scholarly journals Some Similarity Measures for Interval-Valued Picture Fuzzy Sets and Their Applications in Decision Making

Information ◽  
2019 ◽  
Vol 10 (12) ◽  
pp. 369 ◽  
Author(s):  
Peide Liu ◽  
Muhammad Munir ◽  
Tahir Mahmood ◽  
Kifayat Ullah
Keyword(s):  
Decision Making ◽  
Fuzzy Sets ◽  
Real Life ◽  
Similarity Measures ◽  
Intuitionistic Fuzzy Sets ◽  
Distance Measures ◽  
Intuitionistic Fuzzy ◽  
Picture Fuzzy Set ◽  
Picture Fuzzy Sets ◽  
Interval Valued

Similarity measures, distance measures and entropy measures are some common tools considered to be applied to some interesting real-life phenomena including pattern recognition, decision making, medical diagnosis and clustering. Further, interval-valued picture fuzzy sets (IVPFSs) are effective and useful to describe the fuzzy information. Therefore, this manuscript aims to develop some similarity measures for IVPFSs due to the significance of describing the membership grades of picture fuzzy set in terms of intervals. Several types cosine similarity measures, cotangent similarity measures, set-theoretic and grey similarity measures, four types of dice similarity measures and generalized dice similarity measures are developed. All the developed similarity measures are validated, and their properties are demonstrated. Two well-known problems, including mineral field recognition problems and multi-attribute decision making problems, are solved using the newly developed similarity measures. The superiorities of developed similarity measures over the similarity measures of picture fuzzy sets, interval-valued intuitionistic fuzzy sets and intuitionistic fuzzy sets are demonstrated through a comparison and numerical examples.

scholarly journals A Dynamic Interval-Valued Intuitionistic Fuzzy Sets Applied to Pattern Recognition

2013 ◽  
Vol 2013 ◽  
pp. 1-16 ◽  
Author(s):  
Zhenhua Zhang ◽  
Min Wang ◽  
Yong Hu ◽  
Jingyu Yang ◽  
Youpei Ye ◽  
...  
Keyword(s):  
Decision Making ◽  
Pattern Recognition ◽  
Fuzzy Sets ◽  
Medical Diagnosis ◽  
Recognition Accuracy ◽  
Intuitionistic Fuzzy Sets ◽  
Distance Measures ◽  
Intuitionistic Fuzzy ◽  
Simulation Results ◽  
Interval Valued

We present dynamic interval-valued intuitionistic fuzzy sets (DIVIFS), which can improve the recognition accuracy when they are applied to pattern recognition. By analyzing the degree of hesitancy, we propose some DIVIFS models from intuitionistic fuzzy sets (IFS) and interval-valued IFS (IVIFS). And then we present a novel ranking condition on the distance of IFS and IVIFS and introduce some distance measures of DIVIFS satisfying the ranking condition. Finally, a pattern recognition example applied to medical diagnosis decision making is given to demonstrate the application of DIVIFS and its distances. The simulation results show that the DIVIFS method is more comprehensive and flexible than the IFS method and the IVIFS method.

Extension of TOPSIS for Multiple Attribute Decision Making Using Intuitionistic Fuzzy Sets

2012 ◽  
Vol 433-440 ◽  
pp. 4053-4058 ◽  
Author(s):  
Yuan Yuan ◽  
Li Yang He
Keyword(s):  
Decision Making ◽  
Fuzzy Sets ◽  
Quantitative Estimation ◽  
Ideal Point ◽  
Real Life ◽  
Multiple Attribute Decision Making ◽  
Intuitionistic Fuzzy Sets ◽  
Distance Measures ◽  
Intuitionistic Fuzzy ◽  
Multiple Attribute

This electronic document is a “live” template. The various components of your paper [title, text, heads, etc.] are already defined on the style sheet, as illustrated by the portions given in this document. Due to the nature of vagueness inherent to real-life situations, some fuzzy data are deemed to suitable enough to describe the qualitative and/or quantitative estimation for decision making problems. Therefore, a new method for multiple attribute decision making under fuzzy environment is discussed, in which the attribute values take the form of intuitionistic fuzzy numbers. To overcome some disadvantages of existing distance measures like indiscrimination, counterintuitive results and difficulty of interpretation, we introduce a new class of distance for describing the deviation degrees between intuitionistic fuzzy sets. Furthermore, the measure of similarity degree for each alternative to ideal point is calculated through using the new proposed fuzzy distance. A model of TOPSIS is designed with the introduction of the particular closeness coefficient composed of similarity degrees. Then, we extend the TOPSIS method to aggregate the fuzzy information corresponding to each alternative, and rank the alternatives according to their closeness coefficients. Finally, an illustrative example is given to demonstrate the proposed approach practicality and effectiveness.

