Ranking fuzzy numbers with index of optimism

Different methods have been proposed for ranking fuzzy numbers. These include methods based on distances, centroid point, coefficient of variation, and weighted mean value. However, there is still no method that can always give a satisfactory result to every situation; some are counterintuitive and not discriminating. This paper presents an approach for ranking fuzzy numbers with integral value that is an extension of the index of Liou and Wang. This method, that is independent of the type of membership function used, can rank more than two fuzzy numbers simultaneously. This ranking method use an index of optimism to reflect the decision maker's optimistic attitude, but rather it also contains an index of modality that represents the neutrality of the decision maker. The approach is illustrated with numerical examples.

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Multicriteria Group Decision Making Using Fuzzy Approach for Evaluating Criteria of Electrician

International Journal of Electrical and Computer Engineering (IJECE) ◽

10.11591/ijece.v6i5.10946 ◽

2016 ◽

Vol 6 (5) ◽

pp. 2462 ◽

Cited By ~ 2

Author(s):

Wiwien Hadikurniawati ◽

Khabib Mustofa

Keyword(s):

Decision Making ◽

Group Decision Making ◽

Fuzzy Numbers ◽

Group Decision ◽

Selection Process ◽

Subjective Assessment ◽

Fuzzy Approach ◽

Multicriteria Group Decision Making ◽

Alternative Ranking ◽

Index Of Optimism

<p>This paper presents an approach of fuzzy multicriteria group decision making in determining alternatives to solve the selection problem of the electrician through a competency test. Fuzzy approach is used to determine the highest priority of alternative electrician who has knowledge and ability that best fits the given parameters. Linguistic variables are presented by triangular fuzzy numbers. They are used to represent a subjective assessment of the decision-makers so that uncertainty and imprecision in the selection process can be minimized. Fuzzy approach require transforming crisp data to fuzzy numbers. Output of the best alternatives is generated by ranking method. Ranking has been made base on eight criteria which make the evaluation basis of each alternative. Ranking of the results is determined using different value of optimism index (). The fuzzy multi criteria decision making (FMCDM) calculation is using the best alternative using three value of optimism index. The result of calculation shows that the same alternative reached from different index of optimism. This alternative is the highest priority of decision making process.</p>

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Ranking Fuzzy Numbers with a Distance Method using Circumcenter of Centroids and an Index of Modality

Advances in Fuzzy Systems ◽

10.1155/2011/178308 ◽

2011 ◽

Vol 2011 ◽

pp. 1-7 ◽

Cited By ~ 22

Author(s):

P. Phani Bushan Rao ◽

N. Ravi Shankar

Keyword(s):

Decision Making ◽

Decision Maker ◽

Satisfactory Result ◽

Fuzzy Numbers ◽

New Method ◽

Triangular Fuzzy Numbers ◽

Distance Method ◽

Fuzzy Environment ◽

Index Of Optimism

Ranking fuzzy numbers are an important aspect of decision making in a fuzzy environment. Since their inception in 1965, many authors have proposed different methods for ranking fuzzy numbers. However, there is no method which gives a satisfactory result to all situations. Most of the methods proposed so far are nondiscriminating and counterintuitive. This paper proposes a new method for ranking fuzzy numbers based on the Circumcenter of Centroids and uses an index of optimism to reflect the decision maker's optimistic attitude and also an index of modality that represents the neutrality of the decision maker. This method ranks various types of fuzzy numbers which include normal, generalized trapezoidal, and triangular fuzzy numbers along with crisp numbers with the particularity that crisp numbers are to be considered particular cases of fuzzy numbers.

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Multicriteria Group Decision Making Using Fuzzy Approach for Evaluating Criteria of Electrician

International Journal of Electrical and Computer Engineering (IJECE) ◽

10.11591/ijece.v6i5.pp2462-2469 ◽

2016 ◽

Vol 6 (5) ◽

pp. 2462 ◽

Cited By ~ 2

Author(s):

Wiwien Hadikurniawati ◽

Khabib Mustofa

Keyword(s):

Decision Making ◽

Group Decision Making ◽

Fuzzy Numbers ◽

Group Decision ◽

Selection Process ◽

Subjective Assessment ◽

Fuzzy Approach ◽

Multicriteria Group Decision Making ◽

Alternative Ranking ◽

Index Of Optimism

<p>This paper presents an approach of fuzzy multicriteria group decision making in determining alternatives to solve the selection problem of the electrician through a competency test. Fuzzy approach is used to determine the highest priority of alternative electrician who has knowledge and ability that best fits the given parameters. Linguistic variables are presented by triangular fuzzy numbers. They are used to represent a subjective assessment of the decision-makers so that uncertainty and imprecision in the selection process can be minimized. Fuzzy approach require transforming crisp data to fuzzy numbers. Output of the best alternatives is generated by ranking method. Ranking has been made base on eight criteria which make the evaluation basis of each alternative. Ranking of the results is determined using different value of optimism index (). The fuzzy multi criteria decision making (FMCDM) calculation is using the best alternative using three value of optimism index. The result of calculation shows that the same alternative reached from different index of optimism. This alternative is the highest priority of decision making process.</p>

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