Interval-Valued Doubt Fuzzy Ideals in BCK-Algebras

2019 ◽  
Vol 8 (4) ◽  
pp. 101-121
Author(s):  
Tripti Bej ◽  
Madhumangal Pal
Keyword(s):  
Fuzzy Sets ◽  
Fuzzy Set ◽  
Common Features ◽  
Fuzzy Ideal ◽  
Interval Valued

Nearly forty years ago, interval-valued fuzzy sets were propounded by Zadeh as the normal ramification of fuzzy sets. This article focuses on the basics of a theory for such an interval-valued fuzzy set becoming interval-valued doubt fuzzy subalgebra and an interval-valued doubt fuzzy ideal of BCK-algebras. Also, the authors discuss fuzzy translation, fuzzy multiplication of an interval-valued doubt fuzzy subalgebra/ideal of a BCK-algebra. Besides this, the authors have attempted to substantiate a few common features relating them. At the same time, some properties of interval-valued doubt fuzzy ideals under homomorphism are investigated and the product of interval-valued doubt fuzzy ideals in BCK-algebras is also established.

Interval-Valued Fuzzy H-Ideals on ß-Algebra

2020 ◽  
pp. 244-274
Author(s):  
Prakasam Muralikrishna ◽  
Tapan Senapati ◽  
Perumal Hemavathi
Keyword(s):  
Fuzzy Sets ◽  
Fuzzy Set ◽  
Cartesian Product ◽  
Algebraic Structures ◽  
Interval Valued

The notion of interval valued fuzzy set was first introduced by Zadeh as a generalization of fuzzy sets. Using interval valued fuzzy set, various algebraic structures and related topics were discussed. This chapter extends fuzzy H-ideal into interval valued fuzzy H-ideals of β-algebra and deals some related results. It also provides the study on homomorphic images of an interval valued fuzzy H-ideals of β-algebra and the idea of Cartesian product of interval valued fuzzy H-ideals of β-algebra.

scholarly journals A p-Ideal in BCI-Algebras Based on Multipolar Intuitionistic Fuzzy Sets

Mathematics ◽  
2020 ◽  
Vol 8 (6) ◽  
pp. 993
Author(s):  
Jeong-Gon Lee ◽  
Mohammad Fozouni ◽  
Kul Hur ◽  
Young Bae Jun
Keyword(s):  
Fuzzy Sets ◽  
Fuzzy Set ◽  
Intuitionistic Fuzzy Set ◽  
Intuitionistic Fuzzy Sets ◽  
Finite Degree ◽  
Intuitionistic Fuzzy ◽  
Fuzzy Ideal ◽  
The Relationship

In 2020, Kang, Song and Jun introduced the notion of multipolar intuitionistic fuzzy set with finite degree, which is a generalization of intuitionistic fuzzy set, and they applied it to BCK/BCI-algebras. In this paper, we used this notion to study p-ideals of BCI-algebras. The notion of k-polar intuitionistic fuzzy p-ideals in BCI-algebras is introduced, and several properties were investigated. An example to illustrate the k-polar intuitionistic fuzzy p-ideal is given. The relationship between k-polar intuitionistic fuzzy ideal and k-polar intuitionistic fuzzy p-ideal is displayed. A k-polar intuitionistic fuzzy p-ideal is found to be k-polar intuitionistic fuzzy ideal, and an example to show that the converse is not true is provided. The notions of p-ideals and k-polar ( ∈ , ∈ ) -fuzzy p-ideal in BCI-algebras are used to study the characterization of k-polar intuitionistic p-ideal. The concept of normal k-polar intuitionistic fuzzy p-ideal is introduced, and its characterization is discussed. The process of eliciting normal k-polar intuitionistic fuzzy p-ideal using k-polar intuitionistic fuzzy p-ideal is provided.

scholarly journals Foldness of Bipolar Fuzzy Sets and Its Application in BCK/BCI-Algebras

Mathematics ◽  
2019 ◽  
Vol 7 (11) ◽  
pp. 1036
Author(s):  
Young Bae Jun ◽  
Seok-Zun Song
Keyword(s):  
Information Processing ◽  
Fuzzy Sets ◽  
Fuzzy Set ◽  
Negative Information ◽  
Positive Information ◽  
Fuzzy Ideal ◽  
Recent Trends ◽  
Modern Information ◽  
Bipolar Fuzzy Sets

