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A complex intuitionistic fuzzy set (CIFS) has an ability to represent the problems with intuitionistic uncertainty and periodicity, simultaneously. In this paper, we present a new framework for handling complex intuitionistic fuzzy information by combining the CIFSs with competition graphs. We first introduce the concept of complex intuitionistic fuzzy competition graphs along with its two worthwhile extensions, namely, complex intuitionistic fuzzy k-competition and complex intuitionistic fuzzy p-competition graphs. Further, we present complex intuitionistic fuzzy neighborhood graphs and m-step complex intuitionistic fuzzy competition graphs with some of their remarkable results. We also describe an application of complex intuitionistic fuzzy competition graphs along with an algorithm which finds the competition among the applicants competing for the particular jobs possessing the two-dimensional information. Moreover, we provide a comparison analysis of proposed competition graphs with existing graphs to find the validity and superiority of proposed competition graphs.

Knowing the applications of logical algebras in various fields, such as artificial intelligence or coding theory, in this paper, we study some properties of a special class of such algebras, namely finite Wajsberg algebras. For this purpose, we give a representation theorem for finite Wajsberg algebras and give a formula for the number of non-isomorphic Wajsberg algebras of order n; also we give the total number of finite Wajsberg algebras of order n. Since a big value of n involves a lot of computations, as examples, we present and describe all finite Wajsberg algebras of order $$n\le 9$$ .

As a generalization to hesitant fuzzy linguistic term set (HFLTS), double hierarchy hesitant fuzzy linguistic term set (DHHFLTS) is presented which circumvents the weakness of HFLTS in representing complex linguistic terms. DHHFLTS has two linguistic hierarchies with the second hierarchy supplementing the primary which enables decision-makers (DMs) to represent complex linguistic terms better. Motivated by the power of DHHFLTS, in this paper, a new decision framework is presented under DHHFLTS context. Initially, a new aggregation operator called double hierarchy hesitant fuzzy hybrid aggregation (DHHFHA) operator is proposed for sensible aggregation of DMs’ preference information. Further, weights of attributes are calculated by extending statistical variance (SV) method under DHHFLTS context. Objects are prioritized by extending the popular WASPAS (weighted aggregated sum product assessment) method to DHHFLTS context. The applicability and usefulness of the proposed framework are realized by demonstrating a risk management technique (RMT) selection problem for a construction project. Finally, the superiority and weakness of the proposed framework are discussed by comparison with other methods.

In this paper, we have introduced the notion of local and semilocal triangle algebras and propose the theorems that characterize these algebraic structures. Additionally, we have established the new properties of these algebraic structures and discussed the relations between local triangle algebras and some interval valued residuated lattice (IVRL)-filters, such as n-fold IVRL-extended integral filters and IVRL-extended maximal filters. The obtained results proved that the MTL-triangle algebra is a subdirect product of local triangle algebras. Moreover, a correlation was observed between the set of the dense elements and local triangle algebras. Finally, semilocal triangle algebras were introduced and assessed in detail, and an association was observed between the semilocal triangle algebras and quotient triangle algebras. submittedVersion

The aim of this study is to introduce fuzzy filters of Sheffer stroke Hilbert algebra. After defining fuzzy filters of Sheffer stroke Hilbert algebra, it is shown that a quotient structure of this algebra is described by its fuzzy filter. In addition to this, the level filter of a Sheffer stroke Hilbert algebra is determined by its fuzzy filter. Some fuzzy filters of a Sheffer stroke Hilbert algebra are defined by a homomorphism. Normal and maximal fuzzy filters of a Sheffer stroke Hilbert algebra and the relation between them are presented. By giving the Cartesian product of fuzzy filters of a Sheffer stroke Hilbert algebra, various properties are examined. © 2021 - IOS Press. All rights reserved., Ege Üniversitesi: 20772, The authors are thankful to the referees for a careful reading of the paper and for valuable comments and suggestions. This study is partially funded by Ege University Scientific Research Projects Directorate with the Project Number 20772.

