scholarly journals An Extension of TODIM with VIKOR approach based on Gini Simpson Index of Diversity under Picture fuzzy framework to Evaluate Opinion Polls

2021 ◽  
Vol 12 (3) ◽  
pp. 3715-3730
Author(s):  
Sunit Kumar Et.al
Keyword(s):  
Decision Making ◽  
Fuzzy Set ◽  
Hybrid Approach ◽  
Intuitionistic Fuzzy Set ◽  
Point Of View ◽  
Entropy Measure ◽  
Opinion Poll ◽  
Picture Fuzzy Set ◽  
Fuzzy Framework ◽  
Opinion Polls

Cuong and Kreinovich was the first who gives the idea of Picture fuzzy set (PFS), which is an extension of intuitionistic fuzzy set (IFS) by cosidering positive, negative and neutral membership of element. In this paper, we have been worked on new entropy measure of PFS from the probabilistic view point and it’s properties are examined from mathematical point of view. A hybrid aproach is presented with the assistance of TODIM (Portuguese abbreviation for Interactive Multi-Criteria Decision Making) and VIKOR (Vlsekriterijumska Optimizacija I Kompromisno Resenje) methods. Further, we applied it to MCDM (multi criterion decision making) problems with picture fuzzy numbers (PFNs), where the information about criteria synthetic weights is partially known and completely unknown and show its existence with the help of some practical cases. After getting the output, we are able to infer that the proposed hybrid approach is comparatively better so as to handle the uncertainty and vulnerabilities for the decision making problems. Based upon these two approaches we can determine the opinion poll of voting outcomes and then, we compare its result with other MCDM approaches that exists in the literature.

scholarly journals Bellman–Ford algorithm for solving shortest path problem of a network under picture fuzzy environment

2021 ◽  
Author(s):  
Mani Parimala ◽  
Said Broumi ◽  
Karthikeyan Prakash ◽  
Selçuk Topal
Keyword(s):  
Decision Making ◽  
Shortest Path ◽  
Fuzzy Set ◽  
Intuitionistic Fuzzy Set ◽  
Shortest Path Problem ◽  
Point Of View ◽  
The Novel ◽  
Fuzzy Environment ◽  
Picture Fuzzy Set ◽  
Decision Making Problem

AbstractAn elongation of the novel intuitionistic fuzzy set is a picture fuzzy set theory. The demonstration of this has been used to deal with the abstinence criteria in a decision-making problem. The uncertainty in nature occurs sometimes in real-world problems and amidst them, the prominent one is the shortest path problem (SPP) solving. In the last few years, one of the best algorithms on the network for finding SPP is Bellman–Ford. Due to uncertainty in the decision-making process, it becomes difficult for decision-makers for communicating their point of view and judgment with certainty. We conceive of SPP in this contribution via Bellman's algorithm (BA) for a network with trapezoidal picture fuzzy numbers (TPFNs). We introduce a new algorithm to stand the shortest picture fuzzy path between each pair of nodes. A TPFN is considered for the length of all edges. A numerical example for the validation of the presented algorithm has also been proposed. There has also been relative research with existing techniques showing the benefits of the new algorithm.

scholarly journals Distance Based Entropy Measure of Interval-Valued Intuitionistic Fuzzy Sets and Its Application in Multicriteria Decision Making

2018 ◽  
Vol 2018 ◽  
pp. 1-10 ◽  
Author(s):  
Tabasam Rashid ◽  
Shahzad Faizi ◽  
Sohail Zafar
Keyword(s):  
Decision Making ◽  
Fuzzy Set ◽  
Distance Measure ◽  
Intuitionistic Fuzzy Set ◽  
Multicriteria Decision Making ◽  
Fuzzy Entropy ◽  
Entropy Measure ◽  
Multicriteria Decision ◽  
Intuitionistic Fuzzy ◽  
Interval Valued

Fuzzy entropy means the measurement of fuzziness in a fuzzy set and therefore plays a vital role in solving the fuzzy multicriteria decision making (MCDM) and multicriteria group decision making (MCGDM) problems. In this study, the notion of the measure of distance based entropy for uncertain information in the context of interval-valued intuitionistic fuzzy set (IVIFS) is introduced. The arithmetic and geometric average operators are firstly used to aggregate the interval-valued intuitionistic fuzzy information provided by the decision makers (DMs) or experts corresponding to each alternative, and then the fuzzy entropy of each alternative is calculated based on proposed distance measure. Several numerical examples are solved to demonstrate the application to MCDM and MCGDM problems to show the effectiveness of the proposed approach.

