An Advanced Arithmetic Approach to GTIFNs and Its Application in Medical Analysis

2020 ◽  
pp. 1-39
Author(s):  
Palash Dutta
Keyword(s):  
Fuzzy Set ◽  
Fuzzy Numbers ◽  
Arithmetic Operation ◽  
Intuitionistic Fuzzy Set ◽  
Intuitionistic Fuzzy Numbers ◽  
Intuitionistic Fuzzy ◽  
Novel Method ◽  
Set Up ◽  
Decomposition Theorems ◽  
Medical Analysis

Intuitionistic fuzzy set (IFS) is the straight simplification of fuzzy set theory (FST). Nevertheless, estimation of the arithmetic operation on generalized intuitionistic fuzzy number (GIFNs) is a critical apprehension. This paper presents an attempt to set up a novel method for effectively resolving the drawbacks of conform arithmetic operations on generalized triangular intuitionistic fuzzy numbers (GTIFNs). For this purpose, decomposition theorems for generalized trapezoidal intuitionistic fuzzy numbers (GTrFNs) are studied. Numerical examples are illustrated herewith. Finally, to validate the requirement of a novel elucidation, an application in medical analysis has been carried out under this setting.

scholarly journals A Study on IFM/IFG/1 Vacation Queueing System with Breakdown, Repair and Server Timeout in (Triangular, Trapezoidal & Pentagon) Intuitionistic Fuzzy Set using α-Cuts

2021 ◽  
Vol 9 (VIII) ◽  
pp. 456-461
Author(s):  
Y. Saritha
Keyword(s):  
Fuzzy Set ◽  
Fuzzy Numbers ◽  
Queueing System ◽  
Intuitionistic Fuzzy Set ◽  
Fixed Time ◽  
Single Server ◽  
Intuitionistic Fuzzy Numbers ◽  
Intuitionistic Fuzzy ◽  
Waiting Line ◽  
The Membership Function

In this, we studied and investigated IFM/IFG/1 vacation queueing system/waiting line with server breakdowns, repair and server timeout, “by using (Triangular Trapezoidal and Pentagonal) IF (Intuitionistic Fuzzy) numbers with the application of IFS (Intuitionistic fuzzy set). Here we operate single server vacation queueing system in the following manner; when the system finds empty, the server waits for fixed time ’c’ known as server timeout. At the expiration of this time, if no one arrives into the system, then server takes the vacation. If anyone arrived in the system during the timeout period as well as in vacation the server commences the service otherwise, he will go for another vacation. If the system had occurred with a breakdown, just after a break down the server undergoes for repair. After the repaired process is completed the server restarts the service to the arrived customer. By the approach of IFS properties, we develop the membership function of the system performance are of fuzzy nature. Based on IFS α-cut approach the Intuitionistic fuzzy queues are reduced to a family of ICS (Intuitionistic Crisp Set). The numerical results are illustrated to the model.

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.

A new approach to solve fully intuitionistic fuzzy linear programming problem with unrestricted decision variables

2021 ◽  
pp. 1-14
Author(s):  
Manisha Malik ◽  
S. K. Gupta ◽  
I. Ahmad
Keyword(s):  
Linear Programming ◽  
Programming Problem ◽  
Fuzzy Set ◽  
Linear Programming Problem ◽  
Fuzzy Numbers ◽  
Fuzzy Linear Programming ◽  
Planning Problem ◽  
Intuitionistic Fuzzy Numbers ◽  
Intuitionistic Fuzzy ◽  
Decision Variables

In many real-world problems, one may encounter uncertainty in the input data. The fuzzy set theory fits well to handle such situations. However, it is not always possible to determine with full satisfaction the membership and non-membership degrees associated with an element of the fuzzy set. The intuitionistic fuzzy sets play a key role in dealing with the hesitation factor along-with the uncertainity involved in the problem and hence, provides more flexibility in the decision-making process. In this article, we introduce a new ordering on the set of intuitionistic fuzzy numbers and propose a simple approach for solving the fully intuitionistic fuzzy linear programming problems with mixed constraints and unrestricted variables where the parameters and decision variables of the problem are represented by intuitionistic fuzzy numbers. The proposed method converts the problem into a crisp non-linear programming problem and further finds the intuitionistic fuzzy optimal solution to the problem. Some of the key significance of the proposed study are also pointed out along-with the limitations of the existing studies. The approach is illustrated step-by-step with the help of a numerical example and further, a production planning problem is also demonstrated to show the applicability of the study in practical situations. Finally, the efficiency of the proposed algorithm is analyzed with the existing studies based on various computational parameters.

scholarly journals Heavy OWA Operator of Trapezoidal Intuitionistic Fuzzy Numbers and its Application to Multi-Attribute Decision Making

2015 ◽  
Vol 3 (1) ◽  
pp. 86-96 ◽  
Author(s):  
Chunlin Luo ◽  
Xin Tian ◽  
Shuping Wan
Keyword(s):  
Decision Making ◽  
Fuzzy Numbers ◽  
Intuitionistic Fuzzy Set ◽  
Special Kind ◽  
Weighted Averaging ◽  
Owa Operator ◽  
Intuitionistic Fuzzy Numbers ◽  
Intuitionistic Fuzzy ◽  
Multi Attribute Decision Making ◽  
Trapezoidal Intuitionistic Fuzzy Numbers

AbstractHeavy ordered weighted averaging (OWA) operator is important for characterizing the decision maker’s attitudinal character in multi-attribute decision making (MADM) problem with part or total ignorance. This paper develops a new method based on heavy OWA operator to solve the MADM problem in which the attributes are characterized by some trapezoidal intuitionistic fuzzy numbers (TrIFNs). TrIFN, as a special kind of intuitionistic fuzzy set defined on the real numbers, is useful for characterizing the ill-known quantity in reality. Firstly, the operation laws and the cut sets concept for TrIFNs are introduced. Then the authors define the membership and non-membership average indexes. A new ranking method is developed on the basis of the two indexes. In the proposed decision model, the multi-attribute TrIFN values of the candidates are aggregated by the Heavy OWA operator, and ranked by their membership and non-membership average indexes. Lastly, the authors illustrate the proposed method by a numerical example which implies the practicality and effectiveness of the method.

SOME GEOMETRIC AGGREGATION FUNCTIONS AND THEIR APPLICATION TO DYNAMIC MULTIPLE ATTRIBUTE DECISION MAKING IN THE INTUITIONISTIC FUZZY SETTING

2009 ◽  
Vol 17 (02) ◽  
pp. 179-196 ◽  
Author(s):  
G. W. WEI
Keyword(s):  
Decision Making ◽  
Fuzzy Sets ◽  
Membership Function ◽  
Fuzzy Set ◽  
Fuzzy Numbers ◽  
Fuzzy Variable ◽  
Multiple Attribute Decision Making ◽  
Intuitionistic Fuzzy Numbers ◽  
Intuitionistic Fuzzy ◽  
Multiple Attribute

The intuitionistic fuzzy set (IFS) characterized by a membership function and a non-membership function, was introduced by [K. Atanassov, "Intuitionistic fuzzy sets", Fuzzy Sets and Systems20 (1986) 87–96] as a generalization of Zadeh' fuzzy set [L. A. Zadeh, "Fuzzy sets", Information and Control8 (1965) 338–356] to deal with fuzziness and uncertainty. In this paper, the dynamic multiple attribute decision making (DMADM) problems with intuitionistic fuzzy information are investigated. The notions of intuitionistic fuzzy variable and uncertain intuitionistic fuzzy variable are defined, and two new aggregation operators called dynamic intuitionistic fuzzy weighted geometric (DIFWG) operator and uncertain dynamic intuitionistic fuzzy weighted geometric (UDIFWG) operator are proposed. Moreover, a procedure based on the DIFWG and IFWG operators is developed to solve the dynamic intuitionistic fuzzy multiple attribute decision making problems where all the decision information about attribute values takes the form of intuitionistic fuzzy numbers collected at different periods, and a procedure based on the UDIFWG and IIWG operators is developed for uncertain dynamic intuitionistic fuzzy multiple attribute decision making problems under interval uncertainty in which all the decision information about attribute values takes the form of interval-valued intuitionistic fuzzy numbers collected at different periods. Finally, an illustrative example is given to verify the developed approach and to demonstrate its practicality and effectiveness.

