A study on product-sum of triangular fuzzy numbers

We calculate Zadeh’s max-min composition operators for two 3-dimensional triangular fuzzy numbers. We prove that if the 3-dimensional result is limited to 2 dimensions, it is the same as the 2-dimensional result, which is shown as a graph. Since a 3-dimensional graph cannot be drawn, the value of the membership function is expressed with color density. We cut a 3-dimensional triangular fuzzy number by a perpendicular plane passing a vertex, and consider the cut plane as a domain. The value of the membership function for each point on the cut plane is also expressed with color density. The graph expressing the value of the membership function, defined in the plane as a 3-dimensional graph using the z -axis value instead of expressing with color density, is consistent with the results in the 2-dimensional case.

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The Weighted Fuzzy Barycenter

International Journal of Agricultural and Environmental Information Systems ◽

10.4018/ijaeis.2013100103 ◽

2013 ◽

Vol 4 (4) ◽

pp. 48-67 ◽

Cited By ~ 5

Author(s):

Julio Rojas-Mora ◽

Didier Josselin ◽

Jagannath Aryal ◽

Adrien Mangiavillano ◽

Philippe Ellerkamp

Keyword(s):

Membership Function ◽

Forest Fire ◽

Visual Inspection ◽

Fuzzy Numbers ◽

Fire Intensity ◽

Spatial Clusters ◽

Data Set ◽

Weighting Schemes ◽

Fuzzy Solution ◽

The Membership Function

In this paper, the authors present a methodology to solve the weighted barycenter problem when the data is inherently fuzzy. This method, from data clustered by expert visual inspection of maps, calculates bi-dimensional fuzzy numbers from the spatial clusters, which in turn are used to obtain the weighted fuzzy barycenter of a particular area. The authors apply the methodology, to a particularly apt data set of forest fire breakouts in the PACA region of southeastern France, gathered from 1986 to 2008, and sliced into five periods over which the fuzzy weighted barycenter for each one is obtained. Two weighting schemes based on fire intensity and fire density in a cluster were used. The center provided with this fuzzy method provides leeway to planners, which can see how the membership function of the fuzzy solution can be used as a measurement of “appropriateness” of the final location.

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

INTERNATIONAL JOURNAL OF COMPUTERS & TECHNOLOGY ◽

10.24297/ijct.v2i2b.2634 ◽

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.

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A New Method to Support Decision-Making in an Uncertain Environment Based on Normalized Interval-Valued Triangular Fuzzy Numbers and COMET Technique

Symmetry ◽

10.3390/sym12040516 ◽

2020 ◽

Vol 12 (4) ◽

pp. 516 ◽

Cited By ~ 21

Author(s):

Shahzad Faizi ◽

Wojciech Sałabun ◽

Samee Ullah ◽

Tabasam Rashid ◽

Jakub Więckowski

Keyword(s):

Decision Making ◽

Fuzzy Numbers ◽

Simple Problem ◽

Triangular Fuzzy Numbers ◽

Topsis Method ◽

Rank Reversal ◽

Mcdm Method ◽

Interval Valued ◽

Support Decision Making ◽

The Membership Function

Multi-criteria decision-making (MCDM) plays a vibrant role in decision-making, and the characteristic object method (COMET) acts as a powerful tool for decision-making of complex problems. COMET technique allows using both symmetrical and asymmetrical triangular fuzzy numbers. The COMET technique is immune to the pivotal challenge of rank reversal paradox and is proficient at handling vagueness and hesitancy. Classical COMET is not designed for handling uncertainty data when the expert has a problem with the identification of the membership function. In this paper, symmetrical and asymmetrical normalized interval-valued triangular fuzzy numbers (NIVTFNs) are used for decision-making as the solution of the identified challenge. A new MCDM method based on the COMET method is developed by using the concept of NIVTFNs. A simple problem of MCDM in the form of an illustrative example is given to demonstrate the calculation procedure and accuracy of the proposed approach. Furthermore, we compare the solution of the proposed method, as interval preference, with the results obtained in the Technique for Order of Preference by Similarity to Ideal solution (TOPSIS) method (a certain preference number).

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

Advances in Mathematics: Scientific Journal ◽

10.37418/amsj.9.11.32 ◽

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.

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

INTERNATIONAL JOURNAL OF COMPUTERS & TECHNOLOGY ◽

10.24297/ijct.v2i2a.6783 ◽

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.

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