1
|
Ali S, Rahim M, Bajri SA, Ahmad S, Alharbi R, Abd El-Wahed Khalifa H. α,β,γ- Neutrosophic aggregation operators and their applications in the software site selection. Heliyon 2024; 10:e31417. [PMID: 38826747 PMCID: PMC11141350 DOI: 10.1016/j.heliyon.2024.e31417] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/26/2024] [Revised: 05/14/2024] [Accepted: 05/15/2024] [Indexed: 06/04/2024] Open
Abstract
In this paper, we expended the concept of neutrosophic sets (NS) by introducing the idea α , β , γ - neutrosophic set (α , β , γ - NS). The existing models under conventional NSs, fail to adequately address the management of membership degree influence during the aggregation process. While the proposed framework manages the influence of membership degree (MD), indeterminacy membership degree (IMD), and non-membership degree (NMD) by incorporating parameters α , β , and γ . Furthermore, we defined some fundamental operational laws for α , β , γ - NSs and introduced a series of aggregation operators (AOs) to effectively combine α , β , γ - neutrosophic information. Based on these AOs, a new Multiple Criteria Decision Making (MCDM) model is proposed for solving real-life decision-making (DM) challenges. An illustrative case study is presented to showcase the effectiveness of the proposed model in selecting an optimal location for a software office. The article concludes by validating the proposed model's authenticity and effectiveness through a comparative analysis with existing approaches.
Collapse
Affiliation(s)
- Sumbal Ali
- Department of Mathematics and Statistics, Hazara University, Mansehra, 21300, KPK, Pakistan
| | - Muhammad Rahim
- Department of Mathematics and Statistics, Hazara University, Mansehra, 21300, KPK, Pakistan
| | - Sanaa A. Bajri
- Department of Mathematical Sciences, College of Science, Princess Nourah Bint Abdulrahman University, P.O. Box 84428, Riyadh, 11671, Saudi Arabia
| | - Sadique Ahmad
- EIAS: Data Science and Blockchain Laboratory, College of Computer and Information Sciences, Prince Sultan University, Riyadh, 11586, Saudi Arabia
| | - Rabab Alharbi
- Department of Mathematics, College of Science, Qassim University, Buraydah, 51452, Saudi Arabia
| | - Hamiden Abd El-Wahed Khalifa
- Department of Mathematics, College of Science, Qassim University, Buraydah, 51452, Saudi Arabia
- Department of Operations and Management Research, Faculty of Graduate Studies of Statistical Research, Cairo University, Giza, 12613, Egypt
| |
Collapse
|
2
|
Inspection of the Production Lot Using Two Successive Occasions Sampling Under Neutrosophy. INT J COMPUT INT SYS 2022. [DOI: 10.1007/s44196-022-00071-y] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/05/2022] Open
Abstract
AbstractThe efficiency of the measuring tools and operators is a significant part of lot sentencing decisions. These tools have to pass some pre-specified quality levels to avoid problems during the quality assessment scenarios. These measurements have a serious risk to be encountered with any extent of ambiguity, doubt, or indeterminacy due to any of the factors like variation among the operating regimes, warming effects in the hot climatic conditions, the operators’ casual attitude, and so on. These factors as the most significant sources of extraneous variations can deeply affect the efficacy of lot sentencing decisions. Hence, the decision when based on the measurement through the operating tools and these tools have to pass which have fulfilled some adequate standards only then lot sentencing may avoid or save from the rejection of a good lot. The authors have put their focus on dealing with the factors that arise by measuring variability among the measured or determined values despite having the normal population distribution. In this study, the auxiliary information is used to estimate the variable of interest over the two successive occasions under the neutrosophic interval numbers and proved helpful to overcome this issue. The presented approach has discussed that in blurred, doubted, uncertain and undetermined datasets partially or completely, the efficacy of the decision for the whole lot cannot be decided on the single point crisped value. But the range of values around such a single crisp point in the form of neutrosophic theory is proved far better. In this context, the neutrosophic interval number successive sampling-based sampling plan is proposed which is the major contribution to the existing literature. It is explained in terms of operating characteristic function and the plan parameters are determined through the neutrosophic non-linear optimization approach. The comparative analysis is presented with the existing sampling plans and found efficient. Moreover, a real-life industrial dataset is used as an application of the concept.
