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2009 - 2009 IEEE 10th International Conference on Computer-Aided Industrial Design & Conceptual Design
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To identify the best alternative in multicriteria decision-making problems, a multicriteria fuzzy decision-making method based on the weighted correlation coefficient of interval-valued intuitionistic fuzzy sets (IVIFSs) is established in which criterion values for alternatives are IVIFSs and the criterion weights are known information. With the definition of ideal and anti-ideal weighted correlation coefficients, an objective function is constructed to derive the optimal evaluation for the weight of each alternative. The ranking of alternatives and the best one can be determined directly on the basis of the weights of alternatives. The evaluation process is simple and easy to use in practice. Finally, an illustrative example demonstrates the practicality and effectiveness of the proposed method.

2015 - Int. J. Artif. Intell. Tools
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Accurate segmentation of human brain image is an essential step for clinical study of magnetic resonance imaging (MRI) images. However, vagueness and other ambiguity present between the brain tissu...

2015 - OPSEARCH
Arithmetic operations on generalized intuitionistic fuzzy number and its applications to transportation problem

Intuitionistic fuzzy has always been a subject of keen interest, and a rigorous research has also been done on it. However, those research works were mainly based on normal intuitionistic fuzzy- a generalized approach to it could hardly be seen. So in this paper, we have developed a generalized intuitionistic fuzzy number and its arithmetic operations. It is a unique attempt made by us in which for the first time two basic generalized intuitionistic fuzzy numbers namely generalized trapezoidal and generalized triangular intuitionistic fuzzy numbers have been considered to serve the purpose. All arithmetic operations have been formulated on the basis of (α, β)-cut method, vertex method and extension principle method. Comparison among those three methods using an example is given and numerical results have been presented graphically. A new method is proposed to solve generalized intuitionistic fuzzy transportation problem (GIFTP) using ranking function. To validate the proposed method we have solved a GIFTP by assuming transportation cost, supply and demand of the product in generalized intuitionistic fuzzy numbers and the optimum results have been compared with the results of normal intuitionistic fuzzy transportation problem.

2021
Einstein Geometric Aggregation Operators using a Novel Complex Interval-valued Pythagorean Fuzzy Setting with Application in Green Supplier Chain Management

Zeeshan Ali , Tahir Mahmood1, Kifayat Ullah2, Qaisar Khan3 1 Department of Mathematics & Statistics, International Islamic University Islamabad, Pakistan, e-mail: zeeshanalinsr@gmail.com; tahirbakhat@iiu.edu.pk; 2 Department of Mathematics, Riphah International University, Lahore Campus, Pakistan, e-mail: kifayat.khan.dr@gmail.com; 3 Department of Mathematics, University of Huripur, Pakistan, e-mail: qaisar.khan@uoh.edu.pk;

2010 - Journal of Computer Information Systems
A multi-criteria group decision making procedure using interval-valued intuitionistic fuzzy sets

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2007 - IEEE Transactions on Fuzzy Systems
Aggregation Operators and Commuting

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2009 - Expert Systems With Applications
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2017 - Int. J. Uncertain. Fuzziness Knowl. Based Syst.
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This paper studies the conjugate functions related to main connectives of the Intervalvalued Atanassov’s Intuitionistic Fuzzy Logic. The relationships among automorphism classes are formalized by the ϕ-representability theorem, passing from automorphisms to interval-valued intuitionistic automorphisms, also visiting other two ones, intuitionistic automorphisms and interval-valued automorphisms. Additionally, the ϕ-conjugate of an interval-valued Atanassov’s intuitionistic fuzzy negation can be obtained either from an interval-valued fuzzy negation or from an Atanassov’s intuitionistic fuzzy negation, including a discussion presenting such reverse constructions. The ϕ-conjugate of an interval-valued Atanassov’s intuitionistic fuzzy negation not only preserves the main properties of its corresponding fuzzy negation but also of two other ones, the intuitionistic fuzzy negation and interval-valued fuzzy negation. Moreover, an extension of the intuitionistic fuzzy index as well as the correlation coefficient is discussed in terms of fuzzy negations, by considering the Atanassov’s Intuitionistic Fuzzy Logic.

