Interval valued intuitionistic fuzzy sets

Atanassov, Krassimir; Gargov, George

doi:10.1016/0165-0114(89)90205-4

Cited by 2,654 publications

(949 citation statements)

References 2 publications

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“…In 1986, Atanassov (1986 proposed the intuitionistic fuzzy sets which are the extensions of fuzzy sets, and then he further established the relationship between intuitionistic fuzzy sets and interval fuzzy sets in 1989 (Atanassov, Gargov 1989). Intuitionistic fuzzy sets can express the decision maker's preference by three discrete values i.e.…”

Section: Evolution Of Intuitive Decision-making Knowledgementioning

confidence: 99%

“…Because of the complexity of objective things, the fuzziness of human thinking, as well as the limits of decision time, cost and the decision-maker's knowledge, there are still many limitations to express the decision information in the form of intuitionistic fuzzy sets. On the one hand, sometimes, it is difficult for people to express membership degree and non-membership degree by real numbers, so, there are a lot of researches about the extensions of intuitionistic fuzzy sets, for example, the membership degree and non-membership degree are extended to interval numbers (Atanassov, Gargov 1989), triangular fuzzy numbers (Zhang, Liu 2010), fuzzy numbers (Wang, Zhang 2009) and linguistic variables (Chen et al 2015). Obviously, these extensions have improved the ability of intuitionistic fuzzy sets to express uncertain information.…”

Section: Evolution Of Intuitive Decision-making Knowledgementioning

confidence: 99%

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Special Issue “Intuitionistic Fuzzy Theory and Its Application in Economy, Technology and Management”

Лю

2016

Technological and Economic Development of Economy

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Section: Evolution Of Intuitive Decision-making Knowledgementioning

confidence: 99%

Section: Evolution Of Intuitive Decision-making Knowledgementioning

confidence: 99%

Special Issue “Intuitionistic Fuzzy Theory and Its Application in Economy, Technology and Management”

Лю

2016

Technological and Economic Development of Economy

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“…which assigns to each elements x i a membership degree ( ) Atanassov and Gargov (1989) further introduced the interval-valued intuitionistic fuzzy set (IVIFS), which is a generalization of the IFS. The fundamental characteristic of the IVIFS is that the values of its membership function and non-membership function are intervals rather than exact numbers.…”

Section: Preliminariesmentioning

confidence: 99%

“…Wei (2008) utilized the maximizing deviation method for intuitionistic fuzzy multiple attribute decision making with incomplete weight information. Atanassov and Gargov (1989) introduced the concept of interval-valued intuitionistic fuzzy sets (IVIFSs) as a further generalization of that of IFSs, as well as of IVFSs. Atanassov (1994) defined some operational laws of the IVIFSs.…”

Section: Introductionmentioning

confidence: 99%

An Approach to Multiple Attribute Decision Making Based on the Induced Choquet Integral With Fuzzy Number Intuitionistic Fuzzy Information

Wei

Lin

Zhao

et al. 2014

Journal of Business Economics and Management

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Abstract. In this paper, we investigate the multiple attribute decision making problems with fuzzy number intuitionistic fuzzy information. Firstly, some operational laws of fuzzy number intuitionistic fuzzy values, score function and accuracy function of fuzzy number intuitionistic fuzzy values are introduced. Then, we have developed two fuzzy number intuitionistic fuzzy Choquet integral aggregation operators: induced fuzzy number intuitionistic fuzzy choquet ordered averaging (IFNIFCOA) operator and induced fuzzy number intuitionistic fuzzy choquet ordered geometric (IFNIFCOG) operator. The prominent characteristic of the operators is that they can not only consider the importance of the elements or their ordered positions, but also reflect the correlation among the elements or their ordered positions. We have studied some desirable properties of the IFNIFCOA and IFNIFCOG operators, such as commutativity, idempotency and monotonicity, and applied the IFNIFCOA and IFNIFCOGM operators to multiple attribute decision making with fuzzy number intuitionistic fuzzy information. Finally an illustrative example has been given to show the developed method.Keywords: Multiple attribute decision making, Fuzzy number intuitionistic fuzzy values, operational laws, induced fuzzy number intuitionistic fuzzy choquet ordered averaging operator, induced fuzzy number intuitionistic fuzzy choquet ordered geometric operator, Choquet integral.Reference to this paper should be made as follows: Wei, G.; Lin, R.; Zhao, X.; Wang, H.2014. An approach to multiple attribute decision making based on the induced Choquet integral with fuzzy number intuitionistic fuzzy information, Journal of Business Economics and Management 15(2): 277-298.JEL Classification: C61.

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“…This method is more suitable for raster structure [5,6]. IVFSs TOPSIS method in an intuitionistic fuzzy [7]. Zadeh and et al recommend fuzzy logic for management of uncertainty [8].…”

Section: Introductionmentioning

confidence: 99%

Porphyry Copper Mineral Prospectivity Mapping Using Interval Valued Fuzzy Sets Topsis Method in Central Iran

Rad¹,

Busch²

2011

JGIS

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Geospatial Information System (GIS) provide tools to quantitatively analysis and combination of datasets from geological, geophysical, remote sensing and geochemical surveys for decision-making processes. Excellent coverage of well-documented and good quality data enables testing of variable exploration modeling in an efficient way. The study area of this research is the most important part of Cu (Mo) porphyry-type mineralization belt in Iran. There are some well-known porphyry copper deposits in this region like Sarcheshmeh and Meiduk mines, but certainly there are same grounds to search for new porphyry deposits. The risks of developing mineral resources need to be known as accurately as possible, with regarding to all features those are effective in mineralization. These features can be recognized respect to Critical Genetic Factors (CGF's) using Critical Recognition Criteria (CRC) for each type of mineralization. CGF's can be employed for designing a Conceptual Genetic Model (CGM). Evidence maps create on the basis of CGM and then integrate together for production of Mineral Prospectivity Map (MPM). This map categorizes the areas based on their exploration importance. There are several techniques for creation of MPM. Interval Valued Fuzzy Sets (IVFSs) TOPSIS method was applied in this research. This method as a knowledge-driven method, allocate appropriate weights to layers on the basis of the effective membership, non membership, and non-certainty. The fundamental concept of TOPSIS is that the chosen alternatives should have the shortest distance from the positive ideal points (A * ) and the farthest distance from negative ideal points (A -).

show abstract

Interval valued intuitionistic fuzzy sets

Cited by 2,654 publications

References 2 publications

Special Issue “Intuitionistic Fuzzy Theory and Its Application in Economy, Technology and Management”

Special Issue “Intuitionistic Fuzzy Theory and Its Application in Economy, Technology and Management”

An Approach to Multiple Attribute Decision Making Based on the Induced Choquet Integral With Fuzzy Number Intuitionistic Fuzzy Information

Porphyry Copper Mineral Prospectivity Mapping Using Interval Valued Fuzzy Sets Topsis Method in Central Iran

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