On a F-pseudo Z-b-subalgebra

In this article, we apply the concept of a t -intuitionistic fuzzy set to PMS-ideals in PMS-algebras. The notion of the t -intuitionistic fuzzy PMS-ideal of PMS-algebra is introduced, and several related properties are studied. The relationships between a t -intuitionistic fuzzy PMS-ideal and a t -intuitionistic fuzzy PMS-subalgebra of a PMS-algebra, as well as the relationships between an intuitionistic fuzzy PMS-ideal and a t -intuitionistic fuzzy PMS-ideal are discussed in detail. A condition for an intuitionistic fuzzy set to be a t -intuitionistic fuzzy PMS-ideal is provided. The t -intuitionistic fuzzy PMS-ideals of PMS-algebra are described using their α , β level cuts. The homomorphism of a t -intuitionistic fuzzy PMS-ideal of a PMS-algebra is studied, and its homomorphic image and inverse image are explored. The Cartesian product of any two t -intuitionistic fuzzy PMS-ideals is discussed, and some related results are derived. The Cartesian product of the t -intuitionistic fuzzy PMS-ideals is also characterized using its α , β level cuts. The strongest t -intuitionistic fuzzy PMS-relation in a PMS-algebra is defined. Finally, the relationships between the strongest t -intuitionistic fuzzy PMS-relation and t -intuitionistic fuzzy PMS-ideal are studied.

In this paper the notion of fuzzy BE-algebras are introduced. We state and prove some theorems in fuzzy BE-algebras and level subalgebras. Some characterizations of fuzzy subalgebras of BE-algebras are given. Using fuzzy subalgebras, characterizations of Artinian and Noetherian BE-algebras are also established. Finally the notion of fuzzy topological BE-algebras is introduced. We state and prove the Foster’s results on homomorphic images and inverse images in fuzzy topological BE-algebras.

In this paper, we apply the concept of bipolar fuzzy sets to pseudo-UP ideals in pseudo-UP algebras. We prove that the intersection of two bipolar fuzzy pseudo-UP ideals is also a bipolar fuzzy pseudo-UP ideal, while the union of two such ideals does not always result in a bipolar fuzzy pseudo-UP ideal. Additionally, we discuss the concepts of bipolar fuzzy pseudo-UP ideals under homomorphism and explore several related properties. The homomorphic image and inverse image of bipolar fuzzy pseudo-UP ideals in a pseudo-UP algebra are also examined in detail. Furthermore, we study the notion of a bipolar fuzzy pseudo-UP ideal under the Cartesian product of pseudo-UP algebra. The Cartesian product of any two bipolar fuzzy pseudo-UP ideals is also the bipolar fuzzy pseudo-UP ideal of pseudo-UP algebra, and then some related results are obtained. MSC: 03G25, 06D30.

In this paper, the notion of cubic subalgebras of BCH-algebras are introduced. Some characterization of cubic subalgebras of BCH-algebras are given. The homomorphic image and inverse image of cubic subalgebras are studied and investigated some related properties

The aim of this paper is to extend fuzzifying BCH algebra by introducing a unary predicate and by adopting the semantic method of continuous lattice valued logic. We define the concepts of fuzzifying sub algebras, fuzzifying ideals, fuzzifying closed ideals, fuzzifying q-ideals and fuzzifying implicative ideals in BCH-algebras, and discuss the relations among them. How to deal with the homomorphic images and inverse images of fuzzifying ideals, fuzzifying closed ideals, fuzzifying q-ideals and fuzzifying implicative ideals are studied. The product of two fuzzifying ideals (fuzzifying closed ideals, fuzzifying q-ideals and fuzzifying implicative ideals) is investigated.

A probabilistic automaton (pa) is a fuzzy automaton, in which, sum of all fuzzy memberships of the initial states is one and from each state, on an input symbol, the sum of the fuzzy memberships of the transitions is one. In pa, it is shown that, if h : Γ* → Σ* is a morphism and h–1 (λ) = λ, then the image of a recognisable subset of Γ* is a recognisable subset of Σ* and if h is fine, then the inverse image of recognisable subset of Σ* is recognisable. It is also proved that the shuffle product of any two recognisable sets is recognisable.

The concept and properties of cubic sets were first introduced and investigated by Jun et al. in 2011. In this paper, we first introduce the concept of cubic sets in UP-subalgebras and consider the UP-ideals of a UP-algebra. Relationships between the cubic UP-subalgebras and the cubic UP-ideals of a UP-algebra are investigated. In addition, the homomorphic images and the inverse images of the cubic UP-subalgebras and the cubic UP-ideals are also studied. Related properties of UP -algebras and their UP-ideals are explored and discussed. Finally, the Cartesian product of cubic UP-algebras are investigated.