2016 - Int. J. Uncertain. Fuzziness Knowl. Based Syst.
Additive Intuitionistic Fuzzy Aggregation Operators Based on Fuzzy Measure

Intuitionistic fuzzy sets can describe the uncertainty and complexity of the world flexibly, so it has been widely used in multi-attribute decision making. Traditional intuitionistic fuzzy aggregation operators are usually based on the probability measure, namely, they consider that the attributes of objects are independent. But in actual situations, it is difficult to ensure the independence of attributes, so these operators are unsuitable in such situations. Fuzzy measure is able to depict the relationships among the attributes more comprehensively, so it can complement the traditional probability measure in dealing with the multi-attribute decision making problems. In this paper, we first analyze the existing intuitionistic fuzzy operators based on fuzzy measure, then introduce two novel additive intuitionistic fuzzy aggregation operators based on the Shapley value and the Choquet integral, respectively, and show their advantages over other ones.

2008 - Soft Computing
Intuitionistic fuzzy left k-ideals of semirings

We introduce the notion of intuitionistic fuzzy left k-ideals of semirings and investigate their properties and connections with left k-ideals of the corresponding semirings. Next we give some important characterizations of intuitionistic fuzzy left k-ideals of different type and describe various methods of constructions of such intuitionistic fuzzy sets. Finally, we propose some natural classification of intuitionistic fuzzy left k-ideals.

2005 - WEC
Intuitionistic Fuzzy Ideals of BG-Algebras

Abstract — We consider the intuitionistic fuzzification of the concept of subalgebras and ideals in BG-algebras, and investigate some of their properties. Keywords — (Intuitionistic) fuzzy subalgebra, (Intuitionistic) fuzzy ideal, upper (respectively, lower) t-level cut, homomorphism.I. I NTRODUCTION FTER the introduction of the concept of fuzzy sets by Zadeh several researches were conducted on the generalizations of the notion of fuzzy sets. The idea of “ Intuitionistic fuzzy set “ was first published by Atanassov, as a generalization of the notion of the fuzzy set . In this paper, using the Atanssov’s idea, we establish the intuitionistic fuzzification of the concept of subalgebras and ideals in BG-algebras, and investigate some of their properties II. P ERLIMINARIES First we present the fundamental definitions. Definition 2.1. A BG-algebra is a non-empty set X with a constant 0 and a binary operating * satisfying the following axioms: ( )(x ) (0 ) ,for all , .( ) x 0 x,( ) 0,iii y y x x y

2018 - International Journal of Machine Learning and Cybernetics
An approach to interval-valued intuitionistic stochastic multi-criteria decision-making using set pair analysis

This paper proposes an approach to interval-valued intuitionistic stochastic multi-criteria decision-making (MCDM) problems using set pair analysis. This approach is applicable to MCDM problems in which the criterion weights are incomplete or the weights are certain, and evaluation values of alternatives take the form of interval-valued intuitionistic stochastic variables. To begin with, we briefly introduce the concepts of interval-valued intuitionistic fuzzy set, interval-valued intuitionistic stochastic variable, and set pair analysis. Then, we define a new similarity measure between interval-valued intuitionistic fuzzy numbers, after which we establish a mathematical programming model based on the technique for order preference by similarity to an ideal solution method and the maximizing deviation method in order to determine criterion weights. We then use connection degree to represent interval-valued intuitionistic fuzzy information and transform the interval-valued intuitionistic stochastic decision-making matrixes into corresponding connection degree matrixes. Finally, we rank the alternatives according to the value of set pair potential after calculating the connection degree of each alternative. After defining the method, we apply it to a practical decision-making problem and provide a comparison analysis with existing methods to illustrate the feasibility and validity of the proposed approach.

2007 - Systems engineering and electronics
Multiple attribute decision making method based on intuitionistic fuzzy sets

For the multiple attribute decision making in fuzzy conditions,a new multiple attribute decision making method based on intuitionistic fuzzy sets is proposed.First,geometrical illustration of intuitionistic fuzzy sets is presented,the distance between two intuitionistic fuzzy sets is defined,and the form to express the rating of alternatives in intuitionistic fuzzy sets is determined.Second,for the fuzzy environment in which data can not be completely determined,a multiple attribute decision making model based on intuitionistic fuzzy sets is established,the related definitions that fit the model are given,the concept of positive-ideal and negative-ideal schemes are put forward,combining the uncertainty of data as a solution to guaranteeing the exclusiveness of the scheme.Finally,the ranking order of the schemes is determined by comparing the distance between intuitionistic fuzzy sets and positive-ideal and negative-ideal schemes,and an example shows that the method is valid and correct.

