Fuzzy risk analysis based on Ochiai ranking index with Hurwicz criterion for generalized trapezoidal fuzzy numbers

Ramli, Nazirah; Mohamad, Dzulkifli; Ramli, Rizauddin

doi:10.12988/ams.2013.310587

Cited by 3 publications

(3 citation statements)

References 17 publications

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“…The concept of decomposed fuzzy numbers is used to execute the fuzzy arithmetic operations on these Quasi-Gaussian fuzzy numbers and the process of conversion and execution of arithmetic operations has been explained in a later section of this paper. The technique used for determining the minimum of two decomposed fuzzy numbers using the concept of lattice of fuzzy numbers and α -cuts is preferred over other ranking methods like those discussed in the paper by Ramli and Mohamad (2009) using the centroid index that falls under the category of fuzzy scoring techniques. These centroid indexes can be used for ranking of triangular and trapezoidal fuzzy numbers as most of it involves calculating the area under the curve which requires less number of calculations in case of triangular and trapezoidal fuzzy numbers and more calculations when Gaussian fuzzy numbers are involved, thereby increasing the complexity of the operations.…”

Section: Problem Formulationmentioning

confidence: 99%

A Greedy Algorithm for Fuzzy Shortest Path Problem using Quasi-Gaussian Fuzzy Weights

Verma

Shukla

2013

International Journal of Fuzzy System Applications

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Several algorithms exist to determine the shortest path in a network for the crisp case where the weights are real numbers. In the real world, these weights represent parameters like cost, packet arrival time, link capacity etc which are not naturally precise. To model the uncertainty involved, for the first time we use the Gaussian fuzzy numbers as weights and a method has been presented in this paper to determine the fuzzy shortest path. Gaussian membership functions are preferred over other membership functions (triangular and trapezoidal) that are easy to analyze because it is continuous and differentiable enabling efficient gradient based optimization and it is simpler to represent because it requires fewer parameters. The issue of performing fuzzy arithmetic operations to calculate the fuzzy shortest path length and the corresponding fuzzy shortest path in the network has been addressed and to tackle it the concept of decomposed fuzzy numbers has been used. Also, a greedy algorithm which is an extension of Dijkstra’s algorithm for fuzzy shortest path problem has been proposed.

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Section: Problem Formulationmentioning

confidence: 99%

A Greedy Algorithm for Fuzzy Shortest Path Problem using Quasi-Gaussian Fuzzy Weights

Verma

Shukla

2013

International Journal of Fuzzy System Applications

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“…Asady and Zendehnam [3] advised a point nearest to the origin as a de-fuzzified value for the fuzzy number. A review of centroid index ranking methods was reported by Ramli and Mohamad [16]. Various centroid ranking methods are considered and compared showing the fact that no single method in the centroid concept is superior to all other methods since each method appears to have some advantages as well as disadvantages.…”

Section: Introductionmentioning

confidence: 99%

A New Approach of Centroid based Ranking Fuzzy Numbers and its Comparative Reviews

Prasad,

Sinha,

Sen

2024

Comm. Math. Appl.

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The numeric values represented by fuzzy numbers are vague and ranking them according to their location on the real axis is not adequate and logical. Ranking of fuzzy numbers plays a vital role in measuring the degree of importance of different alternatives in decision-making under the fuzzy environment and the comparison of fuzzy numbers reflects that of alternatives. Although a lot of methods for ranking fuzzy numbers exist in the literature, even then none of them is superior to all others. This paper proposes a new method for ranking fuzzy numbers using the coordinates of the centroid point of the fuzzy numbers. It suggests a ranking score for the fuzzy number that multiplies the ordinate and the exponential value of the ratio of the ordinate to the abscissa of the centroid point. The proposed ranking score method can rank two or more fuzzy numbers simultaneously irrespective of their linear or non-linear membership functions. Furthermore, it consistently ranks symmetric fuzzy numbers of the same or different altitudes, images of fuzzy numbers, and the fuzzy numbers that describe the compensation of areas. Comparative reviews show an edge of the proposed method over several representative approaches.

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“…To overcome the limitations of previous studies, Osman et al (2019) proposed the use of FCM based on fuzzy numbers. Fuzzy numbers depict the physical world more realistically and can produce attribute weights at different levels of confidence (Dom, Hasan, Shahidin, & Apandi, 2019;Sulaiman et al, 2017;Ramli & Mohamad, 2009). Nonetheless, Osman et al (2019) used Patra and Mondal (2015)'s similarity measure based on area, height, and distance, which cannot differentiate the degree of similarity for some different pairs of fuzzy numbers.…”

Section: Introductionmentioning

confidence: 99%

Achievement Goals Analysis in the Learning of Calculus Based on Fuzzy Number Conjoint Method

Osman,

Ramli,

Mohd Noor

et al. 2022

JSML

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The conjoint method, which is based on fuzzy sets of numbers, is widely used to describe linguistic values for human preference in an uncertain environment. However, the fuzzy sets used to describe the membership function of linguistic value do not realistically represent the physical world, so the conjoint method can fill the gap and produce more meaningful results. The fuzzy numbers conjoint method is used in this paper to analyze the achievement goals of undergraduates in the learning of calculus. One hundred and seven selected Bachelor of Science (Hons) Mathematics and Bachelor of Science (Hons) Actuarial Science students from one public university in Klang Valley, Selangor, participated in this study. The data for this study, which was distributed via Google form, was based on a previous study's Achievement Goals Questionnaire. The fuzzy number conjoint method with similarity measure based on geometric distance, ambiguity, value, area, left and right height were used to calculate and analyze the data gathered from respondents' opinions of attributes for each linguistic value. The priority of the degree of agreement among undergraduates on the achievement goals in the learning of calculus is worrying as they may not learn all that they possibly could in this subject , getting better grades than most other students , followed by avoiding performing poorly compared to other students in this subject , and doing better than other students with an overall ranking as follows .. The findings of this study can be used to assist and guide academicians and mathematics educators in enhancing students' achievement goals for calculus learning.

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Fuzzy risk analysis based on Ochiai ranking index with Hurwicz criterion for generalized trapezoidal fuzzy numbers

Cited by 3 publications

References 17 publications

A Greedy Algorithm for Fuzzy Shortest Path Problem using Quasi-Gaussian Fuzzy Weights

A Greedy Algorithm for Fuzzy Shortest Path Problem using Quasi-Gaussian Fuzzy Weights

A New Approach of Centroid based Ranking Fuzzy Numbers and its Comparative Reviews

Achievement Goals Analysis in the Learning of Calculus Based on Fuzzy Number Conjoint Method

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