scholarly journals New Aggregation Operator for Triangular Fuzzy Numbers based on the Geometric Means of the Slopes of the L- and R- Membership Functions

2012 ◽  
Vol 2 (2) ◽  
pp. 74-76
Author(s):  
Manju Pandey ◽  
Dr. Nilay Khare
Keyword(s):  
Recent Work ◽  
Membership Function ◽  
Fuzzy Numbers ◽  
Arithmetic Mean ◽  
Aggregation Operator ◽  
Aggregation Operators ◽  
Membership Functions ◽  
Triangular Fuzzy Numbers ◽  
Geometric Means ◽  
The Individual

In recent work authors have proposed four new aggregation operators for triangular and trapezoidal fuzzy numbers based on means of apex angles [1][2][3][4]. Subsequently authors have proposed [5] a new aggregation operator for TFNs based on the arithmetic mean of slopes of the L- and R- membership lines. In this paper the work is extended and a new aggregation operator for TFNs is proposed in which the L- and R- membership function lines of the aggregate TFN have slopes which are the geometric means of the corresponding L- and R- slopes of the individual TFNs. Computation of the aggregate is demonstrated with a numerical example. Corresponding arithmetic and geometric aggregates as well as results from the recent work of the authors on TFN aggregates have also been computed.

New Aggregation Operator for Triangular Fuzzy Numbers based on the Geometric Means of the Slopes of the L- and R- Membership Functions

2018 ◽  
Vol 2 (2a) ◽  
pp. 74-76
Author(s):  
Manju Pandey ◽  
Dr. Nilay Khare
Keyword(s):  
Recent Work ◽  
Membership Function ◽  
Fuzzy Numbers ◽  
Arithmetic Mean ◽  
Aggregation Operator ◽  
Aggregation Operators ◽  
Membership Functions ◽  
Triangular Fuzzy Numbers ◽  
Geometric Means ◽  
The Individual

In recent work authors have proposed four new aggregation operators for triangular and trapezoidal fuzzy numbers based on means of apex angles [1][2][3][4]. Subsequently authors have proposed [5] a new aggregation operator for TFNs based on the arithmetic mean of slopes of the L- and R- membership lines. In this paper the work is extended and a new aggregation operator for TFNs is proposed in which the L- and R- membership function lines of the aggregate TFN have slopes which are the geometric means of the corresponding L- and R- slopes of the individual TFNs. Computation of the aggregate is demonstrated with a numerical example. Corresponding arithmetic and geometric aggregates as well as results from the recent work of the authors on TFN aggregates have also been computed.

scholarly journals A study on product-sum of triangular fuzzy numbers

2021 ◽  
Vol 5 (2) ◽  
pp. 63-67
Author(s):  
Mohamed Ali A ◽  
Rajkumar N
Keyword(s):  
Membership Function ◽  
Fuzzy Numbers ◽  
Triangular Fuzzy Numbers ◽  
Triangular Form ◽  
Finite Sum ◽  
The Membership Function

We  study  the  problem:   if  a˜i,   i  ∈  N   are  fuzzy  numbers  of  triangular  form,  then  what is the membership function of the infinite (or finite) sum -˜a1   +  a˜2   +  · · ·   (defined  via  the sub-product-norm convolution)

SOLVING FUZZY LINEAR PROGRAMMING PROBLEMS WITH MODIFIED S-CURVE MEMBERSHIP FUNCTION

2005 ◽  
Vol 13 (01) ◽  
pp. 97-109 ◽  
Author(s):  
PANDIAN M. VASANT
Keyword(s):  
Linear Programming ◽  
Membership Function ◽  
Fuzzy Numbers ◽  
Numerical Solutions ◽  
Real Life ◽  
Optimization Method ◽  
Fuzzy Linear Programming ◽  
Membership Functions ◽  
Linear Programming Problems ◽  
S Curve

In this paper, we concentrate on two kinds of fuzzy linear programming problems: linear programming problems with only fuzzy resource variables and linear programming problems in which both the resource variables and the technological coefficients are fuzzy numbers. We consider here only the case of fuzzy numbers with modified s-curve membership functions. We propose here the modified s-curve membership function as a methodology for fuzzy linear programming and use it for solving these problems. We also compare the new proposed method with non-fuzzy linear programming optimization method. Finally, we provide real life application examples in production planning and their numerical solutions.