Recent trends in modern information processing have focused on polarizing information, and and bipolar fuzzy sets can be useful. Bipolar fuzzy sets are one of the important tools that can be used to distinguish between positive information and negative information. Positive information, for example, already observed or experienced, indicates what is guaranteed to be possible, and negative information indicates that it is impossible, prohibited, or certainly false. The purpose of this paper is to apply the bipolar fuzzy set to BCK/BCI-algebras. The notion of (translated) k-fold bipolar fuzzy sets is introduced, and its application in BCK/BCI-algebras is discussed. The concepts of k-fold bipolar fuzzy subalgebra and k-fold bipolar fuzzy ideal are introduced, and related properties are investigated. Characterizations of k-fold bipolar fuzzy subalgebra/ideal are considered, and relations between k-fold bipolar fuzzy subalgebra and k-fold bipolar fuzzy ideal are displayed. Extension of k-fold bipolar fuzzy subalgebra is discussed.

scholarly journals UKURAN ENTROPI DAN UKURAN KESAMAAN HIMPUNAN KABUR INTUISIONISTIK BERNILAI INTERVAL

2018 ◽  
Vol 7 (2) ◽  
pp. 61
Author(s):  
Hafizah Ramadhani ◽  
Yanita .
Keyword(s):  
Fuzzy Sets ◽  
Fuzzy Set ◽  
Interval Valued

Abstrak. Dalam kehidupan tidak semua masalah dapat dinilai salah atau benarnya,karena ada berbagai jenis masalah yang mengandung unsur ketidakpastian. L.A. Zadehmemperkenalkan teori himpunan kabur (fuzzy set) yang dapat menjadi alternatif yanglebih baik dalam mencari solusi permasalahan yang mengandung ketidakpastian. Ke-mudian banyak bentuk umum dari himpunan kabur (fuzzy set/FS) yang diusulkandan dikembangkan, diantaranya ada himpunan kabur intuisionistik (Intuitionistic FuzzySets/IFS), himpunan kabur bernilai interval (Interval Valued Fuzzy Sets/IVFS), danhimpunan kabur intuisionistik bernilai interval (Interval Valued Intuitionistic FuzzySets/IVIFS). Dalam teori himpunan kabur ada dua topik yang telah diteliti oleh banyakpeneliti dari berbagai sudut pandang, yaitu ukuran entropi dan ukuran kesamaan him-punan kabur intuisionistik (IFS). Pada tulisan ini akan dibahas mengenai hubunganukuran entropi dan ukuran kesamaan himpunan kabur intuisionistik bernilai interval(IVIFS).Kata Kunci : Himpunan kabur, himpunan kabur intuisionistik, himpunan kabur berni-lai interval, himpunan kabur intuisionistik bernilai interval, ukuran entropi, ukuran ke-samaan

scholarly journals REPRESENTABILITY IN INTERVAL-VALUED FUZZY SET THEORY

2007 ◽  
Vol 15 (03) ◽  
pp. 345-361 ◽  
Author(s):  
GLAD DESCHRIJVER ◽  
CHRIS CORNELIS
Keyword(s):  
Fuzzy Sets ◽  
Set Theory ◽  
Fuzzy Set ◽  
Theoretical Approach ◽  
Fuzzy Set Theory ◽  
Logical Connectives ◽  
Representation Method ◽  
Application Developers ◽  
Interval Valued

Interval-valued fuzzy set theory is an increasingly popular extension of fuzzy set theory where traditional [0,1]-valued membership degrees are replaced by intervals in [0,1] that approximate the (unknown) membership degrees. To construct suitable graded logical connectives in this extended setting, it is both natural and appropriate to "reuse" ingredients from classical fuzzy set theory. In this paper, we compare different ways of representing operations on interval-valued fuzzy sets by corresponding operations on fuzzy sets, study their intuitive semantics, and relate them to an existing, purely order-theoretical approach. Our approach reveals, amongst others, that subtle differences in the representation method can have a major impact on the properties satisfied by the generated operations, and that contrary to popular perception, interval-valued fuzzy set theory hardly corresponds to a mere twofold application of fuzzy set theory. In this way, by making the mathematical machinery behind the interval-valued fuzzy set model fully transparent, we aim to foster new avenues for its exploitation by offering application developers a much more powerful and elaborate mathematical toolbox than existed before.

Interval-Valued Intuitionistic Fuzzy Subnear Rings

2020 ◽  
pp. 213-224
Author(s):  
Amal Kumar Adak
Keyword(s):  
Fuzzy Sets ◽  
Level Set ◽  
Fuzzy Set ◽  
Intuitionistic Fuzzy Set ◽  
Intuitionistic Fuzzy Sets ◽  
Intuitionistic Fuzzy ◽  
The Family ◽  
Interval Valued

The theory of interval-valued intuitionistic fuzzy sets is a generalization of both interval-valued fuzzy sets and intuitionistic fuzzy sets. In this chapter, the notion of interval-valued intuitionistic fuzzy subnear-ring is introduced, and some interesting properties are discussed. Some relations on the family of all interval-valued intuitionistic fuzzy subnear-ring are presented, and some related properties are investigated. Also, the authors represent upper and lower level set of interval-valued intuitionistic fuzzy set.