2003 - 2004 2nd International IEEE Conference on 'Intelligent Systems'. Proceedings (IEEE Cat. No.04EX791)
Intuitionistic fuzzy graph interpretations of multi-person multi-criteria decision making

The generalized net (GNs) are extensions of the ordinary Petri nets and of the other Petri net modifications, while the intuitionistic fuzzy sets (TFSs) are extensions of the fuzzy sets. A GN-model of multi-person multi-criteria decision making process, basing on IF graphs, is constructed.

2007
On Similarity Measures of interval-valued Intuitionistic Fuzzy Sets and Their Application to Pattern Recognitions

The concept of the degree of similarity between interval-valued intuitionistic fuzzy sets (IVIFSs) is introduced, and some distance measures between IVIFSs are defined based on the Hamming distance, the normalized Hamming distance, the weighted Hamming distance, the Euclidean distance, the normalized Euclidean distance, and the weighted Euclidean distance, etc. Then, by combining the Hausdorff metric with the Hamming distance, the Euclidean distance and their weighted versions, two other similarity measures between IVIFSs, i. e., the weighted Hamming distance based on the Hausdorff metric and the weighted Euclidean distance based on the Hausdorff metric, are defined, and then some of their properties are studied. Finally, based on these distance measures, some similarity measures between IVIESs are defined, and the similarity measures are applied to pattern recognitions with interval-valued intuitionistic fuzzy information.

2019 - IEEE Transactions on Fuzzy Systems
Noise Robust Multiobjective Evolutionary Clustering Image Segmentation Motivated by the Intuitionistic Fuzzy Information

Images are always contaminated by noise, increasing uncertainty. Fuzzy set (FS) theory is a useful tool for dealing with uncertainty in images. When comparing with the FS, an intuitionistic fuzzy set (IFS) can better describe the blurred characteristic in images due to the membership, nonmembership, and hesitation degrees. However, when applied to an image segmentation, the IFS cannot completely overcome the influence of noise. With the aim of performing noisy image segmentation under several criteria, this paper defines a noise robust IFS (NR-IFS) for an image and then presents a novel noise robust multiobjective evolutionary intuitionistic fuzzy clustering algorithm (NR-MOEIFC). A majority dominated suppressed similarity measure using the neighborhood statistics and the competitive learning is proposed to obtain the NR-IFS representation for the image corrupted by noise. Then, the NR-IFS is fully used to motivate the whole process of multiobjective evolutionary clustering: first, computing a three-parameter intuitionistic fuzzy distance measure; second, constructing intuitionistic fuzzy fitness functions; third, designing a nonuniform intuitionistic fuzzy mutation operator; and forth, defining an intuitionistic fuzzy cluster validity index to select the optimal solution from the final nondominated solution set. The histogram statistics of NR-IFS are adopted in the NR-MOEIFC to greatly reduce the computational complexity. Experimental results on Berkeley and real magnetic resonance images reveal that the NR-MOEIFC behaves well in noise robustness and segmentation performance while requiring a low time cost.

2007 - Pattern Recognit. Lett.
Similarity measures between intuitionistic fuzzy (vague) sets: A comparative analysis

Existing similarity measures between intuitionistic fuzzy sets/vague sets are analyzed, compared and summarized by their counter-intuitive examples in pattern recognition. The positive aspects of each similarity measure are demonstrated, along with counter cases and discussion of the conditions under which each may not work as desired. The research presented here could benefit selection and applications of similarity measures for intuitionistic fuzzy sets and vague sets in practice.

