Sine Trigonometry Operational Laws for Complex Neutrosophic Sets and Their Aggregation Operators in Material Selection

We investigate the multiple attribute group material selection problems in which the attribute values take the form of interval 2-tuple linguistic information. Firstly, some operational laws and possibility degree of interval 2-tuple linguistic variables are introduced. Then, we develop some interval 2-tuple linguistic aggregation operators called interval 2-tuple hybrid harmonic mean (ITHHM) operator, induced interval 2-tuple ordered weighted harmonic mean (I-ITOWHM) operator, and induced interval 2-tuple hybrid harmonic mean (I-ITHHM) operator and study some desirable properties of the I-ITOWHM operator. In particular, all these operators can be reduced to aggregate 2-tuple linguistic variables. Based on the I-ITHHM and the ITWHM (interval 2-tuple weighted harmonic mean) operators, an approach to multiple attribute group decision-making with interval 2-tuple linguistic information is proposed. Finally, a practical application to material selection problem is given to verify the developed approach and to demonstrate its practicality and effectiveness.

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Decision Support Technique Based on Neutrosophic Yager Aggregation Operators: Application in Solar Power Plant Locations—Case Study of Bahawalpur, Pakistan

Mathematical Problems in Engineering ◽

10.1155/2020/6677676 ◽

2020 ◽

Vol 2020 ◽

pp. 1-21

Author(s):

Shabeer Khan ◽

Saleem Abdullah ◽

Shahzaib Ashraf ◽

Ronnason Chinram ◽

Samruam Baupradist

Keyword(s):

Decision Making ◽

Power Plant ◽

Power Plants ◽

Solar Power ◽

Multicriteria Decision Making ◽

Detailed Comparison ◽

Aggregation Operators ◽

Solar Power Plant ◽

Neutrosophic Sets ◽

Operational Laws

The problem of energy crisis and environmental pollution has been mitigated by the generation and use of solar power; however, the choice of locations for solar power plants is a difficult task because the decision-making process includes political, socio-economic, and environmental aspects. Thus, several adverse consequences have been created by the choice of suboptimal locations. The objective of this paper is to address the integrated qualitative and quantitative multicriteria decision-making framework for the selection of solar power plant locations. Neutrosophic sets (NSs) are the latest extension of the ordinary fuzzy sets. The main characteristic of the neutrosophic sets is satisfying the condition that the sum of the truth, indeterminacy, and falsity grades must be at least zero and at most three. In this research, we establish novel operational laws based on the Yager t-norm and t-conorm under neutrosophic environments (NE). Furthermore, based on these Yager operational laws, we develop a list of novel aggregation operators under NE. In addition, we design an algorithm to tackle the uncertainty to investigating the best solar power plant selection in five potential locations in Pakistan. A numerical example of solar power plant location problem is considered to show the supremacy and effectiveness of the proposed study. Also, a detailed comparison is constructed to evaluate the performance and validity of the established technique.

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Some Interval Neutrosophic Dombi Power Bonferroni Mean Operators and Their Application in Multi–Attribute Decision–Making

Symmetry ◽

10.3390/sym10100459 ◽

2018 ◽

Vol 10 (10) ◽

pp. 459 ◽

Cited By ~ 11

Author(s):

Qaisar Khan ◽

Peide Liu ◽

Tahir Mahmood ◽

Florentin Smarandache ◽

Kifayat Ullah

Keyword(s):

Decision Making ◽

Hybrid Structure ◽

Aggregation Operators ◽

Neutrosophic Sets ◽

Bonferroni Mean ◽

Operational Laws ◽

Multi Attribute Decision Making ◽

Geometric Bonferroni Mean ◽

Dombi Operations ◽

The Impact

The power Bonferroni mean (PBM) operator is a hybrid structure and can take the advantage of a power average (PA) operator, which can reduce the impact of inappropriate data given by the prejudiced decision makers (DMs) and Bonferroni mean (BM) operator, which can take into account the correlation between two attributes. In recent years, many researchers have extended the PBM operator to handle fuzzy information. The Dombi operations of T-conorm (TCN) and T-norm (TN), proposed by Dombi, have the supremacy of outstanding flexibility with general parameters. However, in the existing literature, PBM and the Dombi operations have not been combined for the above advantages for interval-neutrosophic sets (INSs). In this article, we first define some operational laws for interval neutrosophic numbers (INNs) based on Dombi TN and TCN and discuss several desirable properties of these operational rules. Secondly, we extend the PBM operator based on Dombi operations to develop an interval-neutrosophic Dombi PBM (INDPBM) operator, an interval-neutrosophic weighted Dombi PBM (INWDPBM) operator, an interval-neutrosophic Dombi power geometric Bonferroni mean (INDPGBM) operator and an interval-neutrosophic weighted Dombi power geometric Bonferroni mean (INWDPGBM) operator, and discuss several properties of these aggregation operators. Then we develop a multi-attribute decision-making (MADM) method, based on these proposed aggregation operators, to deal with interval neutrosophic (IN) information. Lastly, an illustrative example is provided to show the usefulness and realism of the proposed MADM method. The developed aggregation operators are very practical for solving MADM problems, as it considers the interaction among two input arguments and removes the influence of awkward data in the decision-making process at the same time. The other advantage of the proposed aggregation operators is that they are flexible due to general parameter.

