A distance and set theoretic-based similarity measure for generalized trapezoidal fuzzy numbers

Ahmad, Sharifah Aniza Sayed; Mohamad, Dzulkifli; Sulaiman, Norizam; Shariff, Jamilah Mohd; Abdullah, Kamilah

doi:10.1063/1.5041574

Cited by 10 publications

(6 citation statements)

References 9 publications

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“…There are several SMs that have been proposed by researchers to cater some specific problems and issues under fuzzy environment. In this paper, the SM proposed by Ahmad et al (2018)…”

Section: Similarity Measure (Sm)mentioning

confidence: 99%

“…Using the Hausdorff distance, the geometry information in evaluating the mismatch between two generalized fuzzy numbers can be obtained by considering the geometry shape of membership function of the fuzzy numbers. This SM has the advantage of discriminating two similar shape fuzzy numbers with two different locations effectively (Ahmad et al, 2018…”

Section: Similarity Measure (Sm)mentioning

confidence: 99%

“…The proof of the properties is given in Ahmad et al (2018) and the SM has been validated by using some benchmark sets of fuzzy numbers. It was found that the SM to be comparable with other SM with some additional advantages for some specific cases of comparison.…”

Section: Similarity Measure (Sm)mentioning

confidence: 99%

“…Chen & Chen (2003) proposed a new SM to calculate the degree between two generalized trapezoidal fuzzy numbers based on the centre of gravity (COG) points meanwhile, Yong et al (2004) introduced a new SM based on radius of gyration to cater the drawback of the method of Chen & Chen (2003). Some variants of new SM have been proposed recently such as by Ahmad et al (2018), Mohamad et al (2019) and Wu et al (2020). Some applications of SM in solving real problems are discussed.…”

Section: Introductionmentioning

confidence: 99%

“…In this paper, a similarity-based FIR is proposed for solving fuzzy decision making problem. The SM used is adapted from Ahmad et al (2018) that includes geometric distance, center of gravity, the Hausdorff distance, and Dice similarity index. Each component in the SM has its role to capture some specific features of the fuzzy numbers.…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

Similarity Based Fuzzy Inferior Ratio for Solving Multicriteria Decision Making Problems

Ahmad¹,

Mohamad²,

Azman³

2020

MJoC

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The method of Fuzzy Inferior Ratio (FIR) has been recognized as one of advantageous methods in multi criteria decision-making under fuzzy environment as it considers the element of compromise solution between the positive and negative aspect of the evaluation simultaneously. It is considered as an improvised version of Fuzzy TOPSIS (Technique for Order Preference by Similarity to Ideal Solution) method for solving decision-making problems. However, the FIR utilizes the distance approach in the evaluation in obtaining the compromise solution. A defuzzification process is carried out to transform the fuzzy values into a crisp form. Hence, loss of information may occur in the computation. In this paper, we proposed a similarity-based FIR in order to overcome the above-mentioned problem. A new compromise solution for the proposed FIR is developed and an improvised procedure of FIR is suggested using the similarity measure approach. A comparative analysis between the distance based and the similarity-based FIR is carried out using a case study of preferred client selection for a loan application. The proposed method is found to be effective in solving decision-making problems as the utilization of similarity measure will sufficiently preserve the data information in the computational process of evaluation.

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“…There are several SMs that have been proposed by researchers to cater some specific problems and issues under fuzzy environment. In this paper, the SM proposed by Ahmad et al (2018)…”

Section: Similarity Measure (Sm)mentioning

confidence: 99%

Section: Similarity Measure (Sm)mentioning

confidence: 99%

Section: Similarity Measure (Sm)mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Similarity Based Fuzzy Inferior Ratio for Solving Multicriteria Decision Making Problems

Ahmad¹,

Mohamad²,

Azman³

2020

MJoC

Self Cite

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Multicriteria decision making approach using an efficient novel similarity measure for generalized trapezoidal fuzzy numbers

Dutta

Borah

2021

J Ambient Intell Human Comput

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Multicriteria Decision Making (MCDM) has a huge role to play while ruling out one suitable alternative among a pool of alternatives governed by predefined multiple criteria. Some of the factors like imprecision, lack of information/data, etc., which are present in traditional MCDM processes have showcased their lack of efficiency and hence eventually it has paved the ways for the development of Fuzzy multicriteria decision making (FMCDM). In FMCDM processes, the decision makers can model most of the real-life phenomena by fuzzy information-based preferences. The availability of a wide literature on similarity measure (SM) emphasizes the vital role of SM of generalized fuzzy numbers (GFNs) to conduct accurate and precise decision making in FMCDM problems. Despite having few advantages, most of the existing approaches possessed a certain degree of counter intuitiveness and discrepancies. Thus, we have attempted to propose a novel SM for generalized trapezoidal fuzzy numbers (GTrFNs) which could deliberately overcome the impediments associated with the earlier existing approaches. Moreover, a meticulous comparative study with the existing approaches is also presented. This paper provides us with an improved method to obtain the similarity values between GTrFNs and the proposed SM consists of calculating the prominent features of fuzzy numbers such as expected value and variance. We use fourteen different sets of GTrFNs, to compare the fruition of the present approach with the existing SM approaches. Furthermore, to show the utility and applicability of our proposed measure, we illustrate few practical scenarios such as the launching of an electronic gadget by a company, a problem of medical diagnosis and finally, a proper anti-virus mask selection in light of the recent COVID-19 pandemic. The obtained results with our proposed SM, for the mentioned FMCDM problems, are analytically correct and they depict the efficiency and novelty of the present article.

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An advanced dice similarity measure of generalized fuzzy numbers and its application in multicriteria decision making

Dutta

2020

Arab Journal of Basic and Applied Sciences

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Multicriteria decision making (MCDM) is an important process to select best alternative among a set of alternatives based on preassigned multiple criteria. Presence of uncertainty due to lack of information/data, imprecision, vagueness etc. classical MCDM process becomes more complex and inappropriate. To overcome such types of situations, different types of fuzzy sets are explored and consequently fuzzy multicriteria decision making (FMCDM) was developed. In FMCDM problems, similarity measure of generalized fuzzy numbers plays crucial role in making appropriate decision by choosing best alternative. A handful number of work done on similarity measures are confronted in literature. Even though some advantages of these existing works are encountered, most of the works have impediments. In this regard, an attempt has been made to devise a similarity measure (SM) of GFNs with same or unequal height. It is observed that the proposed SM has the capability to overcome the deficiencies of the available earlier approaches and outplays in all the environments. To showcase the novelty and efficiency of the present SM comparative studies have been performed. Moreover, FMCDM problem has been solved under this setting and found that results obtained by this approach confronts human intuitions and analytical output.

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A distance and set theoretic-based similarity measure for generalized trapezoidal fuzzy numbers

Cited by 10 publications

References 9 publications

Similarity Based Fuzzy Inferior Ratio for Solving Multicriteria Decision Making Problems

Similarity Based Fuzzy Inferior Ratio for Solving Multicriteria Decision Making Problems

Multicriteria decision making approach using an efficient novel similarity measure for generalized trapezoidal fuzzy numbers

An advanced dice similarity measure of generalized fuzzy numbers and its application in multicriteria decision making

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