Entropy Based Pythagorean Probabilistic Hesitant Fuzzy Decision Making Technique and Its Application for Fog-Haze Factor Assessment Problem

The Pythagorean probabilistic hesitant fuzzy set (PyPHFS) is an effective, generalized and powerful tool for expressing fuzzy information. It can cover more complex and more hesitant fuzzy evaluation information. Therefore, based on the advantages of PyPHFSs, this paper presents a new extended fuzzy TOPSIS method for dealing with uncertainty in the form of PyPHFS in real life problems. The paper is divided into three main parts. Firstly, the novel Pythagorean probabilistic hesitant fuzzy entropy measure is established using generalized distance measure under PyPHFS information to find out the unknown weights information of the attributes. The second part consists of the algorithm sets of the TOPSIS technique under PyPHFS environment, where the weights of criteria are completely unknown. Finally, in order to verify the efficiency and superiority of the proposed method, this paper applies some practical examples of the selection of the most critical fog-haze influence factor and makes a detailed comparison with other existing methods.

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

Journal of Intelligent & Fuzzy Systems ◽

10.3233/jifs-202700 ◽

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.

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A Novel Hybrid Fuzzy Grey TOPSIS Method: Supplier Evaluation of a Collaborative Manufacturing Enterprise

Applied Sciences ◽

10.3390/app9183770 ◽

2019 ◽

Vol 9 (18) ◽

pp. 3770 ◽

Cited By ~ 13

Author(s):

Yixiong Feng ◽

Zhifeng Zhang ◽

Guangdong Tian ◽

Amir Mohammad Fathollahi-Fard ◽

Nannan Hao ◽

...

Keyword(s):

Decision Making ◽

Comprehensive Evaluation ◽

Real Life ◽

Fuzzy Topsis ◽

Supplier Evaluation ◽

Manufacturing Enterprise ◽

Collaborative Manufacturing ◽

Life Problems ◽

Order Preference ◽

The Difference

Recently, there is of significant interest in developing multi-criteria decision making (MCDM) techniques with large applications for real-life problems. Making a reasonable and accurate decision on MCDM problems can help develop enterprises better. The existing MCDM methods, such as the grey comprehensive evaluation (GCE) method and the technique for order preference by similarity to an ideal solution (TOPSIS), have their one-sidedness and shortcomings. They neither consider the difference of shape and the distance of the evaluation sequence of alternatives simultaneously nor deal with the interaction that universally exists among criteria. Furthermore, some enterprises cannot consult the best professional expert, which leads to inappropriate decisions. These reasons motivate us to contribute a novel hybrid MCDM technique called the grey fuzzy TOPSIS (FGT). It applies fuzzy measures and fuzzy integral to express and integrate the interaction among criteria, respectively. Fuzzy numbers are employed to help the experts to make more reasonable and accurate evaluations. The GCE method and the TOPSIS are combined to improve their one-sidedness. A case study of supplier evaluation of a collaborative manufacturing enterprise verifies the effectiveness of the hybrid method. The evaluation result of different methods shows that the proposed approach overcomes the shortcomings of GCE and TOPSIS. The proposed hybrid decision-making model provides a more accurate and reliable method for evaluating the fuzzy system MCDM problems with interaction criteria.

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

Mathematical Problems in Engineering ◽

10.1155/2016/4274690 ◽

2016 ◽

Vol 2016 ◽

pp. 1-16 ◽

Cited By ~ 1

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.

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

Mathematical Problems in Engineering ◽

10.1155/2020/5920432 ◽

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.

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A New Approach to Fuzzy TOPSIS Method Based on Entropy Measure under Spherical Fuzzy Information

Entropy ◽

10.3390/e21121231 ◽

2019 ◽

Vol 21 (12) ◽

pp. 1231 ◽

Cited By ~ 11

Author(s):

Omar Barukab ◽

Saleem Abdullah ◽

Shahzaib Ashraf ◽

Muhammad Arif ◽

Sher Afzal Khan

Keyword(s):

