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The concept of complex fuzzy set (CFS) and complex intuitionistic fuzzy set (CIFS) is two recent developments in the field of fuzzy set theory. The significance of these concepts lies in the fact that these concepts assigned membership grades from the unit circle in the plane, i.e., in the form of a complex number instead of [0,1] interval. CFS cannot deal with information of yes and no type, while CIFS works only for a limited range of values. To deal with these kinds of problems, in this article, the further development of the theory of complex Pythagorean fuzzy sets (CPFSs) has been discussed. Some new operations on CPFSs, such as bounded difference, disjoint sum, disjunctive sum, probabilistic sum, bold sum, bold intersection, s-norm and t-norm have been proposed. The distance of two CPFSs has been proposed. This distance measure is then used to define η-equalities of CPFSs. Moreover, we define some new notions for the multicriteria decision-making (MCDM) problems such as the CPF decision-making matrix, CPF maxand mindecision-making matrix, and the distance measure between CPF maxand mindecision-making matrices. An MCDM method has been developed on the proposed novel notions. A real-life example demonstrates that the MCDM method developed in the paper can be utilized to deal with problems of uncertainty. Further, the comparative study of CPFSs with complex intuitionistic fuzzy sets, Pythagorean fuzzy sets, intuitionistic fuzzy sets, complex fuzzy sets, and fuzzy sets is established.

In this paper, we introduce some set-theoretic operations and laws of the IV-CFSSs, such as interval-valued complex fuzzy soft complement, union, intersection, t-norm, s-norm, simple product, Cartesian product, probabilistic sum, simple difference, and the convex linear sum of min and max operators. We define the distance measure of two IV-CFSSs. This distance measure is then used to define the δ-equality of IV-CFSSs. We establish some particular examples and basic results of these operations and laws. Moreover, we use IV-CFSSs in decision-making problems. We develop a new decision-making method using the interval-valued complex fuzzy distance measures under the environments of IV-CFSSs. We discuss the real-life case based on the proposed decision-making method. A real-life example demonstrates that the decision-making method developed in the paper can be utilized to deal with problems of uncertainty. Further, the comparative study of IV-CFSSs with complex fuzzy soft sets, interval-valued fuzzy soft sets, and fuzzy soft sets is established.

AbstractThe main purpose of this paper is to explore the structural properties of Hv-LA-semigroups with respect to generalized cubic relations. Some generalized cubic equivalence relations in Hv-LA-semigroups are investigated. Furthermore, certain results on generalized cubic relations by using the images and pre-images of Hv-LA-semigroups are provided.

It is common knowledge that various models with their limited boundaries of truth and falsehood are not sufficient to detect the reality so there is a need to discover other systems which are able to address the daily life problems. In every branch of science problems arise which abound with uncertainties and imprecisions. Some of these problems are related to human life, some others are subjective while others are objective and classical methods are not sufficient to solve such problems because they can not handle various ambiguities involved. To overcome this problem, Zadeh introduced the concept of a fuzzy set which provides a useful mathematical tool for describing the behavior of systems that are either too complex or are ill-defined to admit precise mathematical analysis by classical methods. Our aim in this paper is to use non-associate algebraic structures such as AG-groupoids and to develop the resulting properties. For the applications of this concept we introduce generalized fuzzy ideals and discuss their properties, specifically we characterize intra regular AG-groupoids using the properties of generalized fuzzy ideals.

In this paper, we introduce and use the concept of $$(\in _{\gamma },\in _{\gamma }\vee q_{\delta })$$ (∈γ,∈γ∨qδ) -fuzzy soft right ideals, to study the structural properties of an $$\mathcal {AG}$$ AG -groupoid. We characterize an intra-regular $$\mathcal {AG}$$ AG -groupoids using the properties of $$(\in _{\gamma },\in _{\gamma }\vee q_{\delta })$$ (∈γ,∈γ∨qδ) -fuzzy soft sets and $$(\in _{\gamma },\in _{\gamma }\vee q_{\delta })$$ (∈γ,∈γ∨qδ) -fuzzy soft right ideals.

