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In this paper, we extend our investigation about the generalized comaximal graph introduced in Biswas et al. (Discrete Math Algorithms Appl 11(1):1950013, 2019a). The generalized comaximal graph is defined as follows: given a finite commutative ring R, the generalized comaximal graph G(R) is an undirected graph with its vertex set comprising elements of R and two distinct vertices u, v are adjacent if and only if there exists a non-zero idempotent e ∈ R such that u R + v R = e R . In this study, we focus on identifying the rings R for which the graph G(R) exhibits planarity. Moreover, we provide a characterization of the class of ring for which G(R) is toroidal, denoted by γ (G (R)) = 1 . Furthermore, we also evaluate the energy of the graph G(R). Finally, we demonstrate that the graph G(R) is always Hamiltonian for any finite commutative ring R. [ABSTRACT FROM AUTHOR]

In this paper, we describe an activity that involves economics and mathematics. It is included in the planning of orientation paths towards university studies within the Mathematical High School Project and is dedicated to students in the last years of high school. In particular, this research will deal with the issue of solving an economic problem using not only real analysis instruments but also geometrical topics concerning Euclidean geometry and topology. Mathematics becomes a language to understand and explain a real life problem, such as determining the optimal position of an airport, a nuclear reactor and so on. Some activities made use of dynamic geometry software and computer simulations. [ABSTRACT FROM AUTHOR]

This article provides a power series summability-based Korovkin type approximation theorem for any sequence of fuzzy positive linear operators. Using the notion of fuzzy modulus of smoothness, we also derive an associated approximation theorem concerning the fuzzy rate of convergence of these operators. Furthermore, through an example, we illustrate that our summability- based Korovin type theorem has an advantage over the fuzzy Korovkin type theorem proved in the seminal paper by Anastassiou (Stud. Univ. Babeş-Bolyai Math L(4):3–10, 2005) [ABSTRACT FROM AUTHOR]

Let R be a commutative ring with 1. In Biswas et al. (Disc Math Algorithms Appl 11(1):1950013, 2019), we introduced a graph G(R) whose vertices are elements of R and two distinct vertices a, b are adjacent if and only if a R + b R = e R for some nonzero idempotent e in R. Let G ′ (R) be the subgraph of G(R) generated by the non-units of R. In this paper, we characterize those rings R for which the graph G ′ (R) is connected and Eulerian. Also we characterize those rings R for which genus of the graph G ′ (R) is ≤ 2 . Finally, we show that the graph G ′ (R) is a line graph of some graph if and only if R is either a regular ring or a local ring. [ABSTRACT FROM AUTHOR]

Solovyov (Fuzzy Sets Syst 159:2567–2585, 2008) introduced the notion of stratified Q-topological spaces, which in turn gives rise to the category Str-Q-TOP of stratified Q-topological spaces (where Q is a fixed member of a fixed variety of Ω -algebras). Singh and Srivastava (Ann. Fuzzy Math. Inform. 12:539–546, 2016) introduced the Q-topological space (Q , ⟨ { i d Q } ∪ { q ̲ ∣ q ∈ Q } ⟩) which is a Sierpinski object in the category Str-Q-TOP. In this paper, motivated by Singh (Fuzzy Sets Syst 159:2611–2615, 2008), we determine the coreflective hull of (Q , ⟨ { i d Q } ∪ { q ̲ ∣ q ∈ Q } ⟩) in the category Str-Q-TOP. We also determine the coreflective hulls of the categories Str-Dis-Q-TOP of discrete Q-topological spaces and Str-Ind-Q-TOP of stratified indiscrete Q-topological spaces, in the category Str-Q-TOP, motivated by Hoffmann (Arch Math 33:258–262, 1979) and Singh and Srivastava (Quaest. Math. 36: 167–179, 2013) [ABSTRACT FROM AUTHOR]

In a society that has to reconcile two areas which are conceptually very distant from each other, such as interdisciplinarity and specialization, the education for young people is essential to form a thought to understand complexity, thanks also to the stimuli deriving from increasingly powerful and interconnected technological and IT environments. So, it is essential to identify teaching–learning processes and methods that allow students to understand and act adequately with a constantly evolving reality. Transdisciplinary themes can be introduced to enrich the students' curriculum by anchoring them strongly to the wealth of emerging technologies, using their potential and designing educational activities focused on technology and attractive to the various spheres of knowledge. In this paper is presented an experimental activity of designing Smart objects in the Internet of Things conducted with students of the "Mathematical High School" project. [ABSTRACT FROM AUTHOR]

In this paper we study the theory Q. We prove a basic result that says that, in a sense explained in the paper, Q can be split into two parts. We prove some consequences of this result. (i) Q is not a poly-pair theory. This means that, in a strong sense, pairing cannot be defined in Q. (ii) Q does not have the Pudlák Property. This means that there two interpretations of $$\mathsf{S}^1_2$$ in Q which do not have a definably isomorphic cut. (iii) Q is not sententially equivalent with $$\mathsf{PA}^-$$ . This tells us that we cannot do much better than mutual faithful interpretability as a measure of sameness of Q and $$\mathsf{PA}^-$$ . We briefly consider the idea of characterizing Q as the minimal-in-some-sense theory of some kind modulo some equivalence relation. We show that at least one possible road towards this aim is closed. [ABSTRACT FROM AUTHOR]

