scholarly journals An intuitionistic fuzzy extension of the CODAS-SORT method

2021 ◽  
Vol 16 ◽  
pp. 110-121
Author(s):  
Abir Ouhibi ◽  
◽  
Hela Moalla Frikha ◽  
Keyword(s):  
Decision Making ◽  
Fuzzy Sets ◽  
Supplier Selection ◽  
Decision Aid ◽  
Euclidean Distance ◽  
Hamming Distance ◽  
Intuitionistic Fuzzy Set ◽  
Multicriteria Decision Aid ◽  
Intuitionistic Fuzzy

Currently, an important issue in multi-criteria decision-making (MCDM) problems are vagueness and lack of precision of decision- -making information because of insufficient data and incapability of the decision maker to process the information. Intuitionistic fuzzy sets (IFS) are a solution to eliminate the vagueness and the uncertainty. While fuzzy sets (FS) deal with ambiguity and vagueness problem, IFSs have more advantages. Moreover, the CODAS-SORT method cannot handle the uncertainty and ambiguity of information provided by human judgments. The aim of this study is to develop an IF extension of CODAS-SORT combining this method with the IFS theory. To achieve this, we use the fuzzy weighted Euclidean distance and fuzzy weighted Hamming distance instead of the crisp distances. A case study of a supplier selection assessment is used to clarify the details of our proposed method. Keywords: multicriteria decision aid, sorting methods, CODAS-SORT, intuitionistic fuzzy set.

scholarly journals An Extended TODIM Method for Group Decision Making with the Interval Intuitionistic Fuzzy Sets

2015 ◽  
Vol 2015 ◽  
pp. 1-9 ◽  
Author(s):  
Yanwei Li ◽  
Yuqing Shan ◽  
Peide Liu
Keyword(s):  
Decision Making ◽  
Fuzzy Sets ◽  
Group Decision Making ◽  
Fuzzy Set ◽  
Group Decision ◽  
Hamming Distance ◽  
Intuitionistic Fuzzy Set ◽  
Intuitionistic Fuzzy Sets ◽  
Intuitionistic Fuzzy ◽  
Multiple Attribute

For a multiple-attribute group decision-making problem with interval intuitionistic fuzzy sets, a method based on extended TODIM is proposed. First, the concepts of interval intuitionistic fuzzy set and its algorithms are defined, and then the entropy method to determine the weights is put forward. Then, based on the Hamming distance and the Euclidean distance of the interval intuitionistic fuzzy set, both of which have been defined, function mapping is given for the attribute. Finally, to solve multiple-attribute group decision-making problems using interval intuitionistic fuzzy sets, a method based on extended TODIM is put forward, and a case that deals with the site selection of airport terminals is given to prove the method.

Complex intuitionistic fuzzy Maclaurin symmetric mean operators and its application to emergency program selection

2021 ◽  
pp. 1-22
Author(s):  
Riaz Ali ◽  
Saleem Abdullah ◽  
Shakoor Muhammad ◽  
Muhammad Naeem ◽  
Ronnason Chinram
Keyword(s):  
Decision Making ◽  
Fuzzy Sets ◽  
Fuzzy Set ◽  
Intuitionistic Fuzzy Set ◽  
Score Functions ◽  
Intuitionistic Fuzzy Numbers ◽  
Intuitionistic Fuzzy ◽  
Program Selection ◽  
Maclaurin Symmetric Mean ◽  
Complex Intuitionistic Fuzzy Set

Due to the indeterminacy and uncertainty of the decision-makers (DM) in the complex decision making problems of daily life, evaluation and aggregation of the information usually becomes a complicated task. In literature many theories and fuzzy sets (FS) are presented for the evaluation of these decision tasks, but most of these theories and fuzzy sets have failed to explain the uncertainty and vagueness in the decision making issues. Therefore, we use complex intuitionistic fuzzy set (CIFS) instead of fuzzy set and intuitionistic fuzzy set (IFS). A new type of aggregation operation is also developed by the use of complex intuitionistic fuzzy numbers (CIFNs), their accuracy and the score functions are also discussed in detail. Moreover, we utilized the Maclaurin symmetric mean (MSM) operator, which have the ability to capture the relationship among multi-input arguments, as a result, CIF Maclarurin symmetric mean (CIFMSM) operator and CIF dual Maclaurin symmetric mean (CIFDMSM) operator are presented and their characteristics are discussed in detail. On the basis of these operators, a MAGDM method is presented for the solution of group decision making problems. Finally, the validation of the propounded approach is proved by evaluating a numerical example, and by the comparison with the previously researched results.

scholarly journals The multicriteria group decision making FlowSort method under uncertainty

2021 ◽  
Vol 16 ◽  
pp. 122-139
Author(s):  
Fedia Daami Remad ◽  
◽  
Hela Moalla Frikha ◽  
Keyword(s):  
Decision Making ◽  
Group Decision Making ◽  
Decision Aid ◽  
Fuzzy Numbers ◽  
Group Decision ◽  
Multiple Criteria ◽  
Multicriteria Decision Aid ◽  
Intuitionistic Fuzzy Numbers ◽  
Intuitionistic Fuzzy ◽  
Multicriteria Group Decision Making

