scholarly journals Measures of Probabilistic Neutrosophic Hesitant Fuzzy Sets and the Application in Reducing Unnecessary Evaluation Processes

Mathematics ◽  
2019 ◽  
Vol 7 (7) ◽  
pp. 649 ◽  
Author(s):  
Songtao Shao ◽  
Xiaohong Zhang
Keyword(s):  
Fuzzy Set ◽  
Information Needs ◽  
Distance Measure ◽  
Similarity Measures ◽  
Hesitant Fuzzy Set ◽  
Fuzzy Information ◽  
Entropy Measures ◽  
Subjective Factor ◽  
Measure Model ◽  
Definition Of

Distance measure and similarity measure have been applied to various multi-criteria decision-making environments, like talent selections, fault diagnoses and so on. Some improved distance and similarity measures have been proposed by some researchers. However, hesitancy is reflected in all aspects of life, thus the hesitant information needs to be considered in measures. Then, it can effectively avoid the loss of fuzzy information. However, regarding fuzzy information, it only reflects the subjective factor. Obviously, this is a shortcoming that will result in an inaccurate decision conclusion. Thus, based on the definition of a probabilistic neutrosophic hesitant fuzzy set (PNHFS), as an extended theory of fuzzy set, the basic definition of distance, similarity and entropy measures of PNHFS are established. Next, the interconnection among the distance, similarity and entropy measures are studied. Simultaneously, a novel measure model is established based on the PNHFSs. In addition, the new measure model is compared by some existed measures. Finally, we display their applicability concerning the investment problems, which can be utilized to avoid redundant evaluation processes.

Extended TOPSIS method based on the entropy measure and probabilistic hesitant fuzzy information and their application in decision support system

2021 ◽  
pp. 1-12
Author(s):  
Muhammad Naeem ◽  
Muhammad Ali Khan ◽  
Saleem Abdullah ◽  
Muhammad Qiyas ◽  
Saifullah Khan
Keyword(s):  
Decision Making ◽  
Fuzzy Set ◽  
Distance Measure ◽  
Group Decision ◽  
Hesitant Fuzzy Set ◽  
Entropy Measure ◽  
Fuzzy Information ◽  
Score Functions ◽  
Fuzzy Environment ◽  
Basic Operating

Probabilistic hesitant fuzzy Set (PHFs) is the most powerful and comprehensive idea to support more complexity than developed fuzzy set (FS) frameworks. In this paper, it can explain a novel, improved TOPSIS-based method for multi-criteria group decision-making (MCGDM) problem through the Probabilistic hesitant fuzzy environment, in which the weights of both experts and criteria are completely unknown. Firstly, we discuss the concept of PHFs, score functions and the basic operating laws of PHFs. In fact, to compute the unknown weight information, the generalized distance measure for PHFs was defined based on the Probabilistic hesitant fuzzy entropy measure. Second, MCGDM will be presented with the PHF information-based decision-making process.

scholarly journals Multi-Attribute Decision-Making Approach Based on Dual Hesitant Fuzzy Information Measures and Their Applications

Mathematics ◽  
2019 ◽  
Vol 7 (9) ◽  
pp. 786 ◽  
Author(s):  
Huiping Chen ◽  
Guiqiong Xu ◽  
Pingle Yang
Keyword(s):  
Decision Making ◽  
Fuzzy Set ◽  
Intuitionistic Fuzzy Set ◽  
Similarity Measures ◽  
Hesitant Fuzzy Set ◽  
Information Measures ◽  
Extended Technique ◽  
Dual Hesitant Fuzzy Set ◽  
Entropy Measures ◽  
Multi Attribute Decision Making

Combining the ideas and advantages of intuitionistic fuzzy set (IFS) and hesitant fuzzy set (HFS), dual hesitant fuzzy set (DHFS) could express uncertain and complex information given by decision makers (DMs) in a more flexible manner. By virtue of the existing measure methods, elements in DHFSs should be of equal length and thus some values must be added into the shorter elements according to the risk preference of DMs. The extension of values will increase the subjectivity of decision-making to some extent, and different extension methods may produce different results. In order to address this issue, we first propose several new forms of distance and similarity measures without adding values. Subsequently, according to the proposed distance and similarity measures, two entropy measures are presented from the viewpoints of complementary set and the fuzziest set, respectively. Furthermore, based on the new distance and entropy measures, an extended technique for order preference by similarity to an ideal solution (TOPSIS) method is proposed for dealing with multi-attribute decision-making problems in the context of DHFS. Finally, two practical examples are analyzed to show the validity and applicability of the proposed method.

scholarly journals Distance and Similarity Measures Including New Hesitant Degree on Hesitant Fuzzy Set

2019 ◽  
Vol 8 (4) ◽  
pp. 9117-9125
Keyword(s):  
Fuzzy Set ◽  
Satisfactory Result ◽  
Distance Measure ◽  
Real Life ◽  
Similarity Measures ◽  
Hesitant Fuzzy Set ◽  
Satisfactory Outcome