In this paper, the notions of hesitant fuzzy dot subalgebras, hesitant fuzzy normal dot subalgebras, and hesitant fuzzy dot ideals of B-algebras are presented, and some of their features are examined, in this study. The homomorphic image and inverse image of hesitant fuzzy dot subalgebras, as well as the hesitant fuzzy dot ideal, are investigated. We also explore some related characteristics of hesitant fuzzy relations on the family of hesitant fuzzy dot subalgebras and hesitant fuzzy dot ideal of B-algebras.

In this paper, the notion of interval-valued fuzzy SA-ideals (briefly i-v fuzzy SA-ideal) in SA-algebras is introduced. Several theorems are stated and proved. The image and inverse image of i-v fuzzy SA-ideals are defined and how the homomorphic images and inverse images of i-v fuzzy SA-ideals become i-v fuzzy SA-ideals in SA-algebras is studied as well.

In this paper, we introduce concepts of T <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">H</sub> -interval- valued fuzzy left ideal, Th-interval-valued fuzzy right ideal, T <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">H</sub> -interval-valued fuzzy ideal and extension principle of interval-valued fuzzy set, investigate some of their properties and structural characteristics and propose some theorems for homomorphic image and its inverse image on T <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">H</sub> -interval-valued fuzzy ideal.

A picture fuzzy set (PFS) is an augmentation of Atanassov’s intuitionistic fuzzy set (IFS). The PFS-based models are useful in the circumstances when we face uncertain and vague information, especially in the case when we need more answers of the form “indeed,” “avoid,” “no,” and “refusal.” It has been considered as an essential tool to deal with unsure data during an investigation. In this manuscript, we explore the idea of a picture fuzzy near-ring (PFNR) and a picture fuzzy ideal (PFI) of a near-ring (NR). We illustrate some basic properties such as union, intersection, homomorphic image, and preimage of PFIs of a NR. Furthermore, there is discussion about the direct product of PFIs of a NR.

The notion of weakly [Formula: see text]-absorbing ideals, introduced as a natural generalization of prime ideals, has gained significant attention in commutative rings. A weakly [Formula: see text]-absorbing ideal of a commutative ring [Formula: see text] ensures that for all [Formula: see text], the inclusion [Formula: see text] and [Formula: see text] implies that at least one of [Formula: see text] or [Formula: see text] belongs to [Formula: see text]. This paper builds upon the existing framework by introducing and exploring weakly [Formula: see text]-[Formula: see text]-absorbing ideals in the context of a multiplicatively closed subset [Formula: see text] of [Formula: see text]. An ideal [Formula: see text], disjoint from [Formula: see text], is defined as weakly [Formula: see text]-[Formula: see text]-absorbing if [Formula: see text] and [Formula: see text] guarantee that [Formula: see text], [Formula: see text], or [Formula: see text] for some [Formula: see text]. We give the fundamental properties of weakly [Formula: see text]-[Formula: see text]-absorbing ideals and investigate their behavior under various ring constructions, such as amalgamation duplications, homomorphic images, direct products and trivial extensions. Notable results include conditions under which the ideals retain the weakly [Formula: see text]-[Formula: see text]-absorbing property and characterizations of these ideals in special commutative rings such as reduced rings and local semiprime rings which are not prime.

Composition, cartesian and direct products of fuzzy multivalued mappings

In this paper an exclusive study of some standard (lattice) algebraic properties for Intuitionistic fuzzy (inverse) images of Intuitionistic fuzzy subsets is done. Further as in crisp setup, characterizations for injectivity and surjectivity of maps in terms of some (lattice) algebraic properties of Intuitionistic fuzzy images and Intuitionistic fuzzy inverse images are performed.

This paper describes a generalized Diophantine fuzzy sets, which can be seen as a generalization of both Diophantine fuzzy sets and Pythagorean fuzzy sets. We define the basic properties of generalized Diophantine fuzzy set, as well as their relationships and distances. We compare Diophantine fuzzy sets with other Diophantine Pythagorean fuzzy sets to demonstrate their importance in the literature. We introduce new operators including necessity, possibility, accuracy function and score function. Furthermore, we discuss the new distance between normalized Euclidean distance and normalized Hamming distance. For a generalized Diophantine fuzzy relation, image and inverse image functions are defined. Numerous real-world applications can be found for the prevalent ideas of intuitionistic fuzzy sets, Pythagorean fuzzy sets, Diophantine fuzzy sets and q-rung orthopair fuzzy sets. Regretfully, these theories about the membership and non-membership grades have their own limits. We provide a new idea the generalized Diophantine fuzzy set that eliminates these limitations by including reference parameters. Compared to other kinds of fuzzy sets, there are more applications for generalized Diophantine fuzzy sets. We offer practical examples that show how different enhanced distances might be used in everyday situations. Additionally, to demonstrate the effectiveness of the suggested approach, flowchart based multi-criteria decision-making is provided and used to a numerical example. The outcomes are assessed for various parameter values. Furthermore, a comparative analysis developed to demonstrate the superiority of the suggested technique over current methodologies.