The so-called non-associative MV-algebras were introduced recently by the first author and J. Kühr in order to have an appropriate tool for certain logics used in expert systems where associativity of the binary operation is excluded, see, e.g., Botur and Halaš (Arch Math Log 48:243–255, 2009). Since implication is an important logical connective in practically every propositional logic, in the present paper we investigate the implication reducts of non-associative MV-algebras. We also determine their structures based on the underlying posets. The natural question when a poset with the greatest element equipped with sectional switching involutions can be organized into an implication NMV-algebra is solved. Moreover, congruence properties of the variety of implication NMV-algebras with, respectively, without zero are investigated. Analogously to classical propositional logic, we introduce a certain kind of Sheffer operation and we obtain a one-to-one correspondence between NMV-algebras and certain algebras built up by a Sheffer-like operation together with a unary operation. [ABSTRACT FROM AUTHOR]

In this paper, inspired by the previous work of Franco Montagna on infinitary axiomatizations for standard $$\mathsf {BL}$$ -algebras, we focus on a uniform approach to the following problem: given a left-continuous t-norm $$*$$ , find an axiomatic system (possibly with infinitary rules) which is strongly complete with respect to the standard algebra This system will be an expansion of Monoidal t-norm-based logic. First, we introduce an infinitary axiomatic system $$\mathsf {L}_*^\infty $$ , expanding the language with $$\Delta $$ and countably many truth constants, and with only one infinitary inference rule, that is inspired in Takeuti-Titani density rule. Then we show that $$\mathsf {L}_*^\infty $$ is indeed strongly complete with respect to the standard algebra . Moreover, the approach is generalized to axiomatize expansions of these logics with additional operators whose intended semantics over [0, 1] satisfy some regularity conditions. [ABSTRACT FROM AUTHOR]

In this paper, we explore some unexplored consequences of Agliano et al. (Studia Logica 87:73-98, 2007) and Agliano and Montagna (J Pure Appl Algebra 181:105-129, 2003) on varieties of BL-algebras and their hoop subreducts. The main topics are: generation by finite algebras, the finite embeddability property and varieties of finite index. [ABSTRACT FROM AUTHOR]

In this paper, inspired by some types of $$BL$$ -algebra filters (deductive systems) introduced in Haveshki et al. (Soft Comput 10:657-664, ), Kondo and Dudek (Soft Comput 12:419-423, ) and Turunen (Arch Math Log 40:467-473, ), we defined residuated lattice versions of them and study them in connection with Van Gasse et al. (Inf Sci 180(16):3006-3020, ), Lianzhen and Kaitai (Inf Sci 177:5725-5738, ), Zhu and Xu (Inf Sci 180:3614-3632, ). Also we consider some relations between these filters and quotient residuated lattice that are constructed via these filters. [ABSTRACT FROM AUTHOR]

In this paper, t-norm based intuitionistic fuzzy submodules are defined, and their various properties are investigated. We also show that if an intuitionistic fuzzy set of a module is an intuitionistic fuzzy submodule with respect to a t-norm, then it is also an intuitionistic fuzzy submodule with respect to the annihilation t-norm. We investigate the nature of intuitionistic fuzzy submodules of a module with the help of their respective cut sets. We obtain some results based on ( α, β)-level sets and t-norm based α-cut sets of an intuitionistic fuzzy submodule with respect to a t-norm T. [ABSTRACT FROM AUTHOR]

Quite recently, Savaş (Appl Math Lett 21:134-141, ), defined the lacunary statistical analogue for double sequence $$X=\{X_{k,l}\}$$ of fuzzy numbers as follows: a double sequence $$X=\{X_{k,l}\}$$ is said to be lacunary P-statistically convergent to $$X_{0}$$ provided that for each $$\epsilon >0$$In this paper we introduce and study double lacunary $$\sigma$$-statistical convergence for sequence of fuzzy numbers and also we get some inclusion theorems. [ABSTRACT FROM AUTHOR]

In this paper, a formula-based fuzzy integral minus fuzzy proportional minus fuzzy derivative (FI − FP − FD) controller is proposed based on the modified conventional parallel PID controller, i.e. parallel integral minus proportional minus derivative (I − P − D) controller, in order to avoid some practical industrial process problems. It freezes the linear structure of conventional parallel I − P − D controller, with analytical formulas. The final shape of the controller is a discrete-time fuzzy version of conventional parallel I − P − D controller. Computer simulation is performed to evaluate the performance of FI − FP − FD controller for setpoint tracking and load-disturbance rejection for some complex processes, such as, first- and second-order process with delay, inverse response process with and without delay and higher order processes. The simulation is done using National Instrument™ software (LabVIEW™). The response of FI − FP − FD controller is compared with the conventional parallel I − P − D controller, tuned with the Ziegler-Nichols tuning technique. It is observed that the FI − FP − FD controller performed much better than conventional I − P/I − P − D controller. Simulation results demonstrate the effectiveness and usefulness of proposed formula-based FI − FP − FD controller. Also, the bounded-input bounded-output (BIBO) stability of the overall fuzzy control system is established with sufficient conditions, using the famous 'Small Gain Theorem'. [ABSTRACT FROM AUTHOR]

Nonlinear optimization algorithms could be divided into local exploitation methods such as Nelder-Mead (NM) algorithm and global exploration ones, such as differential evolution (DE). The former searches fast yet could be easily trapped by local optimum, whereas the latter possesses better convergence quality. This paper proposes hybrid differential evolution and NM algorithm with re-optimization, called as DE-NMR. At first a modified NM, called NMR is presented. It re-optimizes from the optimum point at the first time and thus being able to jump out of local optimum, exhibits better properties than NM. Then, NMR is combined with DE. To deal with equal constraints, adaptive penalty function method is adopted in DE-NMR, which relaxes equal constraints into unequal constrained functions with an adaptive relaxation parameter that varies with iteration. Benchmark optimization problems as well as engineering design problems are used to experiment the performance of DE-NMR, with the number of function evaluation times being employed as the main index of measuring convergence speed, and objective function values as the main index of optimum's quality. Non-parametric tests are employed in comparing results with other global optimization algorithms. