Single-valued Trapezoidal Neutrosophic Numbers Research Articles

Multiple-attribute decision making problems based on SVTNH methods

The neutrosophic set (NS) is a leading tool in modeling of situations involving incomplete, indeterminate and inconsistent information. The single-valued neutrosophic sets (SVNs) is more useful tool than neutrosophic sets in some applications of engineering and scientific problems. In this paper, we study Hamacher operations and operations between single-valued trapezoidal neutrosophic numbers. Then we propose the single-valued trapezoidal neutrosophic Hamacher weighted arithmetic averaging (SVTNHWA) operator, single-valued trapezoidal neutrosophic Hamacher ordered weighted arithmetic averaging (SVTNHOWA) operator, single-valued trapezoidal neutrosophic Hamacher hybrid weighted averaging (SVTNHHWA) operator, single-valued trapezoidal neutrosophic Hamacher weighted geometric averaging (SVTNHWGA) operator and single-valued trapezoidal neutrosophic Hamacher ordered weighted geometric averaging (SVTNHOWGA) operator and single-valued trapezoidal neutrosophic Hamacher hybrid weighted geometric averaging (SVTNHHWGA) operator, and obtain some of their properties. Furthermore, we developed a multiple-attribute decision-making method in single-valued trapezoidal neutrosophic (SVTN) environment based on these operators. Finally, we proposed an application of MADM problem in assessment of potential of software system commercialization.

A novel defuzzification method of SV-trapezoidal neutrosophic numbers and multi-attribute decision making: a comparative analysis

The aim of this paper is to investigate the multiple attribute decision-making (MADM) problems where both the attribute value and attribute weight of alternatives are single-valued trapezoidal neutrosophic numbers (SVTN-numbers). Ranking of SVTN-numbers are always a necessary step in solving the MADM problems under SVTN environment, and the literature review reckoned the existence of six to seven ranking methods. After all the existing ranking methods of SVTN-numbers are examined, we firstly define the concept of centroid point and examine several useful properties of the developed concept. Then, we develop hamming ranking value and Euclidean ranking value of SVTN-numbers to compare the SVTN-numbers. Furthermore, based on the proposed ranking values, we develop a novel defuzzification method to MADM with linguistic information and give a real example deal with manufacturing company to illustrate the feasibility and effectiveness of the developed approach. Finally, we present some examples to compare the proposed method with the existing ranking results and the results verified through comparative analysis.

A Multi-Criteria Group Decision-Making Method with Possibility Degree and Power Aggregation Operators of Single Trapezoidal Neutrosophic Numbers

Single valued trapezoidal neutrosophic numbers (SVTNNs) are very useful tools for describing complex information, because of their advantage in describing the information completely, accurately and comprehensively for decision-making problems. In the paper, a method based on SVTNNs is proposed for dealing with multi-criteria group decision-making (MCGDM) problems. Firstly, the new operations SVTNNs are developed for avoiding evaluation information aggregation loss and distortion. Then the possibility degrees and comparison of SVTNNs are proposed from the probability viewpoint for ranking and comparing the single valued trapezoidal neutrosophic information reasonably and accurately. Based on the new operations and possibility degrees of SVTNNs, the single valued trapezoidal neutrosophic power average (SVTNPA) and single valued trapezoidal neutrosophic power geometric (SVTNPG) operators are proposed to aggregate the single valued trapezoidal neutrosophic information. Furthermore, based on the developed aggregation operators, a single valued trapezoidal neutrosophic MCGDM method is developed. Finally, the proposed method is applied to solve the practical problem of the most appropriate green supplier selection and the rank results compared with the previous approach demonstrate the proposed method’s effectiveness.

Assessment of consumers' motivations to purchase a remanufactured product by applying Fuzzy Delphi method and single valued neutrosophic sets

Abstract Environmental issues have been worldwide matters of concern especially in the recent decade and have made many firms implement end-of-life strategies such as remanufacturing. In prior studies, the supply side of remanufacturing supply chain has been vastly brought into focus compared to the demand side. Motivational factors that encourage consumers to purchase remanufactured products are getting firms attentions in developing effective marketing strategies to assist them being more productive in the current competitive market. However, consumer acceptance of remanufactured products has been regarded as one of the main reasons why remanufacturing has remained a majorly untapped opportunity for improving supply chain productivity. This study aims at exploring the major motivational factors for buying a remanufactured bike based on the consumers' and experts' opinions. Firstly, twelve motivations identified by scrutinising the literature. Secondly, single valued trapezoidal neutrosophic numbers (SVTNN) and trapezoidal neutrosophic weighted arithmetic averaging (TNWAA) operator were employed to obtain seven significant motivations using the survey data collected from potential customers. This method is applied owing to its capability in capturing the uncertainty of consumers' subjective judgements. Thirdly, the resulted seven motivations are prioritised in accordance with the experts' judgements utilising a proposed modified fuzzy Delphi (FD) method. Ultimately, the most significant motivation to purchase a remanufactured bike identified as quality that suggests quality is the major factor affecting purchase decision of a remanufactured bike. It indicates remanufacturers should focus on quality and attempt to improve the quality of products to gain more competitive advantage. The other six factors that should be stressed by remanufacturer's marketing strategies are prioritised as warranty, price, information provision, remanufacturer's reputation, value-added services and retailer's reputation respectively.

TOPSIS Strategy for Multi-Attribute Decision Making with Trapezoidal Neutrosophic Numbers

. Technique for Order Preference by Similarity to Ideal Solution (TOPSIS) is a popular strategy for MultiAttribute Decision Making (MADM). In this paper, weextend the TOPSIS strategy of MADM problems in trapezoidal neutrosophic number environment. The attributevalues are expressed in terms of single-valued trapezoidal neutrosophic numbers. The weight information of attribute is incompletely known or completely unknown. Using the maximum deviation strategy, we develop an optimization model to obtain the weight of the attributes. Then we develop an extended TOPSIS strategy to deal with MADM with single-valued trapezoidal neutrosophic numbers. To illustrate and validate the proposed TOPSIS strategy, we provide a numerical example of MADM problem.

A multi-criteria decision-making method based on single-valued trapezoidal neutrosophic preference relations with complete weight information

Single-valued trapezoidal neutrosophic numbers (SVTNNs) have a strong capacity to depict uncertain, inconsistent, and incomplete information about decisio nmaking problems.

Fuzzy decision-making framework for treatment selection based on the combined QUALIFLEX–TODIM method

ABSTRACTTreatment selection is a multi-criteria decision-making problem of significant concern in the medical field. In this study, a fuzzy decision-making framework is established for treatment selection. The framework mitigates information loss by introducing single-valued trapezoidal neutrosophic numbers to denote evaluation information. Treatment selection has multiple criteria that remarkably exceed the alternatives. In consideration of this characteristic, the framework utilises the idea of the qualitative flexible multiple criteria method. Furthermore, it considers the risk-averse behaviour of a decision maker by employing a concordance index based on TODIM (an acronym in Portuguese of interactive and multi-criteria decision-making) method. A sensitivity analysis is performed to illustrate the robustness of the framework. Finally, a comparative analysis is conducted to compare the framework with several extant methods. Results indicate the advantages of the framework and its better performance compared with the extant methods.

Evaluation of e-commerce websites: An integrated approach under a single-valued trapezoidal neutrosophic environment

E-commerce website evaluation is recognized as a complex multi-criteria decision-making (MCDM) problem involving vast amounts of imprecise and inconsistent evaluation data. Single-valued trapezoidal neutrosophic numbers (SVTNNs), which are elements in single-valued trapezoidal neutrosophic sets (SVTNSs), have a strong capacity to model such complex evaluation information. However, only few studies simultaneously consider the imprecise and inconsistent information inherent in the evaluation data. Moreover, much literature overlooks the different priority levels and interrelationships among criteria. To bridge this gap, this paper outlines a novel integrated decision system consisting of the following three modules: (1) information acquisition; (2) the single-valued trapezoidal neutrosophic decision making trial and evaluation laboratory (SVTN-DEMATEL) module; and (3) the integration module. In this study, we used the information acquisition module to gather the SVTNN information provided by experts, applied the SVTN-DEMATEL module to analyze the causal relationships among criteria, and proposed the integration module for information fusion with consideration of interdependencies and different priority levels of criteria. Furthermore, we conducted a case study to illustrate the effectiveness and feasibility of the proposal along with the sensitivity and comparison analyses to verify its stability and superiority. Finally, conclusions and future research directions were drawn.

Some Maclaurin Symmetric Mean Operators for Single-Valued Trapezoidal Neutrosophic Numbers and Their Applications to Group Decision Making

The Maclaurin symmetric mean (MSM) operator has a desirable property that it can capture the interrelationships among multi-input arguments and it is a generalization of some existing aggregation operators by changing the value of parameter k. The single-valued trapezoidal neutrosophic number (SVTNNs) can more conveniently depict uncertain information in the decision-making process. In order to combine the advantages of MSM operator and the SVTNNs, in this paper, we extend the MSM operator to SVTNNs. Firstly, we reviewed some basic concepts about the MSM operator and the SVTNNs and defined some single-valued trapezoidal neutrosophic MSM operators; then, we studied some properties of them and discussed some special cases of the proposed operators by changing the value of parameter k. Moreover, we developed a method to deal with multi-attributes group decision-making problem based on SVTNWMSM operator. Finally, we verified the validity and reliability of the proposed method by an illustrative example and analyzed its advantages by comparing with other existing methods.

A multi-criteria decision-making method based on single-valued trapezoidal neutrosophic preference relations with complete weight information

Single-valued trapezoidal neutrosophic numbers (SVTNNs) have a strong capacity to depict uncertain, inconsistent, and incomplete information about decision-making problems. Preference relations represent a practical tool for presenting decision makers’ preference information regarding various alternatives. The purpose of this paper is to propose single-valued trapezoidal neutrosophic preference relations (SVTNPRs) as a strategy for tackling multi-criteria decision-making problems. First, this paper briefly reviews basic concepts about neutrosophic sets and SVTNNs and defines a new comparison method and new operations for SVTNNs. Next, two aggregation operators, the single-valued trapezoidal neutrosophic weighted arithmetic average operator and the single-valued trapezoidal neutrosophic weighted geometric average operator, are proposed for applications in information fusion. Then, this paper discusses the definitions of completely consistent SVTNPRs and acceptably consistent SVTNPRs. Finally, we outline a decision-making method based on SVTNPRs to address green supplier selection problems, and we conduct a comparison study and discussion to illustrate the rationality and effectiveness of the decision-making method.

Multi-criteria group decision-making method based on interdependent inputs of single-valued trapezoidal neutrosophic information

Single-valued trapezoidal neutrosophic numbers (SVTNNs) are very useful tools for describing complex information, because they are able to maintain the completeness of the information and describe it accurately and comprehensively. This paper develops a method based on the single-valued trapezoidal neutrosophic normalized weighted Bonferroni mean (SVTNNWBM) operator to address multi-criteria group decision-making (MCGDM) problems. First, the limitations of existing operations for SVTNNs are discussed, after which improved operations are defined. Second, a new comparison method based on score function is proposed. Then, the entropy-weighted method is established in order to obtain objective expert weights, and the SVTNNWBM operator is proposed based on the new operations of SVTNNs. Furthermore, a single-valued trapezoidal neutrosophic MCGDM method is developed. Finally, a numerical example and comparison analysis are conducted to verify the practicality and effectiveness of the proposed approach.