AbstractIn this article we characterize the regular LA-semihypergroups in terms of -cubic (left, right, two sided, bi, generalized bi, interior, quasi)-hyperideals of LA-semihypergroups. Meanwhile, some illustrative examples are given to show the rationality of the definitions popularized in the present paper.

In this paper we introduce and develop the concept of $$(\in ,\in \vee q_{k})$$ (∈,∈∨qk) -cubic hyperideals, $$(\in ,\in \vee q_{k})$$ (∈,∈∨qk) -cubic bi-hyperideals, $$(\in ,\in \vee q_{k})$$ (∈,∈∨qk) -cubic generalized bi-hyperideals, $$(\in ,\in \vee q_{k})$$ (∈,∈∨qk) -cubic interior hyperideals, $$(\in ,{\in } \vee q_{k})$$ (∈,∈∨qk) -cubic quasi-hyperideals. At the end we characterize regular LA-semihypergroups by the properties of these $$(\in ,{\in } \vee q_{k})$$ (∈,∈∨qk) -cubic hyperideals.

This paper aims to apply fuzzy sets and soft sets in combination to investigate algebraic properties of regular AG-groupoids. We initiate (∈γ; ∈γ qδ)-fuzzy soft left ideals (right ideals, bi-ideals and quasi-ideals) over AG-groupoids and explore some related properties. Moreover, we give a number of characterizations for regular AG-groupoids by virtue of various types of fuzzy soft ideals over them.

In this paper, we discuss the further development of the theory of complex fuzzy sets (CFSs). The motivation for this extension is the utility of complex-valued function in membership grade which can express the two-dimensional ambiguous information that is prevalent in time-periodic phenomena. We introduce partial order relation on complex fuzzy sets. This partial order relation is then used to define the complex fuzzy maximal, minimal, maximum, and minimum elements. We propose new distance measures such as complex fuzzy distance measures and a complex fuzzy weighted distance measure. We establish some particular examples and basic results of the partial order relations and distance measures. Moreover, we utilize the complex fuzzy sets in signals and systems, because it is the specific form of the Fourier transform by restricting the range of Fourier transform to a complex unit disc. We establish a new algorithm based on the complex fuzzy distance measures and complex fuzzy weighted distance measures for applications in signals and systems by which we determine the degree of high resemblance of signals to the known signal. Further, the comparative study of the proposed distance measures with the Zhang distance measure, Hamming distance measure, and Normalized Hamming distance measure is discussed.

In this paper, we introduce the concept of $$(\in _{\gamma },\in _{\gamma }\vee q_{\delta })$$ (∈γ,∈γ∨qδ) -fuzzy quasi-ideals in AG-groupoids. We characterize intra-regular AG-groupoids by the properties of these ideals.

The complex fuzzy soft set is a new development in the theory of fuzzy soft systems which discuss two dimensional phenomena. In this paper, we discuss the further development of the theory of complex fuzzy soft sets. We introduce the notions of the distance function and distance matrix for the complex fuzzy soft sets. This distance function is then used to define δ-equalities of complex fuzzy soft sets. We establish some basic results and particular examples on the complex fuzzy soft sets. Moreover, we use complex fuzzy soft sets in signals and systems because its behavior is similar to a Fourier transform in certain cases. We develop a new method based on the distance function and distance matrix of complex fuzzy soft sets for applications in signals and systems by which we identify a reference signal out of the large number of signals detected by a digital receiver. A numerical example of signal detection demonstrates the utility of the concepts of distance function and distance matrix of complex fuzzy soft sets in practice.

In this paper, we introduce (∈γ, ∈γ∨qδ)-fuzzy right ideals in an AG-groupoid. We characterize intra-regular AG-groupoids using the properties of (∈γ, ∈γ∨qδ)-fuzzy subsets and (∈γ, ∈γ∨qδ)-fuzzy right ideals.