Hesitant degree plays an important role for finding the distance and similarity measures between two objects. Many researchers have developed many distance and similarity measures so far but in real life some situations arises where these measures fail to achieve the satisfactory result. In this paper, a new hesitant degree is introduced in the distance and similarity measures so that the limitations which are found can be easily handled with a satisfactory outcome. Finally, the validity of the proposed distance measure is illustrated with a suitable example..

scholarly journals Convexity of hesitant fuzzy sets based on aggregation functions

2020 ◽  
pp. 45-45
Author(s):  
Pedro Huidobro ◽  
Pedro Alonso ◽  
Vladimír Janis ◽  
Susana Montes
Keyword(s):  
Fuzzy Sets ◽  
Fuzzy Set ◽  
Fuzzy Optimization ◽  
Hesitant Fuzzy Set ◽  
Hesitant Fuzzy Sets ◽  
Geometric Properties ◽  
Aggregation Functions ◽  
Definition Of

Convexity is one of the most important geometric properties of sets and a useful concept in many fields of mathematics, like optimization. As there are also important applications making use of fuzzy optimization, it is obvious that the studies of convexity are also frequent. In this paper we have extended the notion of convexity for hesitant fuzzy sets in order to fulfill some necessary properties. Namely, we have found an appropriate definition of convexity for hesitant fuzzy sets on any ordered universe based on aggregation functions such that it is compatible with the intersection, that is, the intersection of two convex hesitant fuzzy sets is a convex hesitant fuzzy set and it fulfills the cut worthy property.

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.

Pythagorean Hesitant Fuzzy Information Aggregation and Their Application to Multi-Attribute Group Decision-Making Problems

2018 ◽  
Vol 29 (1) ◽  
pp. 154-171 ◽  
Author(s):  
Muhammad Sajjad Ali Khan ◽  
Saleem Abdullah ◽  
Asad Ali ◽  
Khaista Rahman
Keyword(s):  
Decision Making ◽  
Fuzzy Set ◽  
Group Decision ◽  
Information Aggregation ◽  
Weighted Averaging ◽  
Hesitant Fuzzy Set ◽  
Fuzzy Information ◽  
New Approach ◽  
Fuzzy Environment ◽  
Multidimensional Evaluation

Abstract In this paper, we introduce the concept of the Pythagorean hesitant fuzzy set (PHFS), which is the generalization of the intuitionistic hesitant fuzzy set under the restriction that the square sum of its membership degrees is ≤1. In decision making with PHFSs, aggregation operators play a key role because they can be used to synthesize multidimensional evaluation values represented as Pythagorean hesitant fuzzy values into collective values. Under PHFS environments, Pythagorean hesitant fuzzy ordered weighted averaging and Pythagorean fuzzy ordered weighted geometric operators are used to aggregate the Pythagorean hesitant fuzzy values. The main advantage of these operators is that they provide more accurate and valuable results. Furthermore, these operators are applied to decision-making problems in which experts provide their preferences in the Pythagorean hesitant fuzzy environment to show the validity, practicality, and effectiveness of the new approach. Finally, we compare the proposed approach to the existing methods.

scholarly journals A Novel Multi-Attribute Group Decision-Making Approach in the Framework of Proportional Dual Hesitant Fuzzy Sets

2019 ◽  
Vol 9 (6) ◽  
pp. 1232 ◽  
Author(s):  
Zia Bashir ◽  
Yasir Bashir ◽  
Tabasam Rashid ◽  
Jawad Ali ◽  
Wei Gao
Keyword(s):  
Decision Making ◽  
Fuzzy Sets ◽  
Group Decision Making ◽  
Fuzzy Set ◽  
Distance Measure ◽  
Group Decision ◽  
Traditional Approach ◽  
Hesitant Fuzzy Set ◽  
Flexible Tool ◽  
Dual Hesitant Fuzzy Set

Making decisions are very common in the modern socio-economic environments. However, with the increasing complexity of the social, today’s decision makers (DMs) face such problems in which they hesitate and irresolute to provide their views. To cope with these uncertainties, many generalizations of fuzzy sets are designed, among them dual hesitant fuzzy set (DHFS) is quite resourceful and efficient in solving problems of a more vague nature. In this article, a novel concept called proportional dual hesitant fuzzy set (PDHFS) is proposed to further improve DHFS. The PDHFS is a flexible tool composed of some possible membership values and some possible non-membership values along with their associated proportions. In the theme of PDHFS, the proportions of membership values and non-membership values are considered to be independent. Some basic operations, properties, distance measure and comparison method are studied for the proposed set. Thereafter, a novel approach based on PDHFSs is developed to solve problems for multi-attribute group decision-making (MAGDM) in a fuzzy situation. It is totally different from the traditional approach. Finally, a practical example is given in order to elaborate the proposed method for the selection of the best alternative and detailed comparative analysis is given in order to validate the practicality.