A complex Pythagorean fuzzy set, an extension of Pythagorean fuzzy set, is a powerful tool to handle two dimension phenomenon. Dombi operators with operational parameters have outstanding flexibility. This article presents certain aggregation operators under complex Pythagorean fuzzy environment, including complex Pythagorean Dombi fuzzy weighted arithmetic averaging (CPDFWAA) operator, complex Pythagorean Dombi fuzzy weighted geometric averaging (CPDFWGA) operator, complex Pythagorean Dombi fuzzy ordered weighted arithmetic averaging (CPDFOWAA) operator and complex Pythagorean Dombi fuzzy ordered weighted geometric averaging (CPDFOWGA) operator. Moreover, this paper explores some fundamental properties of these operators with appropriate elaboration. A decision‐making numerical example related to the selection of bank to purchase loan is given to demonstrate the significance of our proposed approach. Finally, a comparative analysis with existing operators is given to demonstrate the peculiarity of our proposed operators.

In the paper, we introduce some stabilizers and investigate related properties of them in MTL-algebras.Then, we also characterize some special classes of MTL-algebras, for example, IMTL-algebras, integral MTL-algebras, Godel algebras and MV-algebras, in terms of these stabilizers. Moreover, we discuss the relation between stabilizers and several special filters (ideals) in MTL-algebras. Finally, we discuss the relation between these stabilizers and prove that the right implicative stabilizer and right multiplicative stabilizer are order isomorphic. This results also give answers to some open problems, which were proposed by Motamed and Torkzadeh in [Soft Comput, {\bf 21} (2017) 686-693].

This paper presents a new two-tier decision making framework with linguistic preferences for scientific decision making. The major reason for adopting linguistic preference is to ease the process of rating of alternatives by allowing decision makers (DMs) to strongly emphasize their opinion on each alternative. In the first tier, aggregation is done using a newly proposed operator called linguistic based aggregation (LBA), which aggregates linguistic terms directly without making any conversion. The main motivation for this proposal is driven by the previous studies on aggregation theory which reveals that conversion leads to loss of information and formation of virtual sets which are no longer sensible and rational for decision making process. Secondly, in the next tier, a new ranking method called IFSP (intuitionistic fuzzy set based PROMETHEE) is proposed which is an extension to PROMETHEE (preference ranking organization method for enrichment evaluation) under intuitionistic fuzzy set (IFS) context. Unlike previous ranking methods, this ranking method follows a new formulation by considering personal choice of the DMs over each alternative. The main motivation for such formulation is derived from the notion of not just obtaining a suitable alternative but also coherently satisfying the DMs’ viewpoint during decision process. Finally, the practicality of the framework is tested by using supplier selection (SS) problem for an automobile factory. The strength and weakness of the proposed LBA-IFSP framework are verified by comparing with other methods under the realm of theoretical and numerical analysis. The results from the analysis infer that proposed LBA-IFSP framework is rationally coherent to DMs’ viewpoint, moderately consistent with other methods and highly stable and robust against rank reversal issue.

In this paper, we introduce the notions of multiplier, ⊙ -closure operator and modal operator on hoop-algebras. After that, we investigate some algebraic properties of multiplier, ⊙ -closure operator and modal operator on hoop-algebras. Then we study relationships between multiplier and closure operator on hoop-algebras showing that, any monotone modal operator on hoop-algebra serves as a closure operator. Finally we represent image of hoop-algebra under the closure operator can be a hoop-algebra.

In this paper, extension of relative co-annihilator in residuated lattices is introduced for subsets T and Y of residuated lattice L and is denoted by (T, Y ). In this extension, T has a more important role than Y , as expected. It is proved if T is a filter, then co-annihilator of T relative to Y is a filter and is the same as the co-annihilator of T relative to the filter generated by Y. Also some theorems are stated and proved which determine the relationship between this special subset and the other types of filters. Finally, we give some conditions for subsets T and Y of residuated lattices L, for which (T, Y ) is a special subset of L.

This paper introduces the notion of (locally) fuzzy homomorphism in fuzzy hyper BE-subalgebra and makes a connection between fuzzy BE-algebras and hyper BE-algebras via this notion. Considering the fuzzy homomorphism in fuzzy hyper BE-subalgebra, this study defines some equivalence relations in a way that, under some conditions, are regular or strongly regular and so derives fuzzy BE-algebras by quotient of hyper fuzzy BE-subalgebras. In fact, it tries to introduce some strongly regular relations on any hyper BE-algebras by using the concept of fuzzy hyper BE-subalgebras and fuzzy homomorphism. Moreover, the concept of normal fuzzy homomorphism is defined and some new normal fuzzy homomorphisms are introduced to make better connections between fuzzy BE-algebras and fuzzy hyper BE-subalgebras.

