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.

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Special Issue: Algebraic Structures of Neutrosophic Triplets, Neutrosophic Duplets, or Neutrosophic Multisets, Vol. II

Enhancement of images with weak edges faces great challenges in imaging applications. In this study, the authors propose a novel image enhancement approach based on intuitionistic fuzzy sets. The proposed method first divides an image into sub-object and sub-background areas, and then successively implements new fuzzification, hyperbolisation, and defuzzification operations on each area. In this way, an enhanced image is obtained, where the visual quality of region of interest (ROI) is significantly improved. Several types of images are utilised to validate the proposed method with respect to the enhancement performance. Experimental results demonstrate that the proposed algorithm not only works more stably for different types of images, but also has better enhancement performance, in comparison to conventional methods. This is a great merit of such design for discerning specific ROIs.

https://ietresearch.onlinelibrary.wiley.com/doi/epdf/10.1049/iet-ipr.2016.0035

Image enhancement based on intuitionistic fuzzy sets theory

In this communication, a new two parametric intuitionistic fuzzy entropy has been introduced and validated. Some of the properties of the proposed measure are also discussed. In addition to this, a new multiple attribute decision-making (MADM) method based on weighted correlation coefficients and the proposed IF entropy is introduced. The necessity of proposed MADM method has been reasonably established. The method is effectively explained with the help of two numerical examples, and the performance is genuinely compared with some existing MADM methods in the literature. Attribute weights play an important role in the solution of MADM problem. In this paper, two methods of obtaining attributes weights are discussed.

A Novel Fuzzy Decision-Making Method Using Entropy Weights-Based Correlation Coefficients Under Intuitionistic Fuzzy Environment

Role of intuitionistic fuzzy sets (IFSs) in solving multiple attribute decision making (MADM) problem has been established by many researchers. Depending upon the situation, we need different types of entropies based on IFSs. In this paper, we have proposed a new two parametric intuitionistic fuzzy entropy in the settings of IFSs theory. Besides proving some major properties, the proposed entropy is genuinely compared with some other existing entropies in literature. Based on the proposed entropy, a new method for solving MADM problems is introduced. Attribute weights play an eminent role in solving MADM problems. In this communication, two methods of determining the attribute weights are discussed. First is when information about attributes is completely unknown and second is when we have partial information regarding attribute weights. The two methods are effectively explained with the help of three examples. The attribute weights identification based on the proposed intuitionistic fuzzy entropy is offered in context of IFSs.

A New Parametric Intuitionistic Fuzzy Entropy and its Applications in Multiple Attribute Decision Making

The purpose of this paper is to identify critical equipment by dynamically ranking them in interval-valued intuitionistic fuzzy (IVIF) circumstances. Accordingly, the main drawbacks of the conventional failure mode and effects analysis (FMEA) are eliminated. To this end, the authors have presented the interval-valued intuitionistic fuzzy condition-based dynamic weighing method (IVIF-CBDW).,To realize the objective, the authors used the IVIF power weight Heronian aggregation operator to integrate the data extracted from the experts’ opinions. Moreover, the multi-attributive border approximation area comparison (MABAC) method is applied to rank the choices and the IVIF-CBDW method to create dynamic weights appropriate to the conditions of each equipment/failure mode. The authors proposed a robust FMEA model where the main drawbacks of the conventional risk prioritization number were eliminated.,To prove its applicability, this model was used in a case study to rank the equipment of a HL5000 crane barge. Finally, the results are compared with the traditional FMEA methods. It is indicated that the proposed model is much more flexible and provides more rational results.,In this paper, the authors have improved and used the IVIF power weight Heronian aggregation operator to integrate information. Furthermore, to dynamically weigh each equipment (failure mode), they presented the IVIF-CBDW method to determine the weight of each equipment (failure mode) based on its equipment conditions in the O, S and D criteria and provide the basis for the calculation. IVIF-CBDW method is presented in this study for the first time. Moreover, the MABAC method has been performed, to rank the equipment and failure mode. To analyze the information, the authors encoded the model presented in the robust MATLAB software and used it in a real sample of the HL5000 crane barge. Finally, to evaluate the reliability of the model presented in the risk ranking and its rationality, this model was compared with the conventional FMEA, fuzzy TOPSIS method, the method of Liu and the modified method of Liu.

Dynamic prioritization of equipment and critical failure modes: An interval-valued intuitionistic fuzzy condition-based model

We present a brief overview on Intuitionistic fuzzy sets which cuts across some definitions, operations, algebra, modal operators and normalization on Intuitionistic fuzzy set.

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S.O. Akowe

Papers

An Overview On Intuitionistic Fuzzy Sets