This paper deals with the optimal control problem in the giving up smoking model of fractional order. For the eradication of smoking in a community, we introduce three control variables in the form of education campaign, anti-smoking gum, and anti-nicotive drugs/medicine in the proposed fractional order model. We discuss the necessary conditions for the optimality of a general fractional optimal control problem whose fractional derivative is described in the Caputo sense. In order to do this, we minimize the number of potential and occasional smokers and maximize the number of ex-smokers. We use Pontryagin’s maximum principle to characterize the optimal levels of the three controls. The resulting optimality system is solved numerically by MATLAB.

In this paper, we consider the SEIR (Susceptible-Exposed-Infected-Recovered) epidemic model by taking into account both standard and bilinear incidence rates of fractional order. First, the nonnegative solution of the SEIR model of fractional order is presented. Then, the multi-step generalized differential transform method (MSGDTM) is employed to compute an approximation to the solution of the model of fractional order. Finally, the obtained results are compared with those obtained by the fourth-order Runge-Kutta method and non-standard finite difference (NSFD) method in the integer case.

In this work, we consider a nonlinear SEIR (susceptible, exposed, infectious, and removed) endemic model, which describes the dynamics of the interaction between susceptible and infected individuals in a population. The model represents the disease evolution through a system of nonlinear differential equations with variable infectivity which determines that the infectivity of an infected individual may not be constant during the time after infection. To control the spread of infection and to find a vaccination schedule for an endemic situation, we use optimal control strategies which reduce the susceptible, exposed, and infected individuals and increase the total number of recovered individuals. In order to do this, we introduce the optimal control problem with a suitable control function using an objective functional. We first show the existence of an optimal control for the control problem and then derive the optimality system. Finally the numerical simulations of the model is identified to fit realistic measurement which shows the effectiveness of the model.

AbstractIn this paper, we have discussed the direct products of ideals, prime ideals, minimal right ideals in AG-groupoids and AG* -groupoid. We have proved also that every ideal of the direct product of AG* -groupoids is prime if and only if it is an idempotent and the set of ideals of the product is totally ordered under inclusion.

In this paper, we introduce the concept of complex neutrosophic soft matrices. We define some basic operations including complement, union, and intersection on these matrices. We extend the concept of complex neutrosophic soft sets to complex neutrosophic soft matrices and prove related properties. Moreover, we develop an algorithm using complex neutrosophic soft matrices and apply it in signal processing.

In this paper, we introduce types of relations on complex fuzzy sets such as the complex fuzzy (CF) inverse relation, complex fuzzy reflexive relation, complex fuzzy symmetric relation, complex fuzzy antisymmetric relation, complex fuzzy transitive relation, complex fuzzy irreflexive relation, complex fuzzy asymmetric relation, complex fuzzy equivalence relation, and complex fuzzy-order relation. We study some basic results and particular examples of these relations. Moreover, we discuss the applications of complex fuzzy relations in Future Commission Market (FCM). We show that the introduction of CF relations to applications of FCMs can give a significant method for describing the temporal dependence between parameters of a Future Commission Market.

A complex fuzzy set is characterized by a membership function, whose range is not limited to [0, 1], but extended to the unit circle in the complex plane. In this paper, we introduce some new operations and laws of a complex fuzzy set such as disjunctive sum, simple difference, bounded difference, distributive law of union over intersection and intersection over union, equivalence formula, symmetrical difference formula, involution law, absorption law, and idempotent law. We introduce some basic results on complex fuzzy sets with respect to standard complex fuzzy intersection, union, and complement functions corresponding to the same functions for determining the phase term, and we give particular examples of these operations. We use complex fuzzy sets in signals and systems, because its behavior is similar to a Fourier transform in certain cases. Moreover, we develop a new algorithm using complex fuzzy sets for applications in signals and systems by which we identify a reference signal out of large number of signals detected by a digital receiver. We use the inverse discrete Fourier transform of a complex fuzzy set for incoming signals and a reference signal. Thus, a method for measuring the exact values of two signals is provided by which we can identity the reference signal.