Nowadays, companies are paying more attention to supply chain management in order to achieve success in the competitions and keep the customers satisfied. Therefore, supplier selection is of prime importance in a supply chain which has a key role in determining the success or failure of a business. In this paper, fuzzy multi-objective linear programming model with group decision making is presented. Firstly, linguistic variables in the form of interval-valued intuitionistic fuzzy numbers and group decisions are defined. By using TOPSIS method, the weight of each criterion (objective) and weight of each constraint are determined. Then, with defining membership functions of the objectives and membership functions of suppliers’ constraints and using the achieved weights from the previous phase, the supplier selection problem will be converted to fuzzy multi-objective linear programming model which determines the appropriate ordering quantities for each supplier. Finally, two numerical examples for supplier selection are used to demonstrate the practicality and effectiveness of the proposed approach.

In this paper, the notions of commutators and pseudo commutators of elements (subsets) of a BCI-algebra are introduced and some properties are given. The concept of solvable BCI-algebras are also discussed and their properties are investigated. It is proved that the class of solvable BCI-algebras is closed under sub-algebra, cartesian product and inverse image operations.

This article will introduce K-modal BL-logic and investigate some properties of this new logic. Consequently, T -modal BL-logic and S4-modal BL-logic, as schematic extensions of K-modal BL-logic, will be dealt with. Likewise, the algebraic semantics based on each logic will be constructed. Finally, the soundness and completeness theorems of these logics will be proved.

Soft set theory plays a vital role in solving many complicated problems with inherited uncertainty. An n -ary algebraic systems is a generalization of algebraic structures and it is the most natural way for the further development, deeper understanding of their properties. In this paper, we apply soft set theory to an n -ary algebraic systems and introduce the notions of soft n -ary groups and soft n -ary subgroups. Further, some operations on soft sets are extended to the former. Finally, we provide the characterization of soft n -ary subgroups over an n -ary group ( G , f ) and study their related properties.

In this paper, the radical of an implicative filter in Hilbert algebras is studied and some theorems are given on its properties and we show that radical form a closure operator. Also, the radical of the set of all regular elements is characterized. Finally, the notion of semi maximal filter is introduced as a closed set of that closure operator and studied it in detail.

In this paper, we are going to introduce a fundamental relation "δ" on (hyper BE-algebra) dual hyper K-algebra and investigate some properties. We show that quotient of any dual hyper K-algebra via a regular relation is a hyper BE-algebra and this quotient, via any strongly regular relation is a BE-algebra. Furthermore, it shows that "δ" under some condition is transitive and quotient of any weak commutative dual hyper K-algebra via "δ ∗ " is a dual BCK-algebra.

In this paper, we present some new connections between BCK-algebras and binary block codes.

Fuzzy models are becoming useful because of their aim of reducing the differences between the traditional numerical models used in engineering and sciences and the symbolic models used in expert systems. A vague graph is a generalized structure of a fuzzy graph that gives more precision, flexibility, and compatibility to a system when compared with systems that are designed using fuzzy graphs. In this paper, we introduce various types of vague bridges, vague cut-vertices, vague cycles and vague trees in vague graphs, and investigate some of their interesting properties. Most of these various types are defined in terms of levels. We also describe comparison of these types.

A big shortcoming of the simple genetic algorithm is that whenever it converges to a local optimum, its performance is continuously deteriorating, especially in the highly nonlinear problems such as traveling salesman problem (TSP). Therefore, some heuristics such as local search are needed to help genetic algorithm (GA) loops escaping such situations. The critical point in such hybridization is the determining a suitable time for applying local search to the GA population. In this study, a new hybridization of GA and local search based on a new similarity-based control mechanism is proposed, and its behavior on different TSP instances is compared with simple GA. The experimental results show that the proposed hybrid algorithm yields the optimal tour length in most of the cases, especially in the TSP instances with higher complexity.

We study some special sets in MTL-algebras. The notion of the radical of a filter in MTL-algebras is defined and several characterizations of the radical of a filter are given. The sets of dense elements and double complemented elements in MTL-algebras are defined and we state and prove some theorems on the properties of these sets and filters of MTL-algebras. We also prove that the radical of a positive implicative filter of an MTL-algebra is a subset of double complemented elements.

