Trapezoidal fuzzy multi-number and its application to multi-criteria decision-making problems

Uluçay, Vakkas; Deli̇, İrfan; Şahin, Mehmet

doi:10.1007/s00521-016-2760-3

Cited by 35 publications

(27 citation statements)

References 25 publications

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“…The degree of similarity between A and B is calculated as follows: 3 , P(A) 4 , P(B) 1 , P(B) 2 , P(B) 3 1 , P(A) 2 , P(A) 3 , P(A) 4 , P(B) 1 , P(B) 2 , P(B) 3 , 2 , P(A) 3 , P(A) 4 , P(B) 1 , P(B) 2 , P(B) 3 , P(B) 4…”

Section: If a ⊆ B ⊆ C Then S(a C) ≤ S(a B) And S(a C) ≤ S(b C)mentioning

confidence: 99%

“…. Thus, (min{P(A) 1 , P(A) 2 , P(A) 3 , P(A) 4 , P(B) 1 , P(B) 2 , P(B) 3 , P(B) 4 }) = (max{P(A) 1 , P(A) 2 , P(A) 3 , P(A) 4 , P(B) 1 , P(B) 2 , P(B) 3 ii.…”

Section: η Punclassified

“…In 1986, the theory of intuitionistic fuzzy set was first presented by Atanassov [1] to deal with uncertainty of imperfect information. Since the intuitionistic fuzzy set theory was proposed by Atanassov [1], many researches treating imprecision and uncertainty have been developed and studied: for example, trapezoidal fuzzy multi-number [2], intuitionistic fuzzy sets [3][4][5][6][7][8][9][10][11], methodology for ranking triangular intuitionistic fuzzy numbers [12][13][14][15][16][17][18][19][20][21][22][23], intuitionistic trapezoidal fuzzy aggregation operator [21,[24][25][26][27][28][29], interval-valued trapezoidal fuzzy numbers aggregation operator [30][31][32][33], interval-valued generalized intuitionistic fuzzy numbers [26,34], entropy and similarity measure of intuitionistic fuzzy sets [35,36] and so on.…”

Section: Introductionmentioning

confidence: 99%

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Intuitionistic trapezoidal fuzzy multi-numbers and its application to multi-criteria decision-making problems

Uluçay¹,

Deli̇

Şahin

2018

Complex Intell. Syst.

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Intuitionistic trapezoidal fuzzy multi-numbers (ITFM-numbers) are a special intuitionistic fuzzy multiset on a real number set, which are very useful for decision makers to depict their intuitionistic fuzzy multi-preference information. In the ITFMnumbers, the occurrences are more than one with the possibility of the same or the different membership and non-membership functions. In this paper, we define ITFM-numbers based on multiple criteria decision-making problems in which the ratings of alternatives are expressed with ITFM-numbers. Firstly, some operational laws using t-norm and t-conorm are proposed. Then, some aggregation operators on ITFM-numbers are developed. Also, the ranking order of alternative is given according to the similarity of the alternative with respect to the positive ideal solution. Finally, a numerical example is given to verify the developed approach and to demonstrate its practicality and effectiveness.

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Section: If a ⊆ B ⊆ C Then S(a C) ≤ S(a B) And S(a C) ≤ S(b C)mentioning

confidence: 99%

“…. Thus, (min{P(A) 1 , P(A) 2 , P(A) 3 , P(A) 4 , P(B) 1 , P(B) 2 , P(B) 3 , P(B) 4 }) = (max{P(A) 1 , P(A) 2 , P(A) 3 , P(A) 4 , P(B) 1 , P(B) 2 , P(B) 3 ii.…”

Section: η Punclassified

Section: Introductionmentioning

confidence: 99%

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Intuitionistic trapezoidal fuzzy multi-numbers and its application to multi-criteria decision-making problems

Uluçay¹,

Deli̇

Şahin

2018

Complex Intell. Syst.

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“…Later, Uluçay ( 2020 ), introduced a novel method for trapezoidal fuzzy multi-numbers for its application in the MCDM process. Few other works were carried out involving trapezoidal fuzzy multi-numbers which for instance, Uluçay et al ( 2018 ) proposed arithmetic and geometric operators for them, and Şahin et al ( 2020 ) formulated an improved hybrid vector similarity measure for such multi-numbers. Thereafter, Wu et al ( 2020 ) tackled group decision making problems with the help of an improved SM for GFNs.…”

Section: Introductionmentioning

confidence: 99%

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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“…It is obvious that much knowledge in real world situations is fuzzy rather than precise. Fuzzy logic was the base of several extensions of fuzzy set theory and it is successfully used in many discipline of theoretical and practical background [2][3][4]. For the basics of fuzzy logic several texts are available but here we recommend [5].…”

Section: Introductionmentioning

confidence: 99%

Hesitant Fuzzy Graphs and Their Products

Javaid

Kashif

Rashid

2020

Fuzzy Information and Engineering

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In this article, the notion of hesitant fuzzy graph is introduced. It an extended structure of a fuzzy graph that gives more precision, flexibility and compatibility to a system when compared with the system that is designed using fuzzy graphs. Several operations on hesitant fuzzy graphs are defined, namely Cartesian product, composition, tensor product and normal product. Furthermore, the relationship between the degree of vertices of the hesitant fuzzy graphs and the hesitant fuzzy graph obtained by their different products is developed. These operations are highly used in computer science, geometry, algebra, operations research, etc.

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Trapezoidal fuzzy multi-number and its application to multi-criteria decision-making problems

Cited by 35 publications

References 25 publications

Intuitionistic trapezoidal fuzzy multi-numbers and its application to multi-criteria decision-making problems

Intuitionistic trapezoidal fuzzy multi-numbers and its application to multi-criteria decision-making problems

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

Hesitant Fuzzy Graphs and Their Products

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