Collapse
|
3
|
Multiattribute decision-making by logarithmic operational laws in interval neutrosophic environments. GRANULAR COMPUTING 2022. [DOI: 10.1007/s41066-021-00299-7] [Citation(s) in RCA: 2] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 10/19/2022]
|
4
|
Garg H. SVNMPR: A new single‐valued neutrosophic multiplicative preference relation and their application to decision‐making process. INT J INTELL SYST 2021. [DOI: 10.1002/int.22767] [Citation(s) in RCA: 7] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/11/2022]
Affiliation(s)
- Harish Garg
- School of Mathematics Thapar Institute of Engineering and Technology Deemed University Patiala Punjab India
| |
Collapse
|
5
|
Paulraj S, Tamilarasi G. Generalized ordered weighted harmonic averaging operator with trapezoidal neutrosophic numbers for solving MADM problems. JOURNAL OF AMBIENT INTELLIGENCE AND HUMANIZED COMPUTING 2021; 13:4089-4102. [PMID: 34659583 PMCID: PMC8503884 DOI: 10.1007/s12652-021-03509-x] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 02/04/2021] [Accepted: 09/13/2021] [Indexed: 06/13/2023]
Abstract
Harmonic mean is suitable for algebraic calculation and other mathematical treatments and also suitable for directly aggregated negative indicators. In many different situations, harmonic mean improves the flexibility. In this paper, we develop some new aggregation operators under neutrosophic environment and apply with multi attribute decision making (MADM) problems. First, we provide a Single valued trapezoidal neutrosophic Generalized ordered weighted harmonic averaging(SVTNGOWHA) operator which is the extension of single valued trapezoidal neutrosophic ordered weighted harmonic averaging (SVTNOWHA) operator. To fix the operators on the mount, we have tested these methods in few illustrative examples, and the results have been presented.
Collapse
Affiliation(s)
- S. Paulraj
- Department of Mathematics, College of Engineering Guindy, Anna University, Chennai, Tamil Nadu 600025 India
| | - G. Tamilarasi
- Department of Mathematics, College of Engineering Guindy, Anna University, Chennai, Tamil Nadu 600025 India
| |
Collapse
|
6
|
Riaz M, Farid HMA, Karaaslan F, Hashmi MR. Some q-rung orthopair fuzzy hybrid aggregation operators and TOPSIS method for multi-attribute decision-making. JOURNAL OF INTELLIGENT & FUZZY SYSTEMS 2020. [DOI: 10.3233/jifs-192114] [Citation(s) in RCA: 28] [Impact Index Per Article: 7.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022]
Affiliation(s)
- Muhammad Riaz
- Department of Mathematics, University of the Punjab, Lahore, Pakistan
| | | | - Faruk Karaaslan
- Department of Mathematics, Çankırı Karatekin University, Çankırı, Turkey
| | | |
Collapse
|
7
|
Pratihar J, Kumar R, Edalatpanah SA, Dey A. Modified Vogel’s approximation method for transportation problem under uncertain environment. COMPLEX INTELL SYST 2020. [DOI: 10.1007/s40747-020-00153-4] [Citation(s) in RCA: 12] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/24/2022]
Abstract
AbstractThe fuzzy transportation problem is a very popular, well-known optimization problem in the area of fuzzy set and system. In most of the cases, researchers use type 1 fuzzy set as the cost of the transportation problem. Type 1 fuzzy number is unable to handle the uncertainty due to the description of human perception. Interval type 2 fuzzy set is an extended version of type 1 fuzzy set which can handle this ambiguity. In this paper, the interval type 2 fuzzy set is used in a fuzzy transportation problem to represent the transportation cost, demand, and supply. We define this transportation problem as interval type 2 fuzzy transportation problems. The utility of this type of fuzzy set as costs in transportation problem and its application in different real-world scenarios are described in this paper. Here, we have modified the classical Vogel’s approximation method for solved this fuzzy transportation problem. To the best of our information, there exists no algorithm based on Vogel’s approximation method in the literature for fuzzy transportation problem with interval type 2 fuzzy set as transportation cost, demand, and supply. We have used two Numerical examples to describe the efficiency of the proposed algorithm.
