scholarly journals Probabilistic Hesitant Fuzzy Recognition Method Based on Comprehensive Characteristic Distance Measure

2021 ◽  
Vol 2021 ◽  
pp. 1-16
Author(s):  
Ying Liu ◽  
Xin Guan
Keyword(s):  
Distance Measure ◽  
Comparison Method ◽  
Distance Measures ◽  
Hesitant Fuzzy Set ◽  
Recognition Method ◽  
Characteristic Distance ◽  
Multi Attribute Decision Making ◽  
Probabilistic Hesitant Fuzzy Element ◽  
Traditional Approaches ◽  
Fuzzy Recognition

The probabilistic hesitant fuzzy set (PHFS) and probabilistic hesitant fuzzy element (PHFE) have drawn the attention of scholars in recent years and have been applied in several disciplines. However, existing PHFE distance measures have several shortcomings. Therefore, in this study, we propose a new PHFE multi-attribute decision-making (MADM) method, based on the comprehensive characteristic distance measure. First, we devise a new PHFE comparison method and then define the comprehensive characteristic distance measure, based on four characteristics. Finally, based on the traditional TODIM method and prospect theory, we propose a new PHFE recognition method. The comprehensive characteristic distance measure avoids the introduction of errors, including an unequal number of elements and order adjustment. Meanwhile, the four characteristics make the measurement results more comprehensive and reasonable, and applicable to a variety of situations while avoiding counterintuitive phenomena. Compared with traditional approaches, the method in this article selects appropriate parameters according to actual situations to obtain more objective conclusions, which results in better flexibility and operability. Besides, the simulation results verify the effectiveness of this recognition method.

scholarly journals An Extended VIKOR Method for Multiple Attribute Decision Analysis with Bidimensional Dual Hesitant Fuzzy Information

2016 ◽  
Vol 2016 ◽  
pp. 1-16 ◽  
Author(s):  
Min Xue ◽  
Xiaoan Tang ◽  
Nanping Feng
Keyword(s):  
Decision Analysis ◽  
Fuzzy Set ◽  
Distance Measure ◽  
Intuitionistic Fuzzy Set ◽  
Distance Measures ◽  
Hesitant Fuzzy Set ◽  
Entropy Measure ◽  
Vikor Method ◽  
Multiple Attribute ◽  
Generalized Distance

Bidimensional dual hesitant fuzzy (BDHF) set is developed to present preferences of a decision maker or an expert, which is more objective than existing fuzzy sets such as Atanassov’s intuitionistic fuzzy set, hesitant fuzzy set, and dual hesitant fuzzy set. Then, after investigating some distance measures, we define a new generalized distance measure between two BDHF elements with parameterλfor the sake of overcoming some drawbacks in existing distance measures. Covering all possible values of parameterλ, a new approach is designed to calculate the generalized distance measure between two BDHF elements. In order to address complex multiple attribute decision analysis (MADA) problems, an extension of fuzzy VIKOR method in BDHF context is proposed in this paper. In VIKOR method for MADA problems, weight of each attribute indicates its relative importance. To obtain weights of attributes objectively, a new entropy measure with BDHF information is developed to create weight of each attribute. Finally, an evaluation problem of performance of people’s livelihood project in several regions is analyzed by the proposed VIKOR method to demonstrate its applicability and validity.

Multi-attribute decision-making method based on a novel distance measure of linguistic intuitionistic fuzzy sets

2021 ◽  
Vol 40 (1) ◽  
pp. 1147-1160
Author(s):  
Yali Cheng ◽  
Yonghong Li ◽  
Jie Yang
Keyword(s):  
Decision Making ◽  
Fuzzy Sets ◽  
Distance Measure ◽  
Intuitionistic Fuzzy Sets ◽  
Distance Measures ◽  
Intuitionistic Fuzzy ◽  
Multi Attribute Decision Making ◽  
Linguistic Intuitionistic Fuzzy Sets ◽  
Linguistic Scale Function ◽  
Different Response

Linguistic intuitionistic fuzzy sets can qualitatively rather than quantitatively express data in the form of membership degree. But quantitative tools are required to handle qualitative information. Therefore, an improved linguistic scale function, which can more accurately manifest the subjective feelings of decision-makers, is employed to deal with linguistic intuitionistic information. Subsequently, due to some commonly used distance measures do not comprehensively evaluate the information of linguistic intuitionistic fuzzy sets, an improved distance measure of linguistic intuitionistic fuzzy sets is designed. It considers the cross-evaluation information to get more realistic reasoning results. In addition, a new similarity measure defined by nonlinear Gaussian diffusion model is proposed, which can provide different response scales for different information between various schemes. The properties of these measures are also studied in detail. On this basis, a method in linguistic intuitionistic fuzzy environment is developed to handle multi-attribute decision-making problems. Finally, an illustrative example is given to demonstrate the effectiveness of the proposed method and the influence of the parameters is analyzed.

