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 Application of Pythagorean Fuzzy Digraphs in Package Delivery Robots

2021 ◽  
Author(s):  
Kanagaraj Sangeetha ◽  
◽  
Mani X Mani Parimala ◽  
Mohammed A. Al Shumrani ◽  
Said Broumi ◽  
...  
Keyword(s):  
Fuzzy Sets ◽  
Fuzzy Set ◽  
Driving Forces ◽  
Intuitionistic Fuzzy Set ◽  
Score Function ◽  
Fuzzy Graph ◽  
Pythagorean Fuzzy Set ◽  
Intuitionistic Fuzzy ◽  
Package Delivery ◽  
Vertex Set

The fuzzy set concept was developed to cope with uncertainty, whereas traditional sets are intended to deal with certainty. To address flaws in fuzzy set theory, extensions such as Intuitionistic Fuzzy Set (IFS), neutrosophic fuzzy sets, image fuzzy sets, and Pythagorean fuzzy set (PyFS) were developed. Pythagorean fuzzy set is useful tool for more clearly defining hazy concepts. In comparison to other fuzzy models, Pythagorean fuzzy set-based models allow more flexibility in handling human judgement information. The fuzzy graph structure is used to deal with the uncertainty in a network and to characterize its relationship with the non-empty vertex set. Pythagorean fuzzy graph (PyFG) was one of the Intuitionistic Fuzzy Graph (IFG) extensions. PyFG was created to cope with the uncertainty of an object and its relationship with other objects. PyFS and PyFG are the driving forces behind this innovative concept. This work defines Pythagorean Fuzzy Digraph (PyFDG), and PyFDG's score function. An algorithm is proposed for an issue to find the Pythagorean shortest path in package delivery robots.

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.

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 The Maximizing Deviation Method Based on Interval-Valued Pythagorean Fuzzy Weighted Aggregating Operator for Multiple Criteria Group Decision Analysis

2015 ◽  
Vol 2015 ◽  
pp. 1-15 ◽  
Author(s):  
Wei Liang ◽  
Xiaolu Zhang ◽  
Manfeng Liu
Keyword(s):  
Decision Making ◽  
Group Decision Making ◽  
Fuzzy Set ◽  
Group Decision ◽  
Intuitionistic Fuzzy Set ◽  
Pythagorean Fuzzy Set ◽  
Intuitionistic Fuzzy ◽  
Maximizing Deviation Method ◽  
Interval Valued ◽  
Deviation Method

As a new extension of Pythagorean fuzzy set (also called Atanassov’s intuitionistic fuzzy set of second type), interval-valued Pythagorean fuzzy set which is parallel to Atanassov’s interval-valued intuitionistic fuzzy set has recently been developed to model imprecise and ambiguous information in practical group decision making problems. The aim of this paper is to put forward a novel decision making method for handling multiple criteria group decision making problems within interval-valued Pythagorean fuzzy environment based on interval-valued Pythagorean fuzzy numbers (IVPFNs). There are three key issues being addressed in this approach. The first is to introduce an interval-valued Pythagorean fuzzy weighted arithmetic averaging (IVPF-WAA) operator to aggregate the decision data in order to get the overall preference values of alternatives. Some desirable properties of the IVPF-WAA operator are also investigated. Based on the idea of the maximizing deviation method, the second is to establish an optimization model for determining the weights of criteria for each expert. The third is to construct a minimizing consistency optimal model to derive the weights of criteria for the group. Finally, an illustrating example is given to verify the proposed approach.

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.

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.

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 A New Multiple Criteria Decision Making Method and its Application in Cloud Computing for Education

2015 ◽  
Vol 10 (8) ◽  
pp. 21
Author(s):  
Heng Sun
Keyword(s):  
Decision Making ◽  
Cloud Computing ◽  
Membership Function ◽  
Fuzzy Set ◽  
Choquet Integral ◽  
Intuitionistic Fuzzy Set ◽  
Multiple Criteria Decision Making ◽  
Score Function ◽  
Multiple Criteria ◽  
Intuitionistic Fuzzy

Cloud computing can extend the traditional education framework. In education, cloud can provide students and teachers with tools to deploy computing resources on-demand for lectures and labs according to their learning needs. But how to select a perfect cloud server is a key point, which is considered as a multiple criteria decision making problem. So, in this paper, intuitionistic fuzzy set is first introduced to express the decision maker’s views. Intuitionistic fuzzy set (IFS) includes a membership function and a non-membership function. More importantly, a new operator with choquet integral is developed to deal with assessment of education using cloud computing. Meanwhile, score function and accuracy function are demonstrated to obtain the final result. Finally, we develop this method to apply in a case study to show its applicability.

scholarly journals Pythagorean Picture Fuzzy Sets, Part 1- basic notions

2019 ◽  
Vol 35 (4) ◽  
pp. 293-304
Author(s):  
Bui Cong Cuong
Keyword(s):  
Fuzzy Logic ◽  
Fuzzy Sets ◽  
Set Theory ◽  
Fuzzy Set ◽  
Fuzzy Set Theory ◽  
Intuitionistic Fuzzy Set ◽  
Pythagorean Fuzzy Set ◽  
Intuitionistic Fuzzy ◽  
Picture Fuzzy Set ◽  
Picture Fuzzy Sets

Picture fuzzy set (2013) is a generalization of the Zadeh‟ fuzzy set (1965) and the Antanassov‟intuitionistic fuzzy set. The new concept could be useful for many computational intelligentproblems. Basic operators of the picture fuzzy logic were studied by Cuong, Ngan [10,11 ].Newconcept –Pythagorean picture fuzzy set ( PPFS) is a combination of Picture fuzzy set with theYager‟s Pythagorean fuzzy set [12-14].First, in the Part 1 of this paper, we consider basic notionson PPFS as set operators of PPFS‟s , Pythagorean picture relation, Pythagorean picture fuzzy softset. Next, the Part 2 of the paper is devoted to main operators in fuzzy logic on PPFS: picturenegation operator, picture t-norm, picture t-conorm, picture implication operators on PPFS.As aresult we will have a new branch of the picture fuzzy set theory.

Sign in / Sign up

Export Citation Format

Share Document