Collapse
|
8
|
The Generalized Neutrosophic Cubic Aggregation Operators and Their Application to Multi-Expert Decision-Making Method. Symmetry (Basel) 2020. [DOI: 10.3390/sym12040496] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/16/2022] Open
Abstract
In the modern world, the computation of vague data is a challenging job. Different theories are presented to deal with such situations. Amongst them, fuzzy set theory and its extensions produced remarkable results. Samrandache extended the theory to a new horizon with the neutrosophic set (NS), which was further extended to interval neutrosophic set (INS). Neutrosophic cubic set (NCS) is the generalized version of NS and INS. This characteristic makes it an exceptional choice to deal with vague and imprecise data. Aggregation operators are key features of decision-making theory. In recent times several aggregation operators were defined in NCS. The intent of this paper is to generalize these aggregation operators by presenting neutrosophic cubic generalized unified aggregation (NCGUA) and neutrosophic cubic quasi-generalized unified aggregation (NCQGUA) operators. The accuracy and precision are a vital tool to minimize the potential threat in decision making. Generally, in decision making methods, alternatives and criteria are considered to evaluate the better outcome. However, sometimes the decision making environment has more components to express the problem completely. These components are named as the state of nature corresponding to each criterion. This complex frame of work is dealt with by presenting the multi-expert decision-making method (MEDMM).
Collapse
|
9
|
Akram M, Bashir A. Complex fuzzy ordered weighted quadratic averaging operators. GRANULAR COMPUTING 2020. [DOI: 10.1007/s41066-020-00213-7] [Citation(s) in RCA: 17] [Impact Index Per Article: 4.3] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
|
10
|
Garg H. Novel neutrality aggregation operator-based multiattribute group decision-making method for single-valued neutrosophic numbers. Soft comput 2019. [DOI: 10.1007/s00500-019-04535-w] [Citation(s) in RCA: 22] [Impact Index Per Article: 4.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/25/2022]
|
11
|
Jiang D, Hasan MM, Faiz TI, Noor‐E‐Alam M. A possibility distribution‐based multicriteria decision algorithm for resilient supplier selection problems. JOURNAL OF MULTI-CRITERIA DECISION ANALYSIS 2019. [DOI: 10.1002/mcda.1696] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/11/2022]
Affiliation(s)
- Dizuo Jiang
- Department of Mechanical and Industrial EngineeringNortheastern University Boston Massachusetts
| | - Md. Mahmudul Hasan
- Department of Mechanical and Industrial EngineeringNortheastern University Boston Massachusetts
| | - Tasnim Ibn Faiz
- Department of Mechanical and Industrial EngineeringNortheastern University Boston Massachusetts
| | - Md. Noor‐E‐Alam
- Department of Mechanical and Industrial EngineeringNortheastern University Boston Massachusetts
| |
Collapse
|
12
|
Single-Valued Neutrosophic Power Shapley Choquet Average Operators and Their Applications to Multi-Criteria Decision-Making. MATHEMATICS 2019. [DOI: 10.3390/math7111081] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/17/2022]
Abstract
Single-valued neutrosophic sets (SVNSs), which involve in truth-membership, indeterminacy-membership and falsity-membership, play a significant role in describing the decision-makers’ preference information. In this study, a single-valued neutrosophic multi-criteria decision-making (MCDM) approach is developed based on Shapley fuzzy measures and power aggregation operator that takes a correlative relationship among criteria into account and also simultaneously reduces the effects of abnormal preference information. Firstly, two aggregation operators, namely, generalized weighted single-valued neutrosophic power Shapley Choquet average (GWSVNPSCA) operator and generalized weighted single-valued neutrosophic power Shapley Choquet geometric (GWSVNPSCG) operator, are accordingly defined, and the corresponding properties are discussed as well. Secondly, based on the proposed aggregation operators, an integrated MCDM approach is proposed to effectively solve single-valued neutrosophic problems where the weight information is incompletely known. A programming model is constructed to obtain the optimal Shapley fuzzy measure. Next, the proposed operators are utilized to aggregate the decision-makers’ preference information. Finally, a theoretical example with tourism attraction selection is provided to examine the efficacy of the developed approach, in which the results is found reasonable and credible.