Some Measures of Picture Fuzzy Sets and Their Application

2017 ◽  
Vol 3 (2) ◽  
pp. 35
Author(s):  
Nguyen Van Dinh ◽  
Nguyen Xuan Thao
Keyword(s):  
Decision Making ◽  
Fuzzy Sets ◽  
Fuzzy Set ◽  
Distance Measure ◽  
Intuitionistic Fuzzy Set ◽  
Dissimilarity Measure ◽  
Intuitionistic Fuzzy ◽  
Picture Fuzzy Set ◽  
The Difference ◽  
Picture Fuzzy Sets

To measure the difference of two fuzzy sets (FSs) / intuitionistic sets (IFSs), we can use the distance measure and dissimilarity measure between fuzzy sets/intuitionistic fuzzy set. Characterization of distance/dissimilarity measure between fuzzy sets/intuitionistic fuzzy set is important as it has application in different areas: pattern recognition, image segmentation, and decision making. Picture fuzzy set (PFS) is a generalization of fuzzy set and intuitionistic set, so that it have many application. In this paper, we introduce concepts: difference between PFS-sets, distance measure and dissimilarity measure between picture fuzzy sets, and also provide  the formulas for determining these values. We also present an application of dissimilarity measures in the sample recognition problems, can also be considered a decision-making problem.

scholarly journals Evaluation of Investment Policy Based on Multi-Attribute Decision-Making Using Interval Valued T-Spherical Fuzzy Aggregation Operators

Symmetry ◽  
2019 ◽  
Vol 11 (3) ◽  
pp. 357 ◽  
Author(s):  
Kifayat Ullah ◽  
Nasruddin Hassan ◽  
Tahir Mahmood ◽  
Naeem Jan ◽  
Mazlan Hassan
Keyword(s):  
Decision Making ◽  
Fuzzy Set ◽  
Intuitionistic Fuzzy Set ◽  
Aggregation Operators ◽  
Weighted Averaging ◽  
Investment Policies ◽  
Picture Fuzzy Set ◽  
Fuzzy Aggregation ◽  
Multi Attribute Decision Making ◽  
Interval Valued

Expressing the measure of uncertainty, in terms of an interval instead of a crisp number, provides improved results in fuzzy mathematics. Several such concepts are established, including the interval-valued fuzzy set, the interval-valued intuitionistic fuzzy set, and the interval-valued picture fuzzy set. The goal of this article is to enhance the T-spherical fuzzy set (TSFS) by introducing the interval-valued TSFS (IVTSFS), which describes the uncertainty measure in terms of the membership, abstinence, non-membership, and the refusal degree. The novelty of the IVTSFS over the pre-existing fuzzy structures is analyzed. The basic operations are proposed for IVTSFSs and their properties are investigated. Two aggregation operators for IVTSFSs are developed, including weighted averaging and weighted geometric operators, and their validity is examined using the induction method. Several consequences of new operators, along with their comparative studies, are elaborated. A multi-attribute decision-making method in the context of IVTSFSs is developed, followed by a brief numerical example where the selection of the best policy, among a list of investment policies of a multinational company, is to be evaluated. The advantages of using the framework of IVTSFSs are described theoretically and numerically, hence showing the limitations of pre-existing aggregation operators.

An improved fuzzy TODIM method based on entropy measure under Intuitionistic Fuzzy Information

2021 ◽  
Vol 23 (05) ◽  
pp. 464-470
Author(s):  
Sunit Kumar ◽  
◽  
Satish Kumar ◽  
Keyword(s):  
Decision Making ◽  
Fuzzy Set ◽  
Intuitionistic Fuzzy Set ◽  
Score Function ◽  
Entropy Measure ◽  
Multi Criteria Decision Making ◽  
Fuzzy Information ◽  
Numerical Example ◽  
Intuitionistic Fuzzy ◽  
Todim Method

Intuitionistic fuzzy set (IFS) is one of the most extensive and important tool to accommodate more uncertainties than existing fuzzy set structures. In the present paper, we describe an improved entropy based on TODIM procedure for handling multi-criteria decision-making (MCDM) under IF setting and also the weight information is partially known. First, we study the basic notions and operating laws of IFSs, also the accuracy and score function of it. The new entropy has been proposed. Secondly, the IF information-based decision-making technique for MCDM is presented. Lastly, a numerical example is given related, to demonstrate that their results are credible and feasible.

scholarly journals Some Picture Fuzzy Dombi Heronian Mean Operators with Their Application to Multi-Attribute Decision-Making

Symmetry ◽  
2018 ◽  
Vol 10 (11) ◽  
pp. 593 ◽  
Author(s):  
Hongran Zhang ◽  
Runtong Zhang ◽  
Huiqun Huang ◽  
Jun Wang
Keyword(s):  
Decision Making ◽  
Fuzzy Set ◽  
Intuitionistic Fuzzy Set ◽  
Aggregation Operators ◽  
Fuzzy Decision Making ◽  
Good Ability ◽  
Picture Fuzzy Set ◽  
Fuzzy Aggregation ◽  
Multi Attribute Decision Making ◽  
Heronian Mean

As an extension of the intuitionistic fuzzy set (IFS), the recently proposed picture fuzzy set (PFS) is more suitable to describe decision-makers’ evaluation information in decision-making problems. Picture fuzzy aggregation operators are of high importance in multi-attribute decision-making (MADM) within a picture fuzzy decision-making environment. Hence, in this paper our main work is to introduce novel picture fuzzy aggregation operators. Firstly, we propose new picture fuzzy operational rules based on Dombi t-conorm and t-norm (DTT). Secondly, considering the existence of a broad and widespread correlation between attributes, we use Heronian mean (HM) information aggregation technology to fuse picture fuzzy numbers (PFNs) and propose new picture fuzzy aggregation operators. The proposed operators not only fuse individual attribute values, but also have a good ability to model the widespread correlation among attributes, making them more suitable for effectively solving increasingly complicated MADM problems. Hence, we introduce a new algorithm to handle MADM based on the proposed operators. Finally, we apply the newly developed method and algorithm in a supplier selection issue. The main novelties of this work are three-fold. Firstly, new operational laws for PFSs are proposed. Secondly, novel picture fuzzy aggregation operators are developed. Thirdly, a new approach for picture fuzzy MADM is proposed.

scholarly journals Shortest path algorithm of a network via spherical fuzzy digraphs

2021 ◽  
Author(s):  
Parimala Mani ◽  
◽  
Ibtesam Alshammari ◽  
Halimah Alshehri ◽  
◽  
...  
Keyword(s):  
Decision Making ◽  
Fuzzy Sets ◽  
Shortest Path ◽  
Fuzzy Set ◽  
Intuitionistic Fuzzy Set ◽  
Score Function ◽  
Fuzzy Graph ◽  
Shortest Path Algorithm ◽  
Picture Fuzzy Set ◽  
Choice Decision

Many extension and generalization of fuzzy sets have been introduced and studied in the literature. Picture fuzzy set acquired more concentration in the domain of decision making, as many real time circumstances might have choices of more than one and researchers are looking for optimum choice/decision. Spherical fuzzy digraph is a generalization of intuitionistic fuzzy set and fuzzy graph. In this paper, we redefine some preliminary operations of Spherical fuzzy graph and it is referred as spherical fuzzy digraph. We discuss some arithmetic operations and relations among spherical fuzzy digraph. We further proposed a method to solve a shortest path problem using score function.

scholarly journals Entropy Measures for Plithogenic Sets and Applications in Multi-Attribute Decision Making

Mathematics ◽  
2020 ◽  
Vol 8 (6) ◽  
pp. 965
Author(s):  
Shio Gai Quek ◽  
Ganeshsree Selvachandran ◽  
Florentin Smarandache ◽  
J. Vimala ◽  
Son Hoang Le ◽  
...  
Keyword(s):  
Decision Making ◽  
Fuzzy Set ◽  
Intuitionistic Fuzzy Set ◽  
Entropy Measure ◽  
Neutrosophic Sets ◽  
Entropy Measures ◽  
Decision Making Problem ◽  
Multi Attribute Decision Making ◽  
Definition Of ◽  
Attribute Value

Plithogenic set is an extension of the crisp set, fuzzy set, intuitionistic fuzzy set, and neutrosophic sets, whose elements are characterized by one or more attributes, and each attribute can assume many values. Each attribute has a corresponding degree of appurtenance of the element to the set with respect to the given criteria. In order to obtain a better accuracy and for a more exact exclusion (partial order), a contradiction or dissimilarity degree is defined between each attribute value and the dominant attribute value. In this paper, entropy measures for plithogenic sets have been introduced. The requirements for any function to be an entropy measure of plithogenic sets are outlined in the axiomatic definition of the plithogenic entropy using the axiomatic requirements of neutrosophic entropy. Several new formulae for the entropy measure of plithogenic sets are also introduced. The newly introduced entropy measures are then applied to a multi-attribute decision making problem related to the selection of locations.

scholarly journals Picture Fuzzy Geometric Aggregation Operators Based on a Trapezoidal Fuzzy Number and Its Application

Symmetry ◽  
2021 ◽  
Vol 13 (1) ◽  
pp. 119
Author(s):  
Minxia Luo ◽  
Huifeng Long
Keyword(s):  
Decision Making ◽  
Fuzzy Set ◽  
Fuzzy Number ◽  
Intuitionistic Fuzzy Set ◽  
Information Aggregation ◽  
Aggregation Operator ◽  
Aggregation Operators ◽  
Trapezoidal Fuzzy Number ◽  
Picture Fuzzy Set ◽  
Multi Attribute Decision Making

The picture fuzzy set is a generation of an intuitionistic fuzzy set. The aggregation operators are important tools in the process of information aggregation. Some aggregation operators for picture fuzzy sets have been proposed in previous papers, but some of them are defective for picture fuzzy multi-attribute decision making. In this paper, we introduce a transformation method for a picture fuzzy number and trapezoidal fuzzy number. Based on this method, we proposed a picture fuzzy multiplication operation and a picture fuzzy power operation. Moreover, we develop the picture fuzzy weighted geometric (PFWG) aggregation operator, the picture fuzzy ordered weighted geometric (PFOWG) aggregation operator and the picture fuzzy hybrid geometric (PFHG) aggregation operator. The related properties are also studied. Finally, we apply the proposed aggregation operators to multi-attribute decision making and pattern recognition.

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