Density aggregation operators for interval-valued q-rung orthopair fuzzy numbers and their application in multiple attribute decision making

2021 ◽  
pp. 1-14
Author(s):  
Huijuan Guo ◽  
Ruipu Yao
Keyword(s):  
Decision Making ◽  
Fuzzy Numbers ◽  
Multiple Attribute Decision Making ◽  
Aggregation Operator ◽  
Aggregation Operators ◽  
Weighted Arithmetic ◽  
Geometric Average ◽  
Novel Approach ◽  
Multiple Attribute ◽  
Interval Valued

The symmetry between fuzzy evaluations and crisp numbers provides an effective solution to multiple attribute decision making (MADM) problems under fuzzy environments. Considering the effect of information distribution on decision making, a novel approach to MADM problems under the interval-valued q-rung orthopair fuzzy (Iq-ROF) environments is put forward. Firstly, the clustering method of interval-valued q-rung orthopair fuzzy numbers (Iq-ROFNs) is defined. Secondly, Iq-ROF density weighted arithmetic (Iq-ROFDWA) intermediate operator and Iq-ROF density weighted geometric average (Iq-ROFDWGA) intermediate operator are developed based on the density weighted intermediate operators for crisp numbers. Thirdly, combining the density weighted intermediate operators with the Iq-ROF weighted aggregation operators, Iq-ROF density aggregation operators including Iq-ROF density weighted arithmetic (Iq-ROFDWAA) aggregation operator and Iq-ROF density weighted geometric (Iq-ROFDWGG) aggregation operator are proposed. Finally, effectiveness of the proposed method is verified through a numerical example.

SEQUENTIAL CONSENSUS FOR SELECTING QUALIFIED INDIVIDUALS OF A GROUP

2008 ◽  
Vol 16 (supp02) ◽  
pp. 57-68 ◽  
Author(s):  
MIGUEL A. BALLESTER ◽  
JOSÉ LUIS GARCÍA-LAPRESTA
Keyword(s):  
Decision Procedure ◽  
Group Decision ◽  
Ordered Set ◽  
Aggregation Operator ◽  
Aggregation Operators ◽  
Unit Interval ◽  
Recursive Procedure ◽  
Specific Attribute ◽  
Fixed Threshold ◽  
The Individual

In this paper we analyze a group decision procedure that follows a recursive pattern. In the first stage, the members of a group show their opinions on all the individuals of that group, regarding a specific attribute, by means of assessments within an ordered set, e.g. the unit interval or a finite scale. Taking into account this information, some aggregation operators and a family of thresholds, a subgroup of individuals is selected: those members whose collective assessment reach a specific threshold. Now only the opinions of this qualified subgroup are taken into account and a new subgroup emerges in the implementation of the aggregation phase. We analyze how to put in practice this recursive procedure in order to provide a final subgroup of qualified members. We have considered the minimum as aggregation operator. Thus, the collective assessment is just the worst of the individual assessments. This idea corresponds to qualify individuals whenever all the individual assessments reach the fixed threshold.

scholarly journals A Method to Find the Membership Functions of Maximum and Minimum of Fuzzy Numbers

1970 ◽  
Vol 30 ◽  
pp. 89-99
Author(s):  
Shapla Shirin
Keyword(s):  
Membership Function ◽  
Fuzzy Number ◽  
Fuzzy Numbers ◽  
Membership Functions ◽  
New Approach ◽  
The Core ◽  
Decreasing Functions

In this paper, a new approach for computation of membership functions of the maximum and minimum of more than two upper semi-continuous fuzzy numbers has been introduced. This method is also applicable for piece-wise continuous fuzzy numbers or the fuzzy numbers which are only continuous from right or only continuous from left. The core of fuzzy numbers should have a singleton set. Keywords: Continuous fuzzy number; piece-wise continuous fuzzy number; Maximum (MAX) and Minimum (MIN) of fuzzy number; core; α-cut; bounded increasing and bounded decreasing functions; membership function. GANIT J. Bangladesh Math. Soc. (ISSN 1606-3694) 30 (2010) 89-99  DOI: http://dx.doi.org/10.3329/ganit.v30i0.8506

A METHOD FOR FINDING CRITICAL PATH WITH SYMMETRIC OCTAGONAL INTUITIONISTIC FUZZY NUMBERS

2020 ◽  
Vol 9 (11) ◽  
pp. 9273-9286
Author(s):  
N. Rameshan ◽  
D.S. Dinagar
Keyword(s):  
Membership Function ◽  
Fuzzy Number ◽  
Fuzzy Numbers ◽  
Critical Path ◽  
Membership Functions ◽  
Intuitionistic Fuzzy Number ◽  
Lower And Upper Bounds ◽  
Intuitionistic Fuzzy Numbers ◽  
Intuitionistic Fuzzy ◽  
The Membership Function