2012 - Applied Mathematical Modelling
A multi-attribute group decision-making method based on weighted geometric aggregation operators of interval-valued trapezoidal fuzzy numbers

Abstract With respect to the multiple attribute group decision making problems in which the attribute values take the form of generalized interval-valued trapezoidal fuzzy numbers (GITFN), this paper proposed a decision making method based on weighted geometric aggregation operators. First, some operational rules, the distance and comparison between two GITFNs are introduced. Second, the generalized interval-valued trapezoidal fuzzy numbers weighted geometric aggregation (GITFNWGA) operator, the generalized interval-valued trapezoidal fuzzy numbers ordered weighted geometric aggregation (GITFNOWGA) operator, and the generalized interval-valued trapezoidal fuzzy numbers hybrid geometric aggregation (GITFNHGA) operator are proposed, and their various properties are investigated. At the same time, the group decision methods based on these operators are also presented. Finally, an illustrate example is given to show the decision-making steps and the effectiveness of this method.

2010 - Eur. J. Oper. Res.
Fuzzy decision-making method based on the weighted correlation coefficient under intuitionistic fuzzy environment

A multicriteria fuzzy decision-making method based on weighted correlation coefficients using entropy weights is proposed under intuitionistic fuzzy environment for some situations where the information about criteria weights for alternatives is completely unknown. To determine the entropy weights with respect to a set of criteria represented by intuitionistic fuzzy sets (IFSs), we establish an entropy weight model, which can be used to get the criteria weights, and then propose an evaluation formula of weighted correlation coefficient between an alternative and the ideal alternative. The alternatives can be ranked and the most desirable one(s) can be selected according to the weighted correlation coefficients. Finally, two illustrative examples demonstrate the practicality and effectiveness of the proposed method.

2008 - Inf. Sci.
Clustering algorithm for intuitionistic fuzzy sets

The intuitionistic fuzzy set (IFS) theory, originated by Atanassov [K. Atanassov, Intuitionistic fuzzy sets, Fuzzy Sets and Systems 20 (1986) 87-96], has been used in a wide range of applications, such as logic programming, medical diagnosis, pattern recognition, and decision making, etc. However, so far there has been little investigation of the clustering techniques of IFSs. In this paper, we define the concepts of association matrix and equivalent association matrix, and introduce some methods for calculating the association coefficients of IFSs. Then, we propose a clustering algorithm for IFSs. The algorithm uses the association coefficients of IFSs to construct an association matrix, and utilizes a procedure to transform it into an equivalent association matrix. The @l-cutting matrix of the equivalent association matrix is used to cluster the given IFSs. Moreover, we extend the algorithm to cluster interval-valued intuitionistic fuzzy sets (IVIFSs), and finally, demonstrate the effectiveness of our clustering algorithm by experimental results.

Some geometric aggregation operators based on intuitionistic fuzzy sets

Zeshui Xu
|
Ronald R. Yager
|
Zeshui Xu
|
R. Yager

Abstract:The weighted geometric (WG) operator and the ordered weighted geometric (OWG) operator are two common aggregation operators in the field of information fusion. But these two aggregation operators are usually used in situations where the given arguments are expressed as crisp numbers or linguistic values. In this paper, we develop some new geometric aggregation operators, such as the intuitionistic fuzzy weighted geometric (IFWG) operator, the intuitionistic fuzzy ordered weighted geometric (IFOWG) operator, and the intuitionistic fuzzy hybrid geometric (IFHG) operator, which extend the WG and OWG operators to accommodate the environment in which the given arguments are intuitionistic fuzzy sets which are characterized by a membership function and a non-membership function. Some numerical examples are given to illustrate the developed operators. Finally, we give an application of the IFHG operator to multiple attribute decision making based on intuitionistic fuzzy sets.

摘要：加权几何(WG)算子和有序加权几何(OWG)算子是信息融合领域中两种常见的聚集算子。但这两个聚合运算符通常用于给定参数以清晰的数字或语言值表示的情况。本文发展了一些新的几何聚集算子，如直觉模糊加权几何(IFWG)算子、直觉模糊有序加权几何(IFOWG)算子和直觉模糊混合几何(IFHG)算子，它们扩展了WG和OWG算子，以适应给定论元是由隶属函数和非隶属函数表征的直觉模糊集的环境。文中给出了一些数值算例来说明所发展的算子。最后，给出了IFHG算子在基于直觉模糊集的多属性决策中的应用。

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