Several Generalized Interval-Valued 2-Tuple Linguistic Interval Distance Measures and Their Application

2017 ◽  
Vol 25 (05) ◽  
pp. 759-786 ◽  
Author(s):  
Fanyong Meng ◽  
Yige Yuan ◽  
Xiaohong Chen
Keyword(s):  
Decision Making ◽  
Distance Measure ◽  
Decision Makers ◽  
Distance Measures ◽  
Linguistic Variables ◽  
Weighting Vector ◽  
Interval Distance ◽  
Multi Attribute Decision Making ◽  
Optimal Weighting ◽  
Interval Valued

Interval-valued linguistic variables are efficient tools to express the decision makers’ uncertain qualitative judgments. Considering the application of interval-valued linguistic variables, this paper proposes an interval distance measure, which is then used to define interval-valued linguistic interval distance measures by combining the 2-tuple linguistic representation model. To reflect the interactions between elements in a set, three correlative interval distance measures on intervalvalued linguistic variables are proposed. Meanwhile, several models designed to obtain the optimal weighting vector are constructed. After that, an approach to pattern recognition and to multi-attribute decision making with interval-valued linguistic information is developed. Meanwhile, associated examples are offered to demonstrate the concrete application of the proposed procedure.

Intuitionistic Fuzzy Distance-Based Intuitionistic Fuzzy TOPSIS Method and Application to MADM

2017 ◽  
pp. 72-96
Author(s):  
Jiangxia Nan ◽  
Ting Wang ◽  
Jingjing An
Keyword(s):  
Distance Measure ◽  
Fuzzy Topsis ◽  
Distance Measures ◽  
Ideal Solution ◽  
Intuitionistic Fuzzy Numbers ◽  
Metric Properties ◽  
Fuzzy Distance ◽  
Intuitionistic Fuzzy ◽  
Multi Attribute Decision Making ◽  
Negative Ideal Solution

In this paper, an intuitionistic fuzzy (IF) distance measure between two triangular intuitionistic fuzzy numbers (TIFNs) is developed. The metric properties of the proposed IF distance measures are also studied. Then, based on the IF distance, an extended TOPSIS is developed to solve multi-attribute decision making (MADM) problems with the ratings of alternatives on attributes of TIFNs. In this methodology, the IF distances between each alternative and the TIFN positive ideal-solution are calculated as well as the TIFN negative ideal-solution. Then the relative closeness degrees obtained of each alternative to the TIFN positive ideal solution are TIFNs. Based on the ranking methods of TIFNs the alternatives are ranked. A numerical example is examined to the validity and practicability of the method proposed in this paper.

scholarly journals An innovative picture fuzzy distance measure and novel multi-attribute decision-making method

2021 ◽  
Author(s):  
Abdul Haseeb Ganie ◽  
Surender Singh
Keyword(s):  
Decision Making ◽  
Fuzzy Sets ◽  
Distance Measure ◽  
Real Data ◽  
Distance Measures ◽  
Classification Problems ◽  
Data Set ◽  
The Real ◽  
Picture Fuzzy Set ◽  
Multi Attribute Decision Making

AbstractPicture fuzzy set (PFS) is a direct generalization of the fuzzy sets (FSs) and intuitionistic fuzzy sets (IFSs). The concept of PFS is suitable to model the situations that involve more answers of the type yes, no, abstain, and refuse. In this study, we introduce a novel picture fuzzy (PF) distance measure on the basis of direct operation on the functions of membership, non-membership, neutrality, refusal, and the upper bound of the function of membership of two PFSs. We contrast the proposed PF distance measure with the existing PF distance measures and discuss the advantages in the pattern classification problems. The application of fuzzy and non-standard fuzzy models in the real data is very challenging as real data is always found in crisp form. Here, we also derive some conversion formulae to apply proposed method in the real data set. Moreover, we introduce a new multi-attribute decision-making (MADM) method using the proposed PF distance measure. In addition, we justify necessity of the newly proposed MADM method using appropriate counterintuitive examples. Finally, we contrast the performance of the proposed MADM method with the classical MADM methods in the PF environment.