Collapse
|
13
|
Luo S, Liang W, Zhao G. Linguistic neutrosophic power Muirhead mean operators for safety evaluation of mines. PLoS One 2019; 14:e0224090. [PMID: 31648224 PMCID: PMC6813029 DOI: 10.1371/journal.pone.0224090] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/11/2019] [Accepted: 10/04/2019] [Indexed: 11/18/2022] Open
Abstract
Safety is the fundamental guarantee for the sustainable development of mining enterprises. As the safety evaluation of mines is a complex system engineering project, consistent and inconsistent, even hesitant evaluation information may be contained simultaneously. Linguistic neutrosophic numbers (LNNs), as the extensions of linguistic terms, are effective means to entirely and qualitatively convey such evaluation information with three independent linguistic membership functions. The aim of our work is to investigate several mean operators so that the safety evaluation issues of mines are addressed under linguistic neutrosophic environment. During the safety evaluation process of mines, many influence factors should be considered, and some of them may interact with each other. To this end, the Muirhead mean (MM) operators are adopted as they are powerful tools to deal with such situation. On the other hand, to diminish the impacts of irrational data provided by evaluators, the power average (PA) operators are under consideration. Thus, with the combination of MM and PA, the power MM operators and weighted power MM operators are proposed to aggregate linguistic neutrosophic information. Meanwhile, some key points and special cases are studied. The advantages of these operators are that not only the interrelations among any number of inputs can be reflected, but also the effects of unreasonable information can be reduced. Thereafter, a new linguistic neutrosophic ranking technique based on these operators is developed to evaluate the mine safety. Moreover, in-depth discussions are made to show the robust and flexible abilities of our method. Results manifest that the proposed method is successful in dealing with mine safety evaluation issues within linguistic neutrosophic circumstances.
Collapse
Affiliation(s)
- Suizhi Luo
- College of Systems Engineering, National University of Defense Technology, Changsha, Hunan, China
| | - Weizhang Liang
- School of Resources and Safety Engineering, Central South University, Changsha, Hunan, China
- * E-mail:
| | - Guoyan Zhao
- School of Resources and Safety Engineering, Central South University, Changsha, Hunan, China
| |
Collapse
|
14
|
Tao HY, Zhao ML, Ye J. Some aggregation operators of Q-neutrosophic cubic sets for multi-attribute decision making. JOURNAL OF INTELLIGENT & FUZZY SYSTEMS 2019. [DOI: 10.3233/jifs-190116] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/05/2023]
Affiliation(s)
- Hong-Yu Tao
- Department of Civil Engineering,Shaoxing University, Huancheng West Road, Shaoxing, Zhejiang Province,P.R. China
| | - Mei-Ling Zhao
- Department of Electrical Engineering and Automation,Shaoxing University, Huancheng West Road, Shaoxing, Zhejiang Province,P.R. China
| | - Jun Ye
- Department of Electrical Engineering and Automation,Shaoxing University, Huancheng West Road, Shaoxing, Zhejiang Province,P.R. China
| |
Collapse
|
15
|
Rani D, Garg H. Some modified results of the subtraction and division operations on interval neutrosophic sets. J EXP THEOR ARTIF IN 2019. [DOI: 10.1080/0952813x.2019.1592236] [Citation(s) in RCA: 19] [Impact Index Per Article: 3.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/26/2022]
Affiliation(s)
- Dimple Rani
- School of Mathematics, Thapar Institute of Engineering & Technology (Deemed University), Patiala, India
| | - Harish Garg
- School of Mathematics, Thapar Institute of Engineering & Technology (Deemed University), Patiala, India
| |
Collapse
|
16
|