Crisp values are insufficient to model real-life situations and imprecise ideas are frequently represented in multicriteria decision aid analysis. In fact, it is difficult to treat the evaluation criteria precisely and to fix exact preferences rating. The triangular intuitionistic fuzzy numbers succeeded to treat this kind of ambiguity in a great deal of research than other forms of fuzzy representation functions. The field of sorting issues is an active research topic in the multiple criteria decision aid (MCDA). This study extended one of the sorting methods, FLOWSORT, for solving multiple criteria group decision-making problems. This extension described the preferences rating of alternatives as linguistic terms which can be easily expressed in triangular intuitionistic fuzzy numbers. To validate our extension, an illustrative example as well as an empirical comparison with other multi-criteria decision making methods is presented. Keywords: multicriteria group decision making, sorting problematic, intuitionistic fuzzy set, FlowSort method

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 New Distance Measure for Atanassov’s Intuitionistic Fuzzy Sets and Its Application in Decision Making

Symmetry ◽  
2018 ◽  
Vol 10 (10) ◽  
pp. 429 ◽  
Author(s):  
Di Ke ◽  
Yafei Song ◽  
Wen Quan
Keyword(s):  
Decision Making ◽  
Fuzzy Sets ◽  
Fuzzy Set ◽  
Distance Measure ◽  
Intuitionistic Fuzzy Set ◽  
Research Area ◽  
Intuitionistic Fuzzy Sets ◽  
Intuitionistic Fuzzy ◽  
The Difference ◽  
Atanassov’S Intuitionistic Fuzzy Sets

The intuitionistic fuzzy set introduced by Atanassov has greater ability in depicting and handling uncertainty. Intuitionistic fuzzy measure is an important research area of intuitionistic fuzzy set theory. Distance measure and similarity measure are two complementary concepts quantifying the difference and closeness of intuitionistic fuzzy sets. This paper addresses the definition of an effective distance measure with concise form and specific meaning for Atanassov’s intuitionistic fuzzy sets (AIFSs). A new distance measure for AIFSs is defined based on a distance measure of interval values and the transformation from AIFSs to interval valued fuzzy sets. The axiomatic properties of the new distance measure are mathematically investigated. Comparative analysis based in numerical examples indicates that the new distance measure is competent to quantify the difference between AIFSs. The application of the new distance measure is also discussed. A new method for multi-attribute decision making (MADM) is developed based on the technique for order preference by similarity to an ideal solution method and the new distance measure. Numerical applications indicate that the developed MADM method can obtain reasonable preference orders. This shows that the new distance measure is effective and rational from both mathematical and practical points of view.

Project investment decision based on VIKOR interval intuitionistic fuzzy set

2021 ◽  
pp. 1-9 ◽  
Author(s):  
Caichuan Wang ◽  
Jiajun Li
Keyword(s):  
Decision Making ◽  
Fuzzy Sets ◽  
Investment Decision ◽  
Intuitionistic Fuzzy Set ◽  
Reference Value ◽  
Intuitionistic Fuzzy Sets ◽  
Project Investment ◽  
Intuitionistic Fuzzy ◽  
Investment Decision Making ◽  
Decision Making Model

The decision on the investment project is to analyze the feasibility and rationality of the project plan from multiple angles. However, due to the limitations of the actual project investment decision-making, this paper proposes a group decision making method based multifunctional intuitively fuzzy VIKOR interval sets. Firstly, according to the established investment decision-making model, the first round of preliminary candidate project schemes is selected. According to the definition of interval intuitionistic fuzzy sets and the traditional VIKOR method, established the research method of this article, and the project investment decision-making model based on VIKOR interval intuitionistic fuzzy sets is established. Finally, the project schemes are sorted according to the closeness degree of schemes. The results show that when sorting each candidate by Qi value, A4 >  A3 >  A2 >  A1 can be obtained. Because Q4 = 0, Q3 = 0.31, the condition q3-q4 >  0.25 is satisfied. It is concluded that the method can not only meet the needs of actual decision-making, but also has strong operability and practicability. The research results have reference value and guiding significance for project investment decision-making, and can promote the sustainable development of the project.

A New Entropy Measurement for the Analysis of Uncertain Data in MCDA Problems Using Intuitionistic Fuzzy Sets and COPRAS Method

Axioms ◽  
2021 ◽  
Vol 10 (4) ◽  
pp. 335
Author(s):  
Parul Thakur ◽  
Bartłomiej Kizielewicz ◽  
Neeraj Gandotra ◽  
Andrii Shekhovtsov ◽  
Namita Saini ◽  
...  
Keyword(s):  
Decision Making ◽  
Fuzzy Sets ◽  
Uncertain Data ◽  
Intuitionistic Fuzzy Set ◽  
Entropy Method ◽  
Entropy Measure ◽  
Intuitionistic Fuzzy ◽  
Entropy Measurement ◽  
Decision Alternative ◽  
Copras Method