scholarly journals A Decision-making Approach for Choosing a Reliable Product under the Hesitant Fuzzy Environment via a Novel Distance Measure

2020 ◽  
Vol 45 (3) ◽  
pp. 147-159
Author(s):  
Palash Dutta ◽  
Rupjit Saikia
Keyword(s):  
Decision Making ◽  
Distance Measure ◽  
Score Function ◽  
Distance Measures ◽  
Hesitant Fuzzy Set ◽  
Mean Deviation ◽  
Manufacturing Companies ◽  
Digital Products ◽  
Executive Summary ◽  
Fuzzy Environment

Executive Summary In the contemporary time, the reliability of any product has become a big issue from the customer’s perspective due to exponentially mushrooming markets of electronics and digital gadgets. Since the use of digital equipment is tremendously increasing, as a consequence, the production and availability of products are also increasing rampantly. Due to the flooding of digital products, customers often end up in a dilemma regarding the abundant choice and subsequently, become very much dependent upon the reviews of experts and fellow customers as well. In many cases, unfortunately, it is encountered that the products are not reliable enough as suggested by the reviewers. Besides, it is often seen that the manufacturing companies provide almost similar types of features and facilities for products and customers usually end up in a dilemma The confusion gets triggered when varieties of commodities are manufactured and supplied by different manufacturers bearing almost the same features nearly at the same price. In such situations, the reviews of experts and customers already using the product become essential. The reliability of a product relies upon the reviews of the previous customers of the same product. In this article, fuzzy multi-criteria decision-making methodology has been employed to find the reliability of a product considering different features of the product based on the reviews of customers and experts. This paper presents a neo distance measure on hesitant fuzzy set which is found on the notion of score function and mean deviation. Explanatory instances are provided to reveal the distinctiveness and merit of our proposed idea on distance measure over existing distance measures. After that, the proposed distance measure is applied in the decision-making approach for taking up the best electronic products. It is evidenced that the proposed distance measure is beneficial to measure distance degree between two unequal Hesitant Fuzzy Elements (HFEs) without putting extra elements in the shorter HFE. The proposed distance measures can be utilized in the decision-making field in the near future under diverse conditions to display undetermined particulars in a much-clarified manner.

Hesitant fuzzy C-means algorithm and its application in image segmentation†

2020 ◽  
Vol 39 (3) ◽  
pp. 3681-3695
Author(s):  
Wenyi Zeng ◽  
Rong Ma ◽  
Qian Yin ◽  
Xin Zheng ◽  
Zeshui Xu
Keyword(s):  
Image Segmentation ◽  
Fuzzy Set ◽  
Distance Measure ◽  
Hesitant Fuzzy Set ◽  
Natural Image ◽  
Membership Degree ◽  
Fuzzy C Means ◽  
Comprehensive Performance ◽  
Multi Attribute Decision Making ◽  
Fuzzy C Means Algorithm

Image segmentation plays an important role in many fields such as computer vision, pattern recognition, machine learning and so on. In recent years, many variants of standard fuzzy C-means (FCM) algorithm have been proposed to explore how to remove noise and reduce uncertainty. In fact, there are uncertainty on the boundary between different patches in images. Considering that hesitant fuzzy set is a useful tool to deal with uncertainty, in this paper, we merge hesitant fuzzy set with fuzzy C-means algorithm, introduce a new kind of method of fuzzification and defuzzification of image and the distance measure between hesitant fuzzy elements of pixels, present a method to establish hesitant membership degree of hesitant fuzzy element, and propose hesitant fuzzy C-means (HFCM) algorithm. Finally, we compare our proposed HFCM algorithm with some existing fuzzy C-means (FCM) algorithms, and apply HFCM algorithm in natural image, BSDS dataset image, different size images and multi-attribute decision making. These numerical examples illustrate the validity and applicability of our proposed algorithm including its comprehensive performance, reducing running time and almost without loss of accuracy.

scholarly journals Fuzzy Multi-Criteria Decision Making Algorithm under Intuitionistic Hesitant Fuzzy Set with Novel Distance Measure

2020 ◽  
Vol 5 (3) ◽  
pp. 473-487 ◽  
Author(s):  
Rupjit Saikia ◽  
Harish Garg ◽  
Palash Dutta
Keyword(s):  
Decision Making ◽  
Fuzzy Set ◽  
Distance Measure ◽  
Decision Makers ◽  
Distance Measures ◽  
Hesitant Fuzzy Set ◽  
Multi Criteria Decision Making ◽  
Crucial Issue ◽  
Decision Making Problem