scholarly journals On Hesitant Fuzzy Reducible Weighted Bonferroni Mean and Its Generalized Form for Multicriteria Aggregation

2014 ◽  
Vol 2014 ◽  
pp. 1-10 ◽  
Author(s):  
Wei Zhou
Keyword(s):  
Fuzzy Set ◽  
Information Aggregation ◽  
Aggregation Operators ◽  
Research Topic ◽  
Hesitant Fuzzy Set ◽  
Model Parameters ◽  
Fuzzy Information ◽  
Real Situation ◽  
Bonferroni Mean ◽  
Special Cases

Due to convenience and powerfulness in dealing with vagueness and uncertainty of real situation, hesitant fuzzy set has received more and more attention and has been a hot research topic recently. To differently process and effectively aggregate hesitant fuzzy information and capture their interrelationship, in this paper, we propose the hesitant fuzzy reducible weighted Bonferroni mean (HFRWBM) and present its four prominent characteristics, namely, reductibility, monotonicity, boundedness, and idempotency. Then, we further investigate its generalized form, that is, the generalized hesitant fuzzy reducible weighted Bonferroni mean (GHFRWBM). Based on the discussion of model parameters, some special cases of the HFRWBM and GHFRWBM are studied in detail. In addition, to deal with the situation that multicriteria have connections in hesitant fuzzy information aggregation, a three-step aggregation approach has been proposed on the basis of the HFRWBM and GHFRWBM. In the end, we apply the proposed aggregation operators to multicriteria aggregation and give an example to illustrate our results.

scholarly journals Jaccard and Dice Similarity Measures Based on Novel Complex Dual Hesitant Fuzzy Sets and Their Applications

2020 ◽  
Vol 2020 ◽  
pp. 1-25
Author(s):  
Tahir Mahmood ◽  
Ubaid Ur Rehman ◽  
Zeeshan Ali ◽  
Ronnason Chinram
Keyword(s):  
Similarity Measure ◽  
Fuzzy Set ◽  
Real Life ◽  
Similarity Measures ◽  
Hesitant Fuzzy Set ◽  
The Novel ◽  
Dual Hesitant Fuzzy Set ◽  
Life Problems ◽  
Novel Approach ◽  
Operational Laws

Complex dual hesitant fuzzy set (CDHFS) is a combination of two modifications, called complex fuzzy set (CFS) and dual hesitant fuzzy set (DHFS). CDHFS makes two degrees, called membership valued and nonmembership valued in the form of a finite subset of a unit disc in the complex plane, and is a capable method to solve uncertain and unpredictable information in real-life problems. The goal of this study is to describe the notion of CDHFS and its operational laws. The novel approach of the complex interval-valued dual hesitant fuzzy set (CIvDHFS) and its fundamental laws are also described and defended with the help of an example. Further, the vector similarity measures (VSMs), weighted vector similarity measures (WVSMs), hybrid vector similarity measure, and weighted hybrid vector similarity measure are additionally explored. These similarity measures (SM) are applied to the environment of pattern recognition and medical diagnosis to assess the capability and feasibility of the interpreted measures. We additionally solved some numerical examples utilizing the established measures. We examine the dependability and validity of the proposed measures by comparing them with some existing measures. The advantages, comparative analysis, and graphical portrayal of the investigated interpreted measures and existing measures are additionally described in detail.

The distance measures and cross-entropy based on complex fuzzy sets and their application in decision making

2020 ◽  
Vol 39 (3) ◽  
pp. 3351-3374
Author(s):  
Peide Liu ◽  
Zeeshan Ali ◽  
Tahir Mahmood
Keyword(s):  
Decision Making ◽  
Fuzzy Sets ◽  
Similarity Measures ◽  
Decision Makers ◽  
Cross Entropy ◽  
Distance Measures ◽  
Fuzzy Information ◽  
Information Measures ◽  
Entropy Measures ◽  
Magdm Problems

The information measures (IMs) of complex fuzzy information are very useful tools in the areas of machine learning and decision making. In some multi-attribute group decision making (MAGDM) problems, the decision makers can make a decision mostly according to IMs such as similarity measures (SMs), distance measures (DIMs), entropy measures (EMs) and cross-entropy measures (C-EMs) in order to choose the best one. However, the relation between C-EMs and DIMs in the environment of complex fuzzy sets (CFSs) has not been developed and verified. In this manuscript, the notions of DIMs and C-EMs in the environment of CFSs are investigated and the relation between DIMs and EMs in the environment of CFSs is also discussed. The complex fuzzy discrimination measures (CFDMs), the complex fuzzy cross-entropy measures (CFC-EMs), and the symmetry complex fuzzy cross-entropy measures (SCFC-EMs) are proposed. We also examined that the C-EMs satisfied all the conditions of DIMs, and finally proved that C-EMs including CFC-EMs were also a DIMs. In last, we used some practical examples to illustrate the validity and superiority of the proposed method by comparing with other existing methods.

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