Generalized Entropy and Similarity Measure for Interval-Valued Intuitionistic Fuzzy Sets With Application in Decision Making

2021 ◽  
Vol 10 (1) ◽  
pp. 64-93
Author(s):  
Pratiksha Tiwari
Keyword(s):  
Decision Making ◽  
Fuzzy Sets ◽  
Similarity Measure ◽  
Extended Family ◽  
Similarity Measures ◽  
Intuitionistic Fuzzy Sets ◽  
Optimal Point ◽  
Generalized Entropy ◽  
Intuitionistic Fuzzy ◽  
Interval Valued

Interval-valued intuitionistic fuzzy environment is appropriate for most of the practical scenarios involving uncertainty, vagueness, and insufficient information. Entropy, similarity, distance, inclusion, and cross entropy measures are a few methods used for measuring uncertainty and classifying fuzzy sets and its generalizations. Entropy of a fuzzy set describes fuzziness degree of the set and similarity measure measures similarity between two fuzzy or members of its extended family. This paper presents generalized entropy and similarity measures for interval-valued intuitionistic fuzzy sets. Further, the proposed similarity measure is compared with some existing measure of similarity with the help of an illustrative example, and a method is used to define optimal point using the existing information. Finally, entropy and similarity measures are used to identify best alternatives to solve multi-attribute decision making.

Interval-Valued Intuitionistic Fuzzy Sets based Method for Multiple Criteria Decision-Making

2016 ◽  
Vol 5 (4) ◽  
pp. 192-210 ◽  
Author(s):  
Bhagawati Prasad Joshi
Keyword(s):  
Decision Making ◽  
Fuzzy Sets ◽  
Real Life ◽  
Multiple Criteria Decision Making ◽  
Intuitionistic Fuzzy Sets ◽  
Multiple Criteria ◽  
Decision Makers ◽  
Intuitionistic Fuzzy ◽  
Life Problems ◽  
Interval Valued

Due to the huge applications of fuzzy set theory, many generalizations were available in literature. Atanassov (1983) and Atanassov and Gargov (1989) introduced the notions of intuitionistic fuzzy sets (IFSs) and interval-valued intuitionistic fuzzy sets (IVIFSs) respectively. It is observed that IFSs and IVIFSs are more suitable tools for dealing with imprecise information and very powerful in modeling real life problems. However, many researchers made efforts to rank IVIFSs due to its importance in fusion of information. In this paper, a new ranking method is introduced and studied for IVIFSs. The proposed method is compared and illustrated with other existing methods by numerical examples. Then, it is utilized to identify the best alternative in multiple criteria decision-making problems in which criterion values for alternatives are IVIFSs. On the basis of the developed approach, it would provide a powerful way to the decision-makers to make his or her decision under IVIFSs. The validity and applicability of the proposed method are illustrated with practical examples.

scholarly journals Covering-Based Spherical Fuzzy Rough Set Model Hybrid with TOPSIS for Multi-Attribute Decision-Making

Symmetry ◽  
2019 ◽  
Vol 11 (4) ◽  
pp. 547 ◽  
Author(s):  
Shouzhen Zeng ◽  
Azmat Hussain ◽  
Tahir Mahmood ◽  
Muhammad Irfan Ali ◽  
Shahzaib Ashraf ◽  
...  
Keyword(s):  
Decision Making ◽  
Fuzzy Sets ◽  
Rough Set ◽  
Real Life ◽  
Intuitionistic Fuzzy Sets ◽  
Fuzzy Rough Set ◽  
Intuitionistic Fuzzy ◽  
Multi Attribute Decision Making ◽  
Topsis Technique ◽  
Picture Fuzzy Sets