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Multi-Attribute Multi-Perception Decision-Making Based on Generalized T-Spherical Fuzzy Weighted Aggregation Operators on Neutrosophic Sets

Mathematics ◽

10.3390/math7090780 ◽

2019 ◽

Vol 7 (9) ◽

pp. 780 ◽

Cited By ~ 11

Author(s):

Quek ◽

Selvachandran ◽

Munir ◽

Mahmood ◽

Ullah ◽

...

Keyword(s):

Decision Making ◽

Set Theory ◽

Fuzzy Set ◽

Fuzzy Set Theory ◽

Aggregation Operators ◽

Neutrosophic Sets ◽

Operational Laws ◽

Fuzzy Aggregation ◽

Multi Attribute Decision Making ◽

Do So

The framework of the T-spherical fuzzy set is a recent development in fuzzy set theory that can describe imprecise events using four types of membership grades with no restrictions. The purpose of this manuscript is to point out the limitations of the existing intuitionistic fuzzy Einstein averaging and geometric operators and to develop some improved Einstein aggregation operators. To do so, first some new operational laws were developed for T-spherical fuzzy sets and their properties were investigated. Based on these new operations, two types of Einstein aggregation operators are proposed namely the Einstein interactive averaging aggregation operators and the Einstein interactive geometric aggregation operators. The properties of the newly developed aggregation operators were then investigated and verified. The T-spherical fuzzy aggregation operators were then applied to a multi-attribute decision making (MADM) problem related to the degree of pollution of five major cities in China. Actual datasets sourced from the UCI Machine Learning Repository were used for this purpose. A detailed study was done to determine the most and least polluted city for different perceptions for different situations. Several compliance tests were then outlined to test and verify the accuracy of the results obtained via our proposed decision-making algorithm. It was proved that the results obtained via our proposed decision-making algorithm was fully compliant with all the tests that were outlined, thereby confirming the accuracy of the results obtained via our proposed method.

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Algorithm for T-Spherical Fuzzy Multi-Attribute Decision Making Based on Improved Interactive Aggregation Operators

Symmetry ◽

10.3390/sym10120670 ◽

2018 ◽

Vol 10 (12) ◽

pp. 670 ◽

Cited By ~ 20

Author(s):

Harish Garg ◽

Muhammad Munir ◽

Kifayat Ullah ◽

Tahir Mahmood ◽

Naeem Jan

Keyword(s):

Decision Making ◽

Fuzzy Sets ◽

Intuitionistic Fuzzy Sets ◽

Aggregation Operators ◽

Neutrosophic Sets ◽

Counter Example ◽

Operational Laws ◽

Special Cases ◽

Multi Attribute Decision Making ◽

Picture Fuzzy Sets

The objective of this manuscript is to present some new, improved aggregation operators for the T-spherical fuzzy sets, which is an extension of the several existing sets, such as intuitionistic fuzzy sets, picture fuzzy sets, neutrosophic sets, and Pythagorean fuzzy sets. In it, some new, improved operational laws and their corresponding properties are studied. Further, based on these laws, we propose some geometric aggregation operators and study their various relationships. Desirable properties, as well as some special cases of the proposed operators, are studied. Then, based on these proposed operators, we present a decision-making approach to solve the multi-attribute decision-making problems. The reliability of the presented decision-making method is explored with the help of a numerical example and the proposed results are compared with several prevailing studies’ results. Finally, the superiority of the proposed approach is explained with a counter example to show the advantages of the proposed work.

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Approach to Multi-Attribute Decision-Making Methods for Performance Evaluation Process Using Interval-Valued T-Spherical Fuzzy Hamacher Aggregation Information

Axioms ◽

10.3390/axioms10030145 ◽

2021 ◽

Vol 10 (3) ◽

pp. 145

Author(s):

Yun Jin ◽

Zareena Kousar ◽

Kifayat Ullah ◽

Tahir Mahmood ◽

Nimet Yapici Pehlivan ◽

...