In this paper, we first introduce the notion of implication filters in BL-algebras and then state and prove some theorems which determine the relationships of these filters and other filters in BL-algebras. We also introduce the notion of implication BL-algebras and investigate its properties, as well as the relationship of implication BL-algebras and other algebraic structures.

In this paper, we introduce the notion of upper (down) set in BL-algebras and extended upper sets of BL-algebras. Also, the notions of Krull dimension and regular sequence in BL-algebras are introduced and studied in detail.

In this paper we introduce the notion of obstinate filter in BL-algebra A and we state and prove some theorems which determine the relationship between this notion and other types of filters of a BL-algebra and by some examples we show that this notion is different. Also, we prove that if F is an obstinate filter, then F is a Boolean filter hence A/F is a Boolean algebra. Finally, we construct some algorithms for studying the structure of the finite BL-algebras and filters in finite BL-algebras.

Hypergraphs are among the most ubiquitous models of both natural and human-made structures. They can be used to model system architectures and data structures, and to represent a partition, covering and clustering in the area of circuit design. In this paper, we introduce the notions of vague hypergraphs and dual vague hypergraphs and present some of their interesting properties. We also introduce the notion of A-tempered vague hypergraphs and investigate some of their properties.

In this paper, we introduce the notion of bi-Smarandache BL-algebra, bi-weak Smarandache BL-algebra, bi-Q-Smarandache ideal and bi-Q-Smarandache implicative filter, we obtain some related results and construct quotient of bi-Smarandache BL-algebras via MV-algebras (or briefly bi-Smarandache quotient BL-algebra) and prove some theorems. Finally, the notion of bi-strong Smarandache BL-algebra is presented and relationship between bi-strong Smarandache BL-algebra and bi-Smarandache BL-algebra are studied.

In this paper, we introduce the notion of fuzzy filters(ideals) in CI-algebras. We study fuzzy congruence relation in detail and construct quotient of \((X/\bar{\theta}; {\circ}, 1/\bar{\theta})\) via a fuzzy congruence relation on CI-algebra X.

In this paper, we introduce the concept of TL-filter of BL-algebra and study some basic properties. TL-filter generated by L-subsets and the concept of T-congruence L-relations on BL-algebra are introduced and the relationships between TL-filters and T-congruence L-relations on BL-algebra are studied.

In this article, we introduced the notions fuzzy soft subalgebras and fuzzy soft ideal of subtraction algebras. We showed that fuzzy soft image and fuzzy soft inverse image of fuzzy soft ideal are both fuzzy soft ideal under certain conditions. We have studied their related properties in details.

In this paper, generalization of the fuzzy BCK/BCI-algebras of type (α, β)* are introduced. Then we state and prove some theorems that determine the relationship between these notions and subalgebras of BCK/BCI-algebras. Characterizations of (α, β)*-fuzzy subalgebras in a BCK/BCI-algebras are given.

In this paper, we introduced the notion of n-fold obstinate filter in BL-algebras and we stated and proved some theorems, which determine the relationship between this notion and other types of n-fold filters in a BL-algebra. We proved that if F is a 1-fold obstinate filter, then A/F is a Boolean algebra. Several characterizations of n-fold fantastic filters are given, and we show that A is a n-fold fantastic BL-algebra if A is a MV-algebra (n ≥ 1) and A is a 1-fold positive implicative BL-algebra if A is a Boolean algebra. Finally, we construct some algorithms for studying the structure of the finite BL-algebras and n-fold filters in finite BL-algebras.

In this paper, we introduce the notion of fuzzy n-folds (P, implicative and fantastic) ideals in BCH-algebras which is a natural generalization of notion of n-folds (P, implicative and fantastic) ideals in BCH-algebras and we stated and proved some theorems which determines the relationship between these notions. Finally we give some computational Algorithms for these notions.

By two relations belonging to and quasi-coincidence (q) between fuzzy points and fuzzy sets, we define the concept of (±, ±)-fuzzy subalgebras where ±, ± are any two of $${\{\in, q, \in\vee q, \in\wedge q\}}$$ with $${\alpha\neq \in\wedge q}$$. We state and prove some theorems in (±, ±)-fuzzy B-algebras.