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Multi Criterion Decision Making using Intuitionistic Fuzzy Rough Set on Two Universal Sets

T. K. Das, D. P. Acharjya, M. R. Patra
2015 International Journal of Intelligent Systems and Applications  
Therefore, an effort has been made in this paper to process inconsistencies in data with the introduction of intuitionistic fuzzy rough set theory on two universal sets.  ...  It is very tedious to select a best option among an array of alternatives.  ...  Rough set on fuzzy approximation space is further generalized to rough set on intuitionistic fuzzy approximation space [5] .  ... 
doi:10.5815/ijisa.2015.04.04 fatcat:7rbqfvy2azdylnpb7ok5lv3yvu

Soft Interval-Valued Intuitionistic Fuzzy Rough Sets [chapter]

Anjan Mukherjee
2015 Studies in Fuzziness and Soft Computing  
This paper is devoted to the discussions of the combinations of intervalvalued intuitionistic fuzzy set, rough set and soft set.  ...  A new model, namely soft interval-valued intuitionistic fuzzy rough set is proposed and it's properties are derived.  ...  =(f, A) be an interval-valued intuitionistic fuzzy soft set over U and SIVIF=(U, Θ ) be the soft interval-valued intuitionistic fuzzy approximation space.  ... 
doi:10.1007/978-81-322-2458-7_9 fatcat:7czowzaa55fdpp33poychaybv4

A similarity measure of intuitionistic fuzzy soft sets and its application in medical diagnosis

P. Muthukumar, G. Sai Sundara Krishnan
2016 Applied Soft Computing  
Also we apply the notion of weighted rough intuitionistic fuzzy approach to cosine similarity measure for further investigation.  ...  Similarity measure is an important mathematical tool used in medical diagnosis, pattern recognition etc. In this paper a cosine similarity for rough intuitionistic fuzzy set is proposed.  ...  W = (U, R) iscalled an approximation space.  ... 
doi:10.1016/j.asoc.2015.12.002 fatcat:e357jiafqnfallbv3k2i7qwb6a

Rough Atanassov's Intuitionistic Fuzzy Sets Model over Two Universes and Its Applications

Shuqun Luo, Weihua Xu
2014 The Scientific World Journal  
Finally, rough Atanassov's intuitionistic fuzzy sets approach to decision is presented in the generalized approximation space over two universes by considering the problem about how to arrange patients  ...  Furthermore, an illustrated example is employed to demonstrate the conceptual arguments of the model.  ...  [19] proposed Atanassov's intuitionistic fuzzy rough set model over two universes with a constructive approach and discussed the basic properties of this model in fuzzy approximation space.  ... 
doi:10.1155/2014/348683 pmid:24959609 pmcid:PMC4052704 fatcat:lu6fe2f7fba2bbe7ulqqmjdoey

Lacunary statistical convergence in intuitionistic fuzzy n-normed linear spaces

Mausumi Sen, Pradip Debnath
2011 Mathematical and computer modelling  
In this article we introduce the notion of lacunary statistically convergent and lacunary statistically Cauchy sequences in intuitionistic fuzzy n-normed linear spaces and give their characterization.  ...  We show that some properties of lacunary statistical convergence of real sequences also hold for sequences in this space.  ...  Later on fuzzy logic became an important area of research in various branches of mathematics such as metric and topological spaces [2-4], theory of functions [5,6], approximation theory [7], etc.  ... 
doi:10.1016/j.mcm.2011.07.020 fatcat:4uftu43cibd4ho2fyuprtbwplm

Characterization of rough set approximations in Atanassov intuitionistic fuzzy set theory

Lei Zhou, Wei-Zhi Wu
2011 Computers and Mathematics with Applications  
This paper discusses the rough approximations of Atanassov intuitionistic fuzzy sets in crisp and fuzzy approximation spaces in which both constructive and axiomatic approaches are used.  ...  In the axiomatic approach, an operator-oriented characterization of rough sets is proposed, that is, rough intuitionistic fuzzy approximation operators and intuitionistic fuzzy rough approximation operators  ...  An axiomatic approach has been introduced to characterize the intuitionistic fuzzy approximation operators.  ... 
doi:10.1016/j.camwa.2011.05.009 fatcat:qbhwerzjtvbuzbxqg6wtykb7ki

Approximate Fixed point property in Intuitionistic Fuzzy normed sapce [article]

Müzeyyen Ertürk, Vatan Karakaya, M. Mursaleem
2015 arXiv   pre-print
In this paper, we define concept of approximate fixed point property of a function and a set in intuitionistic fuzzy normed space.  ...  Furthermore, we give intuitionistic fuzzy version of some class of maps used in fixed point theory and investigate approximate fixed point property of these maps.  ...  Let X be an intuitionistic fuzzy normed space.  ... 
arXiv:1509.02755v1 fatcat:xuac47q2azbjhfhhowhwegdy3a

Intuitionistic fuzzy rough sets: at the crossroads of imperfect knowledge

Chris Cornelis, Martine De Cock, Etienne E. Kerre
2003 Expert systems  
At the same time, intuitionistic fuzzy sets have been proposed as an attractive extension of fuzzy sets, enriching the latter with extra features to represent uncertainty (on top of vagueness).  ...  We intend to fill an obvious gap by introducing a new definition of intuitionistic fuzzy rough sets, as the most natural generalization of Pawlak's original concept of rough sets.  ...  s (1998) , approach to intuitionistic fuzzy rough sets; they construct an IF rough set (A, B) of a rough set (P, Q).  ... 
doi:10.1111/1468-0394.00250 fatcat:d2nphurk3jhwlht7swj4z7weae