In real life, human opinion cannot be limited to yes or no situations as shown in an ordinary fuzzy sets and intuitionistic fuzzy sets but it may be yes, abstain, no, and refusal as treated in Picture fuzzy sets or in Spherical fuzzy (SF) sets. In this article, we developed a comprehensive model to tackle decision-making problems, where strong points of view are in the favour; neutral; and against some projects, entities, or plans. Therefore, a new approach of covering-based spherical fuzzy rough set (CSFRS) models by means of spherical fuzzy β -neighborhoods (SF β -neighborhoods) is adopted to hybrid spherical fuzzy sets with notions of covering the rough set. Then, by using the principle of TOPSIS (Technique for Order Preference by Similarity to an Ideal Solution) to present the spherical fuzzy, the TOPSIS approach is presented through CSFRS models by means of SF β -neighborhoods. Via the SF-TOPSIS methodology, a multi-attribute decision-making problem is developed in an SF environment. This model has stronger capabilities than intuitionistic fuzzy sets and picture fuzzy sets to manage the vague and uncertainty. Finally, the proposed method is demonstrated through an example of how the proposed method helps us in decision-making problems.

A New Ranking Approach for Interval Valued Intuitionistic Fuzzy Sets and its Application in Decision Making

2019 ◽  
Vol 8 (2) ◽  
pp. 110-125 ◽  
Author(s):  
Pranjal Talukdar ◽  
Palash Dutta
Keyword(s):  
Decision Making ◽  
Fuzzy Sets ◽  
Model Uncertainty ◽  
Real Life ◽  
Intuitionistic Fuzzy Sets ◽  
Multi Criteria Decision Making ◽  
Numerical Examples ◽  
Intuitionistic Fuzzy ◽  
Life Problems ◽  
Interval Valued

Ranking of interval valued intuitionistic fuzzy sets (IVIFSs) plays an important role because of its attraction and applicability to model uncertainty in real life problems. In this article, an attempt has been made to devise a new method for ranking of IVIFSs based on exponential function. The significance of the method is illustrated with the help of some numerical examples and the results are compared with other existing methods. Furthermore, a multi criteria decision making method is presented here to evaluate the final ranking of the alternatives using the proposed ranking method and discussed the consistency of so obtained results.

scholarly journals Solutions of Matrix Games Involving Linguistic Interval-Valued Intuitionistic Fuzzy Sets

2021 ◽  
Author(s):  
Deeba Naqvi ◽  
Rajkumar Verma ◽  
Abha Aggarwal ◽  
Geeta Sachdev
Keyword(s):  
Decision Making ◽  
Fuzzy Sets ◽  
Real Life ◽  
Intuitionistic Fuzzy Sets ◽  
Linguistic Terms ◽  
Matrix Games ◽  
Suggested Approach ◽  
Intuitionistic Fuzzy ◽  
Interval Valued ◽  
Life Decision

Abstract In real-life decision-making challenges, experts quite frequently have a preference for expressing their perspective in natural linguistic terms rather than definite numerical format. These linguistic representation has been utilized to resolve plenty of decision-making problems. This paper displays the thorough study of matrix games where in the payoffs are characterized through linguistic interval-valued intuitionistic fuzzy sets (LIVIFSs). Solution of these matrix games are attained by resolving a duo of linear or nonlinear programming problems, originated through non-linear bi-objective programming problems. Finally, a numerical example is used to demonstrate the applicability of the suggested approach.

Width-based distance measures on interval-valued intuitionistic fuzzy sets

2021 ◽  
pp. 1-13
Author(s):  
Xi Li ◽  
Chunfeng Suo ◽  
Yongming Li
Keyword(s):  
Pattern Recognition ◽  
Fuzzy Sets ◽  
Medical Diagnosis ◽  
Intuitionistic Fuzzy Sets ◽  
Distance Measures ◽  
Intuitionistic Fuzzy ◽  
Interval Valued ◽  
Dissimilarity Function ◽  
Better Than

An essential topic of interval-valued intuitionistic fuzzy sets(IVIFSs) is distance measures. In this paper, we introduce a new kind of distance measures on IVIFSs. The novelty of our method lies in that we consider the width of intervals so that the uncertainty of outputs is strongly associated with the uncertainty of inputs. In addition, better than the distance measures given by predecessors, we define a new quaternary function on IVIFSs to construct the above-mentioned distance measures, which called interval-valued intuitionistic fuzzy dissimilarity function. Two specific methods for building the quaternary functions are proposed. Moreover, we also analyzed the degradation of the distance measures in this paper, and show that our measures can perfectly cover the measures on a simpler set. Finally, we provide illustrative examples in pattern recognition and medical diagnosis problems to confirm the effectiveness and advantages of the proposed distance measures.

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