Generalized Intuitionistic Fuzzy Ideals of BCK∕BCI-algebras Based on 3-valued Logic and Its Computational Study
On the basis of cut sets of the grade of membership of fuzzy point xa to belongingness (∈), or quasi-coincident (q), or belongingness and quasi-coincident(∈∧q), or belongingness or quasi-coincident (∈∨q) to an intuitionistic fuzzy set A of X, an (α,β)-intuitionistic fuzzy ideal of X is introduced by...
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| Format: | Article |
| Language: | English |
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Tsinghua University Press
2017-12-01
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| Series: | Fuzzy Information and Engineering |
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| Online Access: | http://www.sciencedirect.com/science/article/pii/S1616865817303096 |
| _version_ | 1797709278234017792 |
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| author | Chiranjibe Jana Madhumangal Pal |
| author_facet | Chiranjibe Jana Madhumangal Pal |
| author_sort | Chiranjibe Jana |
| collection | DOAJ |
| description | On the basis of cut sets of the grade of membership of fuzzy point xa to belongingness (∈), or quasi-coincident (q), or belongingness and quasi-coincident(∈∧q), or belongingness or quasi-coincident (∈∨q) to an intuitionistic fuzzy set A of X, an (α,β)-intuitionistic fuzzy ideal of X is introduced by applying the Lukasiewicz 3-valued logic, where α,β∈{∈,q,∈∧q,∈∨q} and α≠∈∧q. It is shown that an intuitionistic fuzzy set of X is an (∈,∈)(or (∈,∈∨q) or (∈∧q,∈))-intuitionistic fuzzy ideal of X if and only if A denote an intuitionistic fuzzy ideal with thresholds (0,1) (or (0,0.5) or (0.5,1)) of X respectively. It is observed that A denote an (∈,∈) (or (∈∧q,∈) or (∈,∈∨q))-intuitionistic fuzzy ideal of X if and only if for any p∈(0,1] (or p∈(0,0.5] or p∈(0.5,1]), then Ap served as fuzzy ideal of X respectively. It provided that an intuitiostic fuzzy set is an intuitionistic fuzzy ideal of X with thresholds (s,t) if and only if for any p∈(s,t], then the cut set Ap appear as fuzzy ideal of X. |
| first_indexed | 2024-03-12T06:35:08Z |
| format | Article |
| id | doaj.art-7a52621997ba45af9d8b6f7ed6be3ffc |
| institution | Directory Open Access Journal |
| issn | 1616-8658 |
| language | English |
| last_indexed | 2024-03-12T06:35:08Z |
| publishDate | 2017-12-01 |
| publisher | Tsinghua University Press |
| record_format | Article |
| series | Fuzzy Information and Engineering |
| spelling | doaj.art-7a52621997ba45af9d8b6f7ed6be3ffc2023-09-03T01:23:34ZengTsinghua University PressFuzzy Information and Engineering1616-86582017-12-019445547810.1016/j.fiae.2017.05.002Generalized Intuitionistic Fuzzy Ideals of BCK∕BCI-algebras Based on 3-valued Logic and Its Computational StudyChiranjibe JanaMadhumangal PalOn the basis of cut sets of the grade of membership of fuzzy point xa to belongingness (∈), or quasi-coincident (q), or belongingness and quasi-coincident(∈∧q), or belongingness or quasi-coincident (∈∨q) to an intuitionistic fuzzy set A of X, an (α,β)-intuitionistic fuzzy ideal of X is introduced by applying the Lukasiewicz 3-valued logic, where α,β∈{∈,q,∈∧q,∈∨q} and α≠∈∧q. It is shown that an intuitionistic fuzzy set of X is an (∈,∈)(or (∈,∈∨q) or (∈∧q,∈))-intuitionistic fuzzy ideal of X if and only if A denote an intuitionistic fuzzy ideal with thresholds (0,1) (or (0,0.5) or (0.5,1)) of X respectively. It is observed that A denote an (∈,∈) (or (∈∧q,∈) or (∈,∈∨q))-intuitionistic fuzzy ideal of X if and only if for any p∈(0,1] (or p∈(0,0.5] or p∈(0.5,1]), then Ap served as fuzzy ideal of X respectively. It provided that an intuitiostic fuzzy set is an intuitionistic fuzzy ideal of X with thresholds (s,t) if and only if for any p∈(s,t], then the cut set Ap appear as fuzzy ideal of X.http://www.sciencedirect.com/science/article/pii/S1616865817303096BCK∕BCI-algebrasIntuitionistic fuzzy idealFuzzy pointsCut sets of intuitionistic fuzzy setsLukasiewicz implication operator |
| spellingShingle | Chiranjibe Jana Madhumangal Pal Generalized Intuitionistic Fuzzy Ideals of BCK∕BCI-algebras Based on 3-valued Logic and Its Computational Study Fuzzy Information and Engineering BCK∕BCI-algebras Intuitionistic fuzzy ideal Fuzzy points Cut sets of intuitionistic fuzzy sets Lukasiewicz implication operator |
| title | Generalized Intuitionistic Fuzzy Ideals of BCK∕BCI-algebras Based on 3-valued Logic and Its Computational Study |
| title_full | Generalized Intuitionistic Fuzzy Ideals of BCK∕BCI-algebras Based on 3-valued Logic and Its Computational Study |
| title_fullStr | Generalized Intuitionistic Fuzzy Ideals of BCK∕BCI-algebras Based on 3-valued Logic and Its Computational Study |
| title_full_unstemmed | Generalized Intuitionistic Fuzzy Ideals of BCK∕BCI-algebras Based on 3-valued Logic and Its Computational Study |
| title_short | Generalized Intuitionistic Fuzzy Ideals of BCK∕BCI-algebras Based on 3-valued Logic and Its Computational Study |
| title_sort | generalized intuitionistic fuzzy ideals of bck bci algebras based on 3 valued logic and its computational study |
| topic | BCK∕BCI-algebras Intuitionistic fuzzy ideal Fuzzy points Cut sets of intuitionistic fuzzy sets Lukasiewicz implication operator |
| url | http://www.sciencedirect.com/science/article/pii/S1616865817303096 |
| work_keys_str_mv | AT chiranjibejana generalizedintuitionisticfuzzyidealsofbckbcialgebrasbasedon3valuedlogicanditscomputationalstudy AT madhumangalpal generalizedintuitionisticfuzzyidealsofbckbcialgebrasbasedon3valuedlogicanditscomputationalstudy |