scholarly journals Selection of Vendor Based on Intuitionistic Fuzzy Analytical Hierarchy Process

2014 ◽  
Vol 2014 ◽  
pp. 1-10 ◽  
Author(s):  
Prabjot Kaur
Keyword(s):  
Fuzzy Sets ◽  
Fuzzy Set ◽  
Analytical Hierarchy Process ◽  
Intuitionistic Fuzzy Set ◽  
Pairwise Comparison ◽  
Business Environment ◽  
Global Market ◽  
Intuitionistic Fuzzy Numbers ◽  
Intuitionistic Fuzzy ◽  
Hierarchy Process

Business environment is characterized by greater domestic and international competitive position in the global market. Vendors play a key role in achieving the so-called corporate competition. It is not easy however to identify good vendors because evaluation is based on multiple criteria. In practice, for VSP most of the input information about the criteria is not known precisely. Intuitionistic fuzzy set is an extension of the classical fuzzy set theory (FST), which is a suitable way to deal with impreciseness. In other words, the application of intuitionistic fuzzy sets instead of fuzzy sets means the introduction of another degree of freedom called nonmembership function into the set description. In this paper, we proposed a triangular intuitionistic fuzzy number based approach for the vendor selection problem using analytical hierarchy process. The crisp data of the vendors is represented in the form of triangular intuitionistic fuzzy numbers. By applying AHP which involves decomposition, pairwise comparison, and deriving priorities for the various levels of the hierarchy, an overall crisp priority is obtained for ranking the best vendor. A numerical example illustrates our method. Lastly a sensitivity analysis is performed to find the most critical criterion on the basis of which vendor is selected.

scholarly journals A Novel Method of Ranking Intuitionistic Fuzzy Numbers using Value and θ Multiple of Ambiguity at Flexibility Parameters

2021 ◽  
Author(s):  
Rituparna Chutia
Keyword(s):  
Decision Making ◽  
Decision Maker ◽  
Fuzzy Number ◽  
Fuzzy Numbers ◽  
Intuitionistic Fuzzy Number ◽  
Numerical Examples ◽  
Intuitionistic Fuzzy Numbers ◽  
Intuitionistic Fuzzy ◽  
Novel Method ◽  
Flexibility Parameters

Abstract In this paper a novel method of ordering intuitionistic fuzzy numbers, based on the notions of ‘value’ and θ-multiple of ‘ambiguity’ of an intuitionistic fuzzy number, is developed. Further, the flexibility parameters, of decision-making at (α, β)-levels, are used in the method. These parameters allow the decision-maker to take decisions at various (α, β)-levels of decision-making. Many a times, all the reasonable properties of ranking intuitionistic fuzzy numbers were never checked in the existing studies. However, in this study an utmost attempt is being made to study the reasonable properties thoroughly. Further, the existing methods are mostly based on intuition and the geometry of the intuitionistic fuzzy numbers. However, the proposed method completely complies with the reasonable properties of ranking intuitionistic fuzzy numbers as well as the coherent intuition and the geometry of the intuitionistic fuzzy numbers. Further, newer properties are also being developed in this study. These prove the novelty of the proposed method. Further, a few numerical examples are discussed that demonstrates the proposed method.

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