scholarly journals On an Intuitionistic Fuzzy Form of the Goguen’s Implication

Mathematics ◽  
2021 ◽  
Vol 9 (6) ◽  
pp. 676
Author(s):  
Krassimir Atanassov ◽  
Nora Angelova ◽  
Vassia Atanassova
Keyword(s):  
Basic Properties ◽  
Intuitionistic Fuzzy ◽  
Fuzzy Implication

In the present paper we construct a new intuitionistic fuzzy implication, giving intuitionistic fuzzy form to Goguen’s implication. Some of its basic properties are studied and illustrated with examples. Geometrical interpretations of the different forms of the new implication are given. Other forms of the Goguen’s implication are discussed.

scholarly journals Third Zadeh’s Intuitionistic Fuzzy Implication

Mathematics ◽  
2021 ◽  
Vol 9 (6) ◽  
pp. 619
Author(s):  
Krassimir Atanassov
Keyword(s):  
Basic Properties ◽  
Intuitionistic Fuzzy ◽  
Fuzzy Implication

George Klir and Bo Yuan named after Lotfi Zadeh the implication p→q=max(1−p,min(p,q)) (also Early Zadeh implication). In a series of papers, the author introduced two intuitionistic fuzzy forms of Zadeh’s implication and studied their basic properties. In the present paper, a new (third) intuitionistic fuzzy form of Zadeh’s implication is proposed and some of its properties are studied.

scholarly journals Modifications of Łukasiewicz’s intuitionistic fuzzy implication

2021 ◽  
Vol 27 (3) ◽  
pp. 32-39
Author(s):  
Alžbeta Michalíková ◽  
◽  
Eulalia Szmidt ◽  
Peter Vassilev ◽  
◽  
...  
Keyword(s):  
Basic Properties ◽  
Fuzzy Implications ◽  
Intuitionistic Fuzzy ◽  
Fuzzy Implication

In [6], G. Klir and B. Yuan named after J. Łukasiewicz the implication p \rightarrow q = min(1, p+q). In a series of papers, 198 different intuitionistic fuzzy implications have been introduced, and their basic properties have been studied. Here we introduce six new implications which are modifications of Łukasiewicz’s intuitionistic fuzzy implication, and we describe and prove some of their properties.

scholarly journals Modifications of the Goguen's intuitionistic fuzzy implication

2021 ◽  
Vol 27 (4) ◽  
pp. 20-29
Author(s):  
Janusz Kacprzyk ◽  
◽  
Katarína Čunderlíková ◽  
Nora Angelova ◽  
Krassimir T. Atanassov ◽  
...  
Keyword(s):  
Basic Properties ◽  
Intuitionistic Fuzzy ◽  
Fuzzy Implication

On the basis of the Goguen’s intuitionistic fuzzy implication, seven of its modifications are constructed. Some of their basic properties are studied. The negations, generated by these implications are introduced and some of their properties are also described.

scholarly journals Modifications of the Third Zadeh’s intuitionistic fuzzy implication

2021 ◽  
Vol 27 (1) ◽  
pp. 9-23
Author(s):  
Krassimir Atanassov ◽  
◽  
Nora Angelova ◽  
◽  
Keyword(s):  
Basic Properties ◽  
The Third ◽  
Intuitionistic Fuzzy ◽  
Fuzzy Implication

In [24], G. Klir and B. Yuan named after L. Zadeh the implication p → q = max(1 − p, min(p, q)). In a series of papers, the author introduced two intuitionistic fuzzy forms of Zadeh’s implication and their basic properties have been studied. In the present paper, a new (third) intuitionistic fuzzy form of Zadeh’s implication is given and some of its properties are studied.

scholarly journals Modal Type of Weak Intuitionistic Fuzzy Implications Generated by the Operation Δ

2021 ◽  
Vol 21 (4) ◽  
pp. 137-144
Author(s):  
Piotr Dworniczak ◽  
Lilija Atanassova ◽  
Nora Angelova
Keyword(s):  
Fuzzy Sets ◽  
Intuitionistic Fuzzy Sets ◽  
Basic Properties ◽  
Fuzzy Implications ◽  
Intuitionistic Fuzzy ◽  
Fuzzy Implication ◽  
Modal Type

Abstract In 2020 L. Atanassova has been introduced the new operation Δ over intuitionistic fuzzy sets and over intuitionistic fuzzy pairs. Some of its properties have been studied in 2021 from L. Atanassova and P. Dworniczak. In 2021 L. Atanassova and P. Dworniczak generated an intuitionistic fuzzy implication by the operation Δ, and it has been introduced and some of its basic properties have been described. Here, eight modal type of intuitionistic fuzzy implications are generated by the first one and some of their properties are discussed.