Topology of the Redefined Intuitionistic Fuzzy Rough Sets

Sang Min Yun, Yeon Seok Eom, Seok Jong Lee
2021 International Journal of Fuzzy Logic and Intelligent Systems  
In this paper, we propose a topology for redefined intuitionistic fuzzy rough sets and investigate the basic properties of their subspaces, transition spaces, and continuous functions.  ...  In our previous paper, we proposed a new definition of intuitionistic fuzzy rough sets.  ...  One approach has been to use the concept of intuitionistic fuzzy sets introduced by Atanassov [2] .  ... 
doi:10.5391/ijfis.2021.21.4.369 fatcat:npdwuojeibh4jfk4f732cfqkya

Interval-Valued Intuitionistic Fuzzy Soft Rough Sets [chapter]

Anjan Mukherjee
2015 Studies in Fuzziness and Soft Computing  
Also interval valued intuitionistic fuzzy soft rough set based multi criteria group decision making scheme is presented, which refines the primary evaluation of the whole expert group and enables us to  ...  In this paper the concept of interval valued intuitionistic fuzzy soft rough sets is introduced.  ...  as the soft interval valued intuitionistic fuzzy approximation space.  ... 
doi:10.1007/978-81-322-2458-7_4 fatcat:5yi6yaalivfg7adekvvwhfhtga

A new uncertainty measure of covering-based rough interval-valued intuitionistic fuzzy sets

Tingting Zheng, Maoyin Zhang, Wanrong Zheng, Ligang Zhou
2019 IEEE Access  
INDEX TERMS Covering-based rough intuitionistic fuzzy set (CRIFS), covering-based rough interval-valued intuitionistic fuzzy set (CRIVIFS), covering approximation space, extended uncertainty measure criterion  ...  Furthermore, the criterion is extended to covering-based rough interval-valued intuitionistic fuzzy sets (CRIVIFSs), and the modified roughness method is proposed to measure the uncertainty of CRIVIFSs  ...  For example, in two different covering spaces an intuitionistic fuzzy set with the same lower approximations and the same upper approximations may have two different uncertainty measures.  ... 
doi:10.1109/access.2019.2912410 fatcat:bhf3mxzhrfah5igukmjiatui7e

Recent Fuzzy Generalisations of Rough Sets Theory: A Systematic Review and Methodological Critique of the Literature

Abbas Mardani, Mehrbakhsh Nilashi, Jurgita Antucheviciene, Madjid Tavana, Romualdas Bausys, Othman Ibrahim
2017 Complexity  
Based on the results of this review, we found that there are many challenging issues related to the different application area of fuzzy-rough set theory which can motivate future research studies.  ...  Therefore, in this review study, the attempt is made to provide a comprehensive systematic review of methodologies and applications of recent generalisations discussed in the area of fuzzy-rough set theory  ...  fuzzy probabilistic approximation spaces Huang et al. [125] Intuitionistic fuzzy-rough sets Proposed Fuzzy-rough sets Introduced the intuitionistic fuzzy (IF) graded approximation space  ... 
doi:10.1155/2017/1608147 fatcat:o6khgyofg5g55hwgdj2y6angii

Multi-adjoint based group decision-making under an intuitionistic fuzzy information system

Meishe Liang, Jusheng Mi, Tao Feng, Bin Xie
2019 International Journal of Computational Intelligence Systems  
Based on multi-adjoint and evidence theory, an approach to multi-criteria group decisionmaking(MCGDM) in intuitionistic fuzzy information system is proposed.  ...  After that the belief and plausibility functions are gained by intuitionistic fuzzy probability formulas. Second, the belief intervals of alternatives are acquired by combining all experts' evidence.  ...  is an intuitionistic fuzzy approximate space mentioned in Definition 3.  ... 
doi:10.2991/ijcis.12.1.172 fatcat:mupl2b2qrzb6dhvsxadxh7gsgm

A review of intuitionistic fuzzy topsis for supplier selection

Dickson E.A. Omorogbe
2017 AFRREV STECH An International Journal of Science and Technology  
This paper presented a review of intuitionistic fuzzy TOPSIS (Technique for Order Preference by Similarity to the Ideal Solution) for supplier selection in literature and identified gaps and lapses associated  ...  Fuzzy Set (FS) The fuzzy set theory is used to solve the rigorous theory of approximation and vagueness based on generalization of standard set theory to fuzzy set or numbers (Carlsson and Fuller, 1996  ...  The fuzzy system only provides approximate solution and not exact solution because of it amenability to human reasoning process.  ... 
doi:10.4314/stech.v5i2.7 fatcat:6mzxnkxxerg3bp7ugfgg7hc5gi


Dr. V. S. Subha
2016 Zenodo  
In this paper we apply the concept of rough intuitionistic fuzzy set in ᴦ-semigoup and discuss some of its properties.  ...  We introduce the notion of rough intuitionistic fuzzy left (right, two-sided,bi-,(1,2)-) ideals in ᴦ-semigoup and give some properties of such ideals.  ...  In this paper we substitute Γ-semigroup instead of the universe in Pawlak approximation space and define lower and upper approximation of an intuitionistic fuzzy set in Γ-semigroup and also discuss some  ... 
doi:10.5281/zenodo.3605042 fatcat:bsupo46uy5f6ho2exnhxilwm4a
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