neutrosophic set. Our main focus is on the Hamacher aggregation operators of bipolar neutrosophic, namely, bipolar neutrosophic Hamacher weighted averaging (BNHWA), bipolar neutrosophic Hamacher ordered weighted averaging (BNHOWA), and bipolar neutrosophic Hamacher hybrid averaging (BNHHA) along with their desirable properties. The prime gain of utilizing the suggested methods is that these operators progressively provide total perspective on the issue necessary for the decision makers. These tools provide generalized, increasingly exact, and precise outcomes when compared to the current methods. Finally, as an application, we propose new methods for the multi-criteria group decision-making issues by using the various kinds of bipolar neutrosophic operators with a numerical model. This demonstrates the usefulness and practicality of this proposed approach in real life.

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