Decision making under uncertainty is a crucial issue and most demanding area of research now a days. Intuitionistic hesitant fuzzy set plays important role in dealing with the circumstances in which decision makers judge an alternative with a collection membership grades and a collection of non-membership grades. This paper contributes a novel and advanced distance measure between Intuitionistic Hesitant fuzzy sets (IHFSs). A comparative analysis of the present distance measure with existing measures is performed first. Afterwards, a case study is carried in multi-criteria decision making problem to exhibit the applicability and rationality of the proposed distance measure. The advantage of the proposed distance measure over the existing distance measures is that in case of deficit number of elements in IHFs, a decision maker can evaluate distance measure without adding extra elements to make them equivalent and furthermore, it works in successfully in all the situations.

scholarly journals Probabilistic Single-Valued (Interval) Neutrosophic Hesitant Fuzzy Set and Its Application in Multi-Attribute Decision Making

Symmetry ◽  
2018 ◽  
Vol 10 (9) ◽  
pp. 419 ◽  
Author(s):  
Songtao Shao ◽  
Xiaohong Zhang ◽  
Yu Li ◽  
Chunxin Bo
Keyword(s):  
Decision Making ◽  
Fuzzy Set ◽  
Comparison Method ◽  
Weighted Averaging ◽  
Hesitant Fuzzy Set ◽  
Probability Interval ◽  
New Approach ◽  
Main Research ◽  
Multi Attribute Decision Making ◽  
Special Case

The uncertainty and concurrence of randomness are considered when many practical problems are dealt with. To describe the aleatory uncertainty and imprecision in a neutrosophic environment and prevent the obliteration of more data, the concept of the probabilistic single-valued (interval) neutrosophic hesitant fuzzy set is introduced. By definition, we know that the probabilistic single-valued neutrosophic hesitant fuzzy set (PSVNHFS) is a special case of the probabilistic interval neutrosophic hesitant fuzzy set (PINHFS). PSVNHFSs can satisfy all the properties of PINHFSs. An example is given to illustrate that PINHFS compared to PSVNHFS is more general. Then, PINHFS is the main research object. The basic operational relations of PINHFS are studied, and the comparison method of probabilistic interval neutrosophic hesitant fuzzy numbers (PINHFNs) is proposed. Then, the probabilistic interval neutrosophic hesitant fuzzy weighted averaging (PINHFWA) and the probability interval neutrosophic hesitant fuzzy weighted geometric (PINHFWG) operators are presented. Some basic properties are investigated. Next, based on the PINHFWA and PINHFWG operators, a decision-making method under a probabilistic interval neutrosophic hesitant fuzzy circumstance is established. Finally, we apply this method to the issue of investment options. The validity and application of the new approach is demonstrated.

scholarly journals Multi-Attribute Decision-Making Based on Preference Perspective with Interval Neutrosophic Sets in Venture Capital

Mathematics ◽  
2019 ◽  
Vol 7 (3) ◽  
pp. 257 ◽  
Author(s):  
Yanran Hong ◽  
Dongsheng Xu ◽  
Kaili Xiang ◽  
Han Qiao ◽  
Xiangxiang Cui ◽  
...  
Keyword(s):  
Decision Making ◽  
Venture Capital ◽  
Euclidean Distance ◽  
Distance Measure ◽  
Distance Measures ◽  
Neutrosophic Sets ◽  
Todim Method ◽  
Multi Attribute Decision Making ◽  
Parameter Interval ◽  
Interval Neutrosophic Sets

Fuzzy information in venture capital can be well expressed by neutrosophic numbers, and TODIM method is an effective tool for multi-attribute decision-making. The distance measure is an essential step in TODIM method. The keystone of this paper is to define several new distance measures, in particular the improved interval neutrosophic Euclidean distance, and these measures are applied in the TODIM method for multi-attribute decision-making. Firstly, the normalized generalized interval neutrosophic Hausdorff distance is defined and proved to be valid in this paper. Secondly, we define a weighted parameter interval neutrosophic distance and discuss whether different weight parameters affect the decision result based on TODIM method. Thirdly, considering the preference perspective of decision-makers in behavioral economics, we define the improved interval neutrosophic Euclidean distance with the known parameter of risk preference. Finally, an application example is given to compare the effects of different parameters on the result and discuss the feasibility of these two distance measures in TODIM method.

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