Multiattribute decision-making by logarithmic operational laws in interval neutrosophic environments

2022 ◽  
Author(s):  
Tipu Sultan Haque ◽  
Avishek Chakraborty ◽  
Hussam Alrabaiah ◽  
Shariful Alam
Keyword(s):  
Decision Making ◽  
Operational Laws

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

Axioms ◽  
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.

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

Mathematics ◽  
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.

scholarly journals TODIM Method for Multiple Attribute Group Decision Making under 2-Tuple Linguistic Neutrosophic Environment

Symmetry ◽  
2018 ◽  
Vol 10 (10) ◽  
pp. 486 ◽  
Author(s):  
Jie Wang ◽  
Guiwu Wei ◽  
Mao Lu
Keyword(s):  
Decision Making ◽  
Group Decision Making ◽  
Group Decision ◽  
New Method ◽  
Calculating Method ◽  
Fuzzy Environment ◽  
Operational Laws ◽  
Multiple Attribute ◽  
Todim Method ◽  
Magdm Problems

In this article, we extend the original TODIM (Portuguese acronym for Interactive Multi-Criteria Decision Making) method to the 2-tuple linguistic neutrosophic fuzzy environment to propose the 2TLNNs TODIM method. In the extended method, we use 2-tuple linguistic neutrosophic numbers (2TLNNs) to present the criteria values in multiple attribute group decision making (MAGDM) problems. Firstly, we briefly introduce the definition, operational laws, some aggregation operators and the distance calculating method of 2TLNNs. Then, the calculation steps of the original TODIM model are presented in simplified form. Thereafter, we extend the original TODIM model to the 2TLNNs environment to build the 2TLNNs TODIM model, our proposed method, which is more reasonable and scientific in considering the subjectivity of DM’s behaviors and the dominance of each alternative over others. Finally, a numerical example for the safety assessment of a construction project is proposed to illustrate the new method, and some comparisons are also conducted to further illustrate the advantages of the new method.

scholarly journals Dual Generalized Nonnegative Normal Neutrosophic Bonferroni Mean Operators and Their Application in Multiple Attribute Decision Making

Information ◽  
2018 ◽  
Vol 9 (8) ◽  
pp. 201 ◽  
Author(s):  
Jiongmei Mo ◽  
Han-Liang Huang
Keyword(s):  
Decision Making ◽  
Score Function ◽  
Information Aggregation ◽  
Multiple Attribute Decision Making ◽  
Ranking Method ◽  
Bonferroni Mean ◽  
Operational Laws ◽  
Multiple Attribute ◽  
Geometric Bonferroni Mean ◽  
Neutrosophic Number

For multiple attribute decision making, ranking and information aggregation problems are increasingly receiving attention. In a normal neutrosophic number, the ranking method does not satisfy the ranking principle. Moreover, the proposed operators do not take into account the correlation between any aggregation arguments. In order to overcome the deficiencies of the existing ranking method, based on the nonnegative normal neutrosophic number, this paper redefines the score function, the accuracy function, and partial operational laws. Considering the correlation between any aggregation arguments, the dual generalized nonnegative normal neutrosophic weighted Bonferroni mean operator and dual generalized nonnegative normal neutrosophic weighted geometric Bonferroni mean operator were investigated, and their properties are presented. Here, these two operators are applied to deal with a multiple attribute decision making problem. Example results show that the proposed method is effective and superior.

scholarly journals Fuzzy Linguistic Induced Ordered Weighted Averaging Operator and Its Application

2012 ◽  
Vol 2012 ◽  
pp. 1-10 ◽  
Author(s):  
Sidong Xian
Keyword(s):  
Decision Making ◽  
Group Decision Making ◽  
Group Decision ◽  
Weighted Averaging ◽  
Attribute Weights ◽  
Operational Laws ◽  
Multiple Attribute ◽  
Ordered Weighted Averaging Operator ◽  
Fuzzy Linguistic ◽  
Magdm Problems

With respect to multiple attribute group decision making (MAGDM) problems, in which the attribute weights take the form of real numbers, and the attribute values take the form of fuzzy linguistic scale variables, a decision analysis approach is proposed. In this paper, we develop a new fuzzy linguistic induce OWA (FLIOWA) operator and analyze the properties of it by utilizing some operational laws of fuzzy linguistic scale variables. A method based on the FLIOWA operators for multiple attribute group decision making is presented. Finally, a numerical example is used to illustrate the applicability and effectiveness of the proposed method.

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

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.

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

Kybernetes ◽  
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.

scholarly journals A Novel Approach towards Bipolar Soft Sets and Their Applications

2020 ◽  
Vol 2020 ◽  
pp. 1-11
Author(s):  
Tahir Mahmood
Keyword(s):  
Decision Making ◽  
Algebraic Structures ◽  
Soft Sets ◽  
New Approach ◽  
Basic Properties ◽  
Novel Approach ◽  
Operational Laws

The notion of bipolar soft sets has already been defined, but in this article, the notion of bipolar soft sets has been redefined, called T-bipolar soft sets. It is shown that the new approach is more close to the concept of bipolarity as compared to the previous ones, and further it is discussed that so far in the study of soft sets and their generalizations, the concept introduced in this manuscript has never been discussed earlier. We have also discussed the operational laws of T-bipolar soft sets and their basic properties. In the end, we have deliberated the algebraic structures associated with T-bipolar soft sets and the applications of T-bipolar soft sets in decision-making problems.

scholarly journals TOPSIS Method Based on Complex Spherical Fuzzy Sets with Bonferroni Mean Operators

Mathematics ◽  
2020 ◽  
Vol 8 (10) ◽  
pp. 1739
Author(s):  
Zeeshan Ali ◽  
Tahir Mahmood ◽  
Miin-Shen Yang
Keyword(s):  
Decision Making ◽  
Fuzzy Sets ◽  
Unit Interval ◽  
Polar Coordinates ◽  
Topsis Method ◽  
Bonferroni Mean ◽  
Operational Laws ◽  
Special Cases ◽  
Order Preference ◽  
Multi Attribute Decision Making

The theory of complex spherical fuzzy sets (CSFSs) is a mixture of two theories, i.e., complex fuzzy sets (CFSs) and spherical fuzzy sets (SFSs), to cope with uncertain and unreliable information in realistic decision-making situations. CSFSs contain three grades in the form of polar coordinates, e.g., truth, abstinence, and falsity, belonging to a unit disc in a complex plane, with a condition that the sum of squares of the real part of the truth, abstinence, and falsity grades is not exceeded by a unit interval. In this paper, we first consider some properties and their operational laws of CSFSs. Additionally, based on CSFSs, the complex spherical fuzzy Bonferroni mean (CSFBM) and complex spherical fuzzy weighted Bonferroni mean (CSFWBM) operators are proposed. The special cases of the proposed operators are also discussed. A multi-attribute decision making (MADM) problem was chosen to be resolved based on the proposed CSFBM and CSFWBM operators. We then propose the Technique for Order Preference by Similarity to an Ideal Solution (TOPSIS) method based on CSFSs (CSFS-TOPSIS). An application example is given to delineate the proposed methods and a close examination is undertaken. The advantages and comparative analysis of the proposed approaches are also presented.

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