Research on Interval-valued Intuitionistic Fuzzy Multi-attribute Decision Making Based on Projection Model

2019 ◽  
Vol 13 ◽  
Author(s):  
Sha Fu ◽  
Xi-long Qu ◽  
Ye-zhi Xiao ◽  
Hang-jun Zhou ◽  
Yun Zhou
Keyword(s):  
Decision Making ◽  
Set Theory ◽  
Fuzzy Set ◽  
Fuzzy Set Theory ◽  
Ideal Point ◽  
Projection Model ◽  
Intuitionistic Fuzzy ◽  
Fuzzy Ideal ◽  
Multi Attribute Decision Making ◽  
Interval Valued

Background: Regarding the multi-attribute decision making where the decision information is the interval-valued intuitionistic fuzzy number and the attribute weight information is not completely determined. Method: Intuitionistic fuzzy set theory introduces non-membership function, as an extension of the fuzzy set theory, it has certain advantages in solving complex decision making problems. a projection model based interval-valued intuitionistic fuzzy multi-attribute decision making scheme was proposed in this study. The objective weight of the attribute was obtained using improved interval-valued intuitionistic fuzzy entropy, and thus the comprehensive weight of the attribute was obtained according to the preference information. Results: In the aspect of the decision-making matrix processing, the concept of interval-valued intuitionistic fuzzy ideal point and its related concepts were defined, the score vector of each scheme was calculated, the projection model was constructed to measure the similarity between each scheme and the interval-valued intuitionistic fuzzy ideal point, and the scheme was sorted according to the projection value. Conclusion: The efficiency and usability of the proposed approach are considered on the case study.

SMETS-MAGREZ AXIOMS FOR R-IMPLICATORS IN INTERVAL-VALUED AND INTUITIONISTIC FUZZY SET THEORY

2005 ◽  
Vol 13 (04) ◽  
pp. 453-464 ◽  
Author(s):  
GLAD DESCHRIJVER ◽  
ETIENNE E. KERRE
Keyword(s):  
Fuzzy Sets ◽  
Set Theory ◽  
Fuzzy Set ◽  
Fuzzy Set Theory ◽  
Intuitionistic Fuzzy Set ◽  
Membership Degree ◽  
Triangular Norms ◽  
Intuitionistic Fuzzy ◽  
Special Lattice ◽  
Interval Valued

Interval-valued fuzzy sets constitute an extension of fuzzy sets which give an interval approximating the "real" (but unknown) membership degree. Interval-valued fuzzy sets are equivalent to intuitionistic fuzzy sets in the sense of Atanassov which give both a membership degree and a non-membership degree, whose sum must be smaller than or equal to 1. Both are equivalent to L-fuzzy sets w.r.t. a special lattice L*. In fuzzy set theory, an important class of triangular norms is the class of those that satisfy the residuation principle. In a previous paper5 we gave a construction for t-norms on L* satisfying the residuation principle which are not t-representable. In this paper we investigate the Smets-Magrez axioms and some other properties for the residual implicator generated by such t-norms.

scholarly journals Cubic q-Rung Orthopair Fuzzy Heronian Mean Operators and Their Applications to Multi-Attribute Group Decision Making

Mathematics ◽  
2020 ◽  
Vol 8 (7) ◽  
pp. 1125
Author(s):  
Baosheng Zhang ◽  
Tahir Mahmood ◽  
Jabbar Ahmmad ◽  
Qaisar Khan ◽  
Zeeshan Ali ◽  
...  
Keyword(s):  
Decision Making ◽  
Fuzzy Sets ◽  
Group Decision Making ◽  
Fuzzy Set ◽  
Group Decision ◽  
Decision Makers ◽  
The Given ◽  
Interval Valued ◽  
Heronian Mean ◽  
Selection Of

The cubic q-rung orthopair fuzzy set (Cq-ROFS) contains much more information to determine the interval valued q-rung orthopair fuzzy sets (IVq-ROFSs) and q-rung orthopair fuzzy sets (q-ROFSs) simultaneously for coping with the vagueness in information. It provides more space for decision makers (DMs) to describe their opinion in the environment of fuzzy set (FS) theory. In this paper, firstly, we introduce the conception of Cq-ROFS and their characteristics. Further, the Heronian mean (HM) operator based on Cq-ROFS, called the weighted HM operator, are explored. To overcome the deficiency of HM operator and keeping in mind the partitioned structure in real decision situations, we offer Cubic q-rung orthopair fuzzy partitioned HM operator and its weighted shape. An algorithm of the proposed operators based on multi-attribute group decision making (MAGDM) problems for the selection of best alternative among the given ones is established. Lastly, we provide an example to depict the authenticity and advantages of the exposed methods by contrasting with other existing drawbacks.

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