The concept of this paper represents finding fuzzy critical path using octagonal fuzzy number. In project scheduling, a new method has been approached to identify the critical path by using Symmetric Octagonal Intuitionistic Fuzzy Number (SYMOCINTFN). For getting a better solution, we use the fuzzy octagonal number rather than other fuzzy numbers. The membership functions of the earliest and latest times of events are by calculating lower and upper bounds of the earliest and latest times considering octagonal fuzzy duration. The resulting conditions omit the negative and infeasible solution. The membership function takes up an essential role in finding a new solution. Based on membership function, fuzzy number can be identified in different categories such as Triangular, Trapezoidal, pentagonal, hexagonal, octagonal, decagonal, hexa decagonal fuzzy numbers etc.

scholarly journals Picture Fuzzy Interaction Partitioned Heronian Aggregation Operators for Hotel Selection

Mathematics ◽  
2019 ◽  
Vol 8 (1) ◽  
pp. 3 ◽  
Author(s):  
Suizhi Luo ◽  
Lining Xing
Keyword(s):  
Decision Making ◽  
Fuzzy Sets ◽  
Fuzzy Numbers ◽  
Aggregation Operator ◽  
Aggregation Operators ◽  
Decision Makers ◽  
Sensitivity Analyses ◽  
Special Cases ◽  
Different Parts

Picture fuzzy numbers (PFNs), as the generalization of fuzzy sets, are good at fully expressing decision makers’ opinions with four membership degrees. Since aggregation operators are simple but powerful tools, this study aims to explore some aggregation operators with PFNs to solve practical decision-making problems. First, new operational rules, the interaction operations of PFNs, are defined to overcome the drawbacks of existing operations. Considering that interrelationships may exist only in part of criteria, rather than all of the criteria in reality, the partitioned Heronian aggregation operator is modified with PFNs to deal with this condition. Then, desirable properties are proved and several special cases are discussed. New decision-making methods with these presented aggregation operators are suggested to process hotel selection issues. Last, their practicability and merits are certified by sensitivity analyses and comparison analyses with other existing approaches. The results indicate that our methods are feasible to address such situations where criteria interact in the same part, but are independent from each other at different parts.

scholarly journals A computational method for fuzzy arithmetic operations

1970 ◽  
Vol 4 (1) ◽  
pp. 18-22 ◽  
Author(s):  
Thowhida Akther ◽  
Sanwar Uddin Ahmad
Keyword(s):  
Membership Function ◽  
Interval Arithmetic ◽  
Fuzzy Number ◽  
Fuzzy Numbers ◽  
Computational Method ◽  
Fuzzy Arithmetic ◽  
Membership Functions ◽  
Computer Implementation ◽  
Arithmetic Operations ◽  
International University

In this paper, a computer implementation to evaluate the arithmetic operations on two fuzzy numbers with linear membership functions has been developed. The fuzzy arithmetic approached by the interval arithmetic is used here. The algorithm of the developed method with a numerical example is also provided. Using this method four basic arithmetic operations between any two TFNs can be evaluated without complexity. Keywords: Fuzzy arithmetic, Fuzzy number, Membership Function, Interval arithmetic, α - cut. DOI: 10.3329/diujst.v4i1.4350 Daffodil International University Journal of Science and Technology Vol.4(1) 2009 pp.18-22

Intuitionistic Fuzzy Hybrid Weighted Arithmetic Mean and Its Application in Decision Making

2019 ◽  
Vol 27 (03) ◽  
pp. 353-373
Author(s):  
Weize Wang ◽  
Jerry M. Mendel
Keyword(s):  
Decision Making ◽  
Membership Function ◽  
Arithmetic Mean ◽  
Aggregation Operators ◽  
Total Order ◽  
Intuitionistic Fuzzy ◽  
Weighted Arithmetic ◽  
Multi Attribute Decision Making ◽  
A Company ◽  
Interval Valued

Atanassov’s intuitionistic fuzzy sets (AIFSs), characterized by a membership function, a non-membership function, and a hesitancy function, is a generalization of a fuzzy set. There are various intuitionistic fuzzy hybrid weighted aggregation operators to deal with multi-attribute decision making problems which consider the importance degrees of the arguments and their ordered positions simultaneously. However, these existing hybrid weighed aggregation operators are not monotone with respect to the total order on intuitionistic fuzzy values (AIFVs), which is undesirable. Based on the Łukasiewicz triangular norm, we propose an intuitionistic fuzzy hybrid weighted arithmetic mean, which is monotone with respect to the total order on AIFVs, and therefore is a true generalization of such operations. We give an example that a company intends to select a project manager to illustrate the validity and applicability of the proposed aggregation operator. Moreover, we extend this kind of hybrid weighted arithmetic mean to the interval-valued intuitionistic fuzzy environments.

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