scholarly journals Interval valued neutrosophic sets and multi-attribute decision-making based on generalized weighted aggregation operator

2015 ◽  
Vol 29 (6) ◽  
pp. 2697-2706 ◽  
Author(s):  
Zhao Aiwu ◽  
Du Jianguo ◽  
Guan Hongjun
Keyword(s):  
Decision Making ◽  
Aggregation Operator ◽  
Neutrosophic Sets ◽  
Multi Attribute Decision Making ◽  
Interval Valued

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.

Diagnosis of lumbar degenerative disc disease by using Lp-spaces related to generalized interval-valued m-polar neutrosophic choquet integral Operator

2021 ◽  
pp. 2150063
Author(s):  
Masooma Raza Hashmi ◽  
Muhammad Riaz
Keyword(s):  
Choquet Integral ◽  
Score Function ◽  
Aggregation Operator ◽  
Disc Disease ◽  
Neutrosophic Sets ◽  
Lumbar Degenerative Disc Disease ◽  
Degenerative Disc ◽  
Ranking Index ◽  
Interval Valued

Innovative and astonishing developments in the field of spine analysis can commence with this manuscript. The lumbar disks ([Formula: see text] to [Formula: see text]) are most commonly impaired by degeneration due to their long-standing degeneration and associated strain. We investigate the indications, purposes, risk factors, and therapies of lumbar degenerated disc disease (L-DDD). We assume that the degeneration of five discs creates many effects, making it difficult to differentiate between the different types of degenerated discs and their seriousness. Since the indeterminacy and falsity portions of science or clinical diagnosis are often ignored. Due to this complexity, the reliability of the patient’s progress report cannot be calculated, nor can the period of therapy be measured. The revolutionary concept of interval-valued m-polar neutrosophic Choquet integral aggregation operator (IVmPNCIAO) is proposed to eliminate these problems. We associate generalized interval-valued m-polar neutrosophic Choquet integral aggregation operator (GIVmPNCIAO) with the statistical formulation of [Formula: see text]-spaces and use it to identify the actual kind of degenerative disc in the lumbar spine. For the classification of interval-valued m-polar neutrosophic numbers (IVMPNNs), we set the ranking index and score function. These concepts are appropriate and necessary in order to better diagnose degeneration by associating it with mathematical modeling. We construct a pre-diagnosis map based on the fuzzy interval [0,1] to classify the types of degenerative discs. We develop an algorithm by using GIVmPNCIAO based on interval-valued m-polar neutrosophic sets (IVMPNNs) to identify the degenerative disc appropriately and to choose the most exquisite treatment for the corresponding degeneration of every patient. Furthermore, we discuss the sensitivity analysis with parameter [Formula: see text] in GIVmPNCIAO to investigate the patient’s improvement record.

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.

scholarly journals Hybrid Weighted Arithmetic and Geometric Aggregation Operator of Neutrosophic Cubic Sets for MADM

Symmetry ◽  
2019 ◽  
Vol 11 (2) ◽  
pp. 278 ◽  
Author(s):  
Lilian Shi ◽  
Yue Yuan
Keyword(s):  
Decision Making ◽  
Weighted Average ◽  
Aggregation Operator ◽  
Aggregation Operators ◽  
Arithmetic Average ◽  
Weighted Arithmetic ◽  
Geometric Average ◽  
Multi Attribute Decision Making

Neutrosophic cubic sets (NCSs) can express complex multi-attribute decision-making (MADM) problems with its interval and single-valued neutrosophic numbers simultaneously. The weighted arithmetic average (WAA) and geometric average (WGA) operators are common aggregation operators for handling MADM problems. However, the neutrosophic cubic weighted arithmetic average (NCWAA) and neutrosophic cubic geometric weighted average (NCWGA) operators may result in some unreasonable aggregated values in some cases. In order to overcome the drawbacks of the NCWAA and NCWGA, this paper developed a new neutrosophic cubic hybrid weighted arithmetic and geometric aggregation (NCHWAGA) operator and investigates its suitability and effectiveness. Then, we established a MADM method based on the NCHWAGA operator. Finally, a MADM problem with neutrosophic cubic information was provided to illustrate the application and effectiveness of the proposed method.

scholarly journals Generalized Distance-Based Entropy and Dimension Root Entropy for Simplified Neutrosophic Sets

Entropy ◽  
2018 ◽  
Vol 20 (11) ◽  
pp. 844 ◽  
Author(s):  
Wen-Hua Cui ◽  
Jun Ye
Keyword(s):  
Decision Making ◽  
Entropy Measure ◽  
Entropy Theory ◽  
Neutrosophic Sets ◽  
Numerical Example ◽  
Entropy Measures ◽  
Interval Valued ◽  
Generalized Distance

In order to quantify the fuzziness in the simplified neutrosophic setting, this paper proposes a generalized distance-based entropy measure and a dimension root entropy measure of simplified neutrosophic sets (NSs) (containing interval-valued and single-valued NSs) and verifies their properties. Then, comparison with the existing relative interval-valued NS entropy measures through a numerical example is carried out to demonstrate the feasibility and rationality of the presented generalized distance-based entropy and dimension root entropy measures of simplified NSs. Lastly, a decision-making example is presented to illustrate their applicability, and then the decision results indicate that the presented entropy measures are effective and reasonable. Hence, this study enriches the simplified neutrosophic entropy theory and measure approaches.

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