In this paper, we propose a new intuitionistic entropy measurement for multi-criteria decision-making (MCDM) problems. The entropy of an intuitionistic fuzzy set (IFS) measures uncertainty related to the data modelling as IFS. The entropy of fuzzy sets is widely used in decision support methods, where dealing with uncertain data grows in importance. The Complex Proportional Assessment (COPRAS) method identifies the preferences and ranking of decisional variants. It also allows for a more comprehensive analysis of complex decision-making problems, where many opposite criteria are observed. This approach allows us to minimize cost and maximize profit in the finally chosen decision (alternative). This paper presents a new entropy measurement for fuzzy intuitionistic sets and an application example using the IFS COPRAS method. The new entropy method was used in the decision-making process to calculate the objective weights. In addition, other entropy methods determining objective weights were also compared with the proposed approach. The presented results allow us to conclude that the new entropy measure can be applied to decision problems in uncertain data environments since the proposed entropy measure is stable and unambiguous.

MODELS FOR MULTIPLE ATTRIBUTE DECISION MAKING WITH INTUITIONISTIC FUZZY INFORMATION

2007 ◽  
Vol 15 (03) ◽  
pp. 285-297 ◽  
Author(s):  
Z. S. XU
Keyword(s):  
Decision Making ◽  
Fuzzy Sets ◽  
Membership Function ◽  
Fuzzy Set ◽  
Intuitionistic Fuzzy Set ◽  
Multiple Attribute Decision Making ◽  
Fuzzy Information ◽  
Attribute Weights ◽  
Intuitionistic Fuzzy ◽  
Multiple Attribute

The intuitionistic fuzzy set (IFS) characterized by a membership function and a non-membership function, was introduced by Atanassov [K. Atanassov, "Intuitionistic fuzzy sets", Fuzzy Sets and Systems 20 (1986) 87–96] as a generalization of Zadeh' fuzzy set [L. A. Zadeh, "Fuzzy Sets", Information and Control 8 (1965) 338–353] to deal with fuzziness and uncertainty. In this paper, we investigate the multiple attribute decision making (MADM) problems, in which the information about attribute weights is incomplete, and the attribute values are expressed in intuitionistic fuzzy numbers (IFNs). We first define the concept of intuitionistic fuzzy ideal solution (IFIS), and then, based on the IFIS and the distance measure, we establish some optimization models to derive the attribute weights. Furthermore, based on the developed models, we develop some procedures for the rankings of alternatives under different situations, and extend the developed models and procedures to handle the MADM problems with interval-valued intuitionistic fuzzy information. Finally, we give some illustrative examples to verify the effectiveness and practicability of the developed models and procedures.

scholarly journals Extended Fuzzy Sets and Their Applications

Mathematics ◽  
2021 ◽  
Vol 9 (7) ◽  
pp. 770
Author(s):  
Bahram Farhadinia ◽  
Francisco Chiclana
Keyword(s):  
Decision Making ◽  
Fuzzy Sets ◽  
Fuzzy Set ◽  
Intuitionistic Fuzzy Set ◽  
Score Function ◽  
Pythagorean Fuzzy Set ◽  
Intuitionistic Fuzzy ◽  
Algebraic Operations ◽  
Innovative Concept

This contribution deals with introducing the innovative concept of extended fuzzy set (E-FS), in which the S-norm function of membership and non-membership grades is less than or equal to one. The proposed concept not only encompasses the concept of the fuzzy set (FS), but it also includes the concepts of the intuitionistic fuzzy set (IFS), the Pythagorean fuzzy set (PFS) and the p-rung orthopair fuzzy set (p-ROFS). In order to explore the features of the E-FS concept, set and algebraic operations on E-FSs, average and geometric operations of E-FSs are studied and an E-FS score function is defined. The superiority of the E-FS concept is further confirmed with a score-based decision making technique in which the concepts of FS, IFS, PFS and p-ROFS do not make sense.

scholarly journals Algorithm for solving the decision-making problems based on correlation coefficients under cubic intuitionistic fuzzy information: a case study in watershed hydrological system

2021 ◽  
Author(s):  
Harish Garg ◽  
Gagandeep Kaur
Keyword(s):  
Decision Making ◽  
Fuzzy Sets ◽  
Correlation Coefficients ◽  
Mathematical Concept ◽  
Intuitionistic Fuzzy Sets ◽  
Fundamental Properties ◽  
Intuitionistic Fuzzy ◽  
Hydrological System ◽  
Interval Valued

AbstractCubic intuitionistic fuzzy sets (CIFSs) are a powerful and relevant medium for expressing imprecise information to solve the decision-making problems. The conspicuous feature of their mathematical concept is that it considers simultaneously the hallmarks of both the intuitionistic fuzzy sets (IFSs) and interval-valued IFSs. The present paper is divided into two parts: (i) defining the correlation measures for the CIFSs; (ii) introducing the decision-making algorithm for the CIFS information. Furthermore, few of the fundamental properties of these measures are examined in detail. Based on this, we define a novel algorithm to solve the multi-criteria decision-making process and illustrate numerical examples related to watershed’s hydrological geographical areas, global recruitment problem and so on. A contrastive analysis with several existing studies is also administered to test the effectiveness and verify the proposed method.

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