Nancy, Garg H. A novel divergence measure and its based TOPSIS method for multi criteria decision-making under single-valued neutrosophic environment. JOURNAL OF INTELLIGENT & FUZZY SYSTEMS 2019. [DOI: 10.3233/jifs-18040] [Citation(s) in RCA: 41] [Impact Index Per Article: 8.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022]
Affiliation(s)
- Nancy
- School of Mathematics, Thapar Institute of Engineering & Technology (Deemed University), Patiala, Punjab, India
| | - Harish Garg
- School of Mathematics, Thapar Institute of Engineering & Technology (Deemed University), Patiala, Punjab, India
| |
Collapse
|
17
|
Some Root Level Modifications in Interval Valued Fuzzy Graphs and Their Generalizations Including Neutrosophic Graphs. MATHEMATICS 2019. [DOI: 10.3390/math7010072] [Citation(s) in RCA: 25] [Impact Index Per Article: 5.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/16/2022]
Abstract
Fuzzy graphs (FGs) and their generalizations have played an essential role in dealing with real-life problems involving uncertainties. The goal of this article is to show some serious flaws in the existing definitions of several root-level generalized FG structures with the help of some counterexamples. To achieve this, first, we aim to improve the existing definition for interval-valued FG, interval-valued intuitionistic FG and their complements, as these existing definitions are not well-defined; i.e., one can obtain some senseless intervals using the existing definitions. The limitations of the existing definitions and the validity of the new definitions are supported with some examples. It is also observed that the notion of a single-valued neutrosophic graph (SVNG) is not well-defined either. The consequences of the existing definition of SVNG are discussed with the help of examples. A new definition of SVNG is developed, and its improvement is demonstrated with some examples. The definition of an interval-valued neutrosophic graph is also modified due to the shortcomings in the current definition, and the validity of the new definition is proved. An application of proposed work is illustrated through a decision-making problem under the framework of SVNG, and its performance is compared with existing work.
Collapse
|
18
|
Generalized Cubic Intuitionistic Fuzzy Aggregation Operators Using t-Norm Operations and Their Applications to Group Decision-Making Process. ARABIAN JOURNAL FOR SCIENCE AND ENGINEERING 2018. [DOI: 10.1007/s13369-018-3532-4] [Citation(s) in RCA: 55] [Impact Index Per Article: 9.2] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 10/28/2022]
|
19
|
Multi-Criteria Decision-Making Method Based on Prioritized Muirhead Mean Aggregation Operator under Neutrosophic Set Environment. Symmetry (Basel) 2018. [DOI: 10.3390/sym10070280] [Citation(s) in RCA: 44] [Impact Index Per Article: 7.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/17/2022] Open
Abstract
The aim of this paper is to introduce some new operators for aggregating single-valued neutrosophic (SVN) information and to apply them to solve the multi-criteria decision-making (MCDM) problems. Single-valued neutrosophic set, as an extension and generalization of an intuitionistic fuzzy set, is a powerful tool to describe the fuzziness and uncertainty, and Muirhead mean (MM) is a well-known aggregation operator which can consider interrelationships among any number of arguments assigned by a variable vector. In order to make full use of the advantages of both, we introduce two new prioritized MM aggregation operators, such as the SVN prioritized MM (SVNPMM) and SVN prioritized dual MM (SVNPDMM) under SVN set environment. In addition, some properties of these new aggregation operators are investigated and some special cases are discussed. Furthermore, we propose a new method based on these operators for solving the MCDM problems. Finally, an illustrative example is presented to testify the efficiency and superiority of the proposed method by comparing it with the existing method.
Collapse
|