Decision Making ◽

Fuzzy Set ◽

Distance Measure ◽

Fuzzy Topsis ◽

Decision Makers ◽

Entropy Measure ◽

Fuzzy Decision ◽

Fuzzy Information ◽

Comparative Results ◽

Robot Selection

Spherical fuzzy set (SFS) is one of the most important and extensive concept to accommodate more uncertainties than existing fuzzy set structures. In this article, we will describe a novel enhanced TOPSIS-based procedure for tackling multi attribute group decision making (MAGDM) issues under spherical fuzzy setting, in which the weights of both decision-makers (DMs) and criteria are totally unknown. First, we study the notion of SFSs, the score and accuracy functions of SFSs and their basic operating laws. In addition, defined the generalized distance measure for SFSs based on spherical fuzzy entropy measure to compute the unknown weights information. Secondly, the spherical fuzzy information-based decision-making technique for MAGDM is presented. Lastly, an illustrative example is delivered with robot selection to reveal the efficiency of the proposed spherical fuzzy decision support approach, along with the discussion of comparative results, to prove that their results are feasible and credible.

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Two-person game with hesitant fuzzy payoff: An application in MADM

RAIRO - Operations Research ◽

10.1051/ro/2021149 ◽

2021 ◽

Author(s):

Jishu Jana ◽

Sankar Kumar Roy

Keyword(s):

Decision Making ◽

Negative Impact ◽

Real Life ◽

Multiple Attribute Decision Making ◽

Hesitant Fuzzy Set ◽

Matrix Game ◽

Life Problems ◽

Multiple Attribute ◽

Fuzzy Payoff ◽

Person Game

Hesitant Fuzzy Set (HFS) permits the membership function having a collection of probable values which are more effective for modelling the real-life problems. Multiple Attribute Decision Making (MADM) process apparently assesses multiple conflicting attribute in decision making. In traditional decision making problems, each player is moving independently whereas in reality it is seen that each player aims to maximize personal profit which causes a negative impact on other player. MADM problem treats with candidate to the best alternative corresponding to the several attributes. Here, we present an MADM problem under hesitant fuzzy information and then transforming it into two-person matrix game, referred to herein as MADM game. The Technique for Order Preference by Similarity to Ideal Solution (TOPSIS) is one of the prominent approach for solving the MADM problems. In this work, we develop the TOPSIS based on Ordered Weighted Aggregation (OWA) operator and hybrid hesitant fuzzy normalized Euclidean distance. Then the two approaches, namely Hybrid Hesitant Fuzzy Ordered Weighted Aggregation-TOPSIS (HHFOWA-TOPSIS) and the Linear Programming Problem (LPP) are applied to solve the formulated MADM game. For solving MADM game, we apply LPP by considering the various values of $\alpha, \psi$, and HHFOWA-TOPSIS for finding the optimal alternative according to their scores. An investment selection problem is included to explain the feasibility and superiority of our formulated approaches. A comparison analysis is drawn among the obtained results which are derived from the two approaches. LPP and HHFOWA-TOPSIS provide the best alternative for the proposed problem. Finally, conclusions about our findings and outlooks are described.

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A Short Primer on the Correlation Coefficient of Vague Sets

International Journal of Fuzzy System Applications ◽

10.4018/ijfsa.2011040105 ◽

2011 ◽

Vol 1 (2) ◽

pp. 55-69 ◽

Cited By ~ 15

Author(s):

John Robinson P. ◽

Henry Amirtharaj E.C.

Keyword(s):

Fuzzy Sets ◽

Correlation Coefficient ◽

Real Life ◽

Detailed Comparison ◽

Intuitionistic Fuzzy Sets ◽

Vague Set ◽

Practical Applications ◽

Vague Sets ◽

Intuitionistic Fuzzy ◽

Life Problems

Intuitionistic fuzzy sets and vague sets are generalizations of the concept of fuzzy sets. Various researchers have studied the vagueness of data through vague sets, and it was later demonstrated that vague sets are indeed intuitionistic fuzzy sets. Since its entry in the literature, vague set theory has received increased attention. Many real life problems involve information in the form of vague values, due to the increasing complexity of the socio-economic environment and the vagueness of the inherent subjective nature of human thinking. Instead of using point-based membership as in fuzzy sets, interval-based membership is used in a vague set. This paper presents a detailed comparison between vague sets and intuitionistic fuzzy sets, from various perspectives of algebraic properties, graphical representations, and practical applications. Methods of calculating the correlation coefficient of intuitionistic fuzzy sets and interval-valued intuitionistic fuzzy sets are already found in the literature. This paper defines the correlation coefficient of vague sets through simple examples.

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

International Journal of Recent Technology and Engineering - 2 ◽

10.35940/ijrte.d8809.118419 ◽

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..

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