Keyword(s):

Decision Making ◽

Fuzzy Set ◽

Evaluation Process ◽

Aggregation Operators ◽

Weighted Averaging ◽

Membership Degree ◽

Operational Laws ◽

Multi Attribute Decision Making ◽

Interval Valued ◽

Do So

Interval-valued T-spherical fuzzy set (IVTSFS) handles uncertain and vague information by discussing their membership degree (MD), abstinence degree (AD), non-membership degree (NMD), and refusal degree (RD). MD, AD, NMD, and RD are defined in terms of closed subintervals of that reduce information loss compared to the T-spherical fuzzy set (TSFS), which takes crisp values from intervals; hence, some information may be lost. The purpose of this manuscript is to develop some Hamacher aggregation operators (HAOs) in the environment of IVTSFSs. To do so, some Hamacher operational laws based on Hamacher t-norms (HTNs) and Hamacher t-conorms (HTCNs) are introduced. Using Hamacher operational laws, we develop some aggregation operators (AOs), including an interval-valued T-spherical fuzzy Hamacher (IVTSFH) weighted averaging (IVTSFHWA) operator, an IVTSFH-ordered weighted averaging (IVTSFHOWA) operator, an IVTSFH hybrid averaging (IVTSFHHA) operator, an IVTSFH-weighted geometric (IVTSFHWG) operator, an IVTSFH-ordered weighted geometric (IVTSFHOWG) operator, and an IVTSFH hybrid geometric (IVTSFHHG) operator. The validation of the newly developed HAOs is investigated, and their basic properties are examined. In view of some restrictions, the generalization and proposed HAOs are shown, and a multi-attribute decision-making (MADM) procedure is explored based on the HAOs, which are further exemplified. Finally, a comparative analysis of the proposed work is also discussed with previous literature to show the superiority of our work.

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A Novel Multi-Criteria Group Decision-Making Approach Based on Bonferroni and Heronian Mean Operators under Hesitant 2-Tuple Linguistic Environment

Mathematics ◽

10.3390/math9131489 ◽

2021 ◽

Vol 9 (13) ◽

pp. 1489

Author(s):

Shahzad Faizi ◽

Wojciech Sałabun ◽

Nisbha Shaheen ◽

Atiq ur Rehman ◽

Jarosław Wątróbski

Keyword(s):

Decision Making ◽

Group Decision Making ◽

Group Decision ◽

Weighted Average ◽

Aggregation Operators ◽

Bonferroni Mean ◽

Operational Laws ◽

Geometric Bonferroni Mean ◽

The Individual ◽

Heronian Mean

Ambiguous and uncertain facts can be handled using a hesitant 2-tuple linguistic set (H2TLS), an important expansion of the 2-tuple linguistic set. The vagueness and uncertainty of data can be grabbed by using aggregation operators. Therefore, aggregation operators play an important role in computational processes to merge the information provided by decision makers (DMs). Furthermore, the aggregation operator is a potential mechanism for merging multisource data which is synonymous with cooperative preference. The aggregation operators need to be studied and analyzed from various perspectives to represent complex choice situations more readily and capture the diverse experiences of DMs. In this manuscript, we propose some valuable operational laws for H2TLS. These new operational laws work through the individual aggregation of linguistic words and the collection of translation parameters. We introduced a hesitant 2-tuple linguistic weighted average (H2TLWA) operator to solve multi-criteria group decision-making (MCGDM) problems. We also define hesitant 2-tuple linguistic Bonferroni mean (H2TLBM) operator, hesitant 2-tuple linguistic geometric Bonferroni mean (H2TLGBM) operator, hesitant 2-tuple linguistic Heronian mean (H2TLHM) operator, and a hesitant 2-tuple linguistic geometric Heronian mean (H2TLGHM) operator based on the novel operational laws proposed in this paper. We define the aggregation operators for addition, subtraction, multiplication, division, scalar multiplication, power and complement with their respective properties. An application example and comparison analysis were examined to show the usefulness and practicality of the work.

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Single-valued neutrosophic Einstein interactive aggregation operators with applications for material selection in engineering design: case study of cryogenic storage tank

Complex & Intelligent Systems ◽

10.1007/s40747-021-00626-0 ◽

2022 ◽

Author(s):

Hafiz Muhammad Athar Farid ◽

Muhammad Riaz

Keyword(s):

Engineering Design ◽

Design Process ◽

Material Selection ◽

Weighted Averaging ◽

Optimal Decision ◽

Smooth Approximation ◽

Neutrosophic Sets ◽

Cryogenic Storage ◽

Design Case Study ◽

Einstein Operations

AbstractSingle-valued neutrosophic sets (SVNSs) and their application to material selection in engineering design. Liquid hydrogen is a feasible ingredient for energy storage in a lightweight application due to its high gravimetric power density. Material selection is an essential component in engineering since it meets all of the functional criteria of the object. Materials selection is a time-consuming as well as a critical phase in the design process. Inadequate material(s) selection can have a detrimental impact on a manufacturer’s production, profitability, and credibility. Multi-criteria decision-making (MCDM) is an important tool in the engineering design process that deals with complexities in material selection. However, the existing MCDM techniques often produce conflicting results. To address such problems, an innovative aggregation technique is proposed for material selection in engineering design based on truthness, indeterminacy, and falsity indexes of SVNSs. Taking advantage of SVNSs and smooth approximation with interactive Einstein operations, single-valued neutrosophic Einstein interactive weighted averaging and geometric operators are proposed. Based on proposed AOs, a robust MCDM approach is proposed for material selection in engineering design. A practical application of the proposed MCDM approach for material selection of cryogenic storage containers is developed. Additionally, the authenticity analysis and comparison analysis are designed to discuss the validity and rationality of the optimal decision.

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A New Multi-Attribute Decision Making Method with Single-Valued Neutrosophic Graphs

10.54216/ijns.0110202 ◽

2020 ◽

pp. 76-86

Author(s):

admin admin ◽

◽

Wenhui Bai ◽

...

Keyword(s):

Decision Making ◽

Graph Theory ◽

Comparative Analysis ◽

Fuzzy Graph ◽

Neutrosophic Sets ◽

Inconsistent Information ◽

Operational Laws ◽

Engineering Economy ◽

Multi Attribute Decision Making

In most realistic situations, the theory and method of multi-attribute decision-making have been widely used in different fields, such as engineering, economy, management, military, and others. Although many studies in some extended fuzzy contexts have been explored with multi-attribute decision-making, it is widely recognized that single-valued neutrosophic sets can describe incomplete, indeterminate and inconsistent information more easier. In this paper, aiming at addressing multi-attribute decision-making problems with single-valued neutrosophic information, related models and multi-attribute decision-making approaches based on the fuzzy graph theory are studied. In specific, the notion of single-valued neutrosophic sets and graphs is firstly introduced together with several common operational laws. Then a multi-attribute decision making method based on single-valued neutrosophic graphs is established. Finally, an illustrative example and a comparative analysis are conducted to verify the feasibility and efficiency of the proposed method.

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Pythagorean probabilistic hesitant fuzzy aggregation operators and their application in decision-making

Kybernetes ◽

10.1108/k-11-2020-0747 ◽

2021 ◽

Vol ahead-of-print (ahead-of-print) ◽

Author(s):

Bushra Batool ◽

Saleem Abdullah ◽

Shahzaib Ashraf ◽

Mumtaz Ahmad

Keyword(s):

Decision Making ◽

Fuzzy Number ◽

Weighted Average ◽

Aggregation Operators ◽

Content Type ◽

Operational Laws ◽

Fuzzy Aggregation ◽

Emergency Decision Making ◽

Emergency Decision ◽

Established Technique

PurposeThis is mainly because the restrictive condition of intuitionistic hesitant fuzzy number (IHFN) is relaxed by the membership functions of Pythagorean probabilistic hesitant fuzzy number (PyPHFN), so the range of domain value of PyPHFN is greatly expanded. The paper aims to develop a novel decision-making technique based on aggregation operators under PyPHFNs. For this, the authors propose Algebraic operational laws using algebraic norm for PyPHFNs. Furthermore, a list of aggregation operators, namely Pythagorean probabilistic hesitant fuzzy weighted average (PyPHFWA) operator, Pythagorean probabilistic hesitant fuzzy weighted geometric (PyPHFWG) operator, Pythagorean probabilistic hesitant fuzzy ordered weighted average (PyPHFOWA) operator, Pythagorean probabilistic hesitant fuzzy ordered weighted geometric (PyPHFOWG) operator, Pythagorean probabilistic hesitant fuzzy hybrid weighted average (PyPHFHWA) operator and Pythagorean probabilistic hesitant fuzzy hybrid weighted geometric (PyPHFHWG) operator, are proposed based on the defined algebraic operational laws. Also, interesting properties of these aggregation operators are discussed in detail.Design/methodology/approachPyPHFN is not only a generalization of the traditional IHFN, but also a more effective tool to deal with uncertain multi-attribute decision-making problems.FindingsIn addition, the authors design the algorithm to handle the uncertainty in emergency decision-making issues. At last, a numerical case study of coronavirus disease 2019 (COVID-19) as an emergency decision-making is introduced to show the implementation and validity of the established technique. Besides, the comparison of the existing and the proposed technique is established to show the effectiveness and validity of the established technique.Originality/valuePaper is original and not submitted elsewhere.

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