scholarly journals Intuitionistic Fuzzy Normed Subrings and Intuitionistic Fuzzy Normed Ideals

Mathematics ◽  
2020 ◽  
Vol 8 (9) ◽  
pp. 1594
Author(s):  
Nour Abed Alhaleem ◽  
Abd Ghafur Ahmad
Keyword(s):  
Inverse Image ◽  
Ring Homomorphism ◽  
Basic Properties ◽  
Intuitionistic Fuzzy ◽  
Normed Ring

The main goal of this paper is to introduce the notion of intuitionistic fuzzy normed rings and to establish basic properties related to it. We extend normed rings by incorporating the idea of intuitionistic fuzzy to normed rings, we develop a new structure of fuzzy rings which will be called an intuitionistic fuzzy normed ring. As an extension of intuitionistic fuzzy normed rings, we define the concept of intuitionistic fuzzy normed subrings and intuitionistic fuzzy normed ideals. Some essential operations specially subset, complement, union, intersection and several properties relating to the notion of generalized intuitionistic fuzzy normed rings are identified. Homomorphism and isomorphism of intuitionistic fuzzy normed subrings are characterized. We identify the image and the inverse image of intuitionistic fuzzy normed subrings under ring homomorphism and study their elementary properties. Some properties of intuitionistic fuzzy normed rings and relevant examples are presented.

scholarly journals The Interval-Valued Intuitionistic Fuzzy Optimized Weighted Bonferroni Means and Their Application

2013 ◽  
Vol 2013 ◽  
pp. 1-10 ◽  
Author(s):  
Ya-ming Shi ◽  
Jian-min He
Keyword(s):  
Decision Making ◽  
Group Decision Making ◽  
Group Decision ◽  
Practical Case ◽  
Basic Properties ◽  
Bonferroni Mean ◽  
Intuitionistic Fuzzy ◽  
Fuzzy Environment ◽  
Aggregation Techniques ◽  
Interval Valued

We investigate and propose two new Bonferroni means, that is, the optimized weighted BM (OWBM) and the generalized optimized weighted BM (GOWBM), whose characteristics are to reflect the preference and interrelationship of the aggregated arguments and can satisfy the basic properties of the aggregation techniques simultaneously. Further, we propose the interval-valued intuitionistic fuzzy optimized weighted Bonferroni mean (IIFOWBM) and the generalized interval-valued intuitionistic fuzzy optimized weighted Bonferroni mean (GIIFOWBM) and detailed study of their desirable properties such as idempotency, monotonicity, transformation, and boundary. Finally, based on IIFOWBM and GIIFOWBM, we give an approach to group decision making under the interval-valued intuitionistic fuzzy environment and utilize a practical case involving the assessment of a set of agroecological regions in Hubei Province, China, to illustrate the developed methods.

scholarly journals λ-Statistical Convergence of Sequences of Functions in Intuitionistic Fuzzy Normed Spaces

2012 ◽  
Vol 2012 ◽  
pp. 1-14 ◽  
Author(s):  
Vatan Karakaya ◽  
Necip Şimşek ◽  
Müzeyyen Ertürk ◽  
Faik Gürsoy
Keyword(s):  
Uniform Convergence ◽  
Pointwise Convergence ◽  
Statistical Convergence ◽  
Normed Spaces ◽  
Basic Properties ◽  
Intuitionistic Fuzzy ◽  
Convergence Of Sequences ◽  
Intuitionistic Fuzzy Normed Spaces ◽  
Convergent Sequences

We studyλ-statistically convergent sequences of functions in intuitionistic fuzzy normed spaces. We define concept ofλ-statistical pointwise convergence andλ-statistical uniform convergence in intuitionistic fuzzy normed spaces and we give some basic properties of these concepts.

scholarly journals Intuitionistic Fuzzy Normed Prime Ideal and Some of Their Characteristics

2021 ◽  
Author(s):  
Tekalign Regasa Ashale
Keyword(s):  
Prime Ideal ◽  
Membership Function ◽  
Prime Ideals ◽  
Basic Properties ◽  
Intuitionistic Fuzzy

This Paper intends to introduce the notion of prime ideals of Intuitionistic fuzzy normed Rings and to establish basic properties related to it. It investigates these notions and shown anew Result using intuinistic fuzzy points and non membership function incorparating with t-norm and s-norm to show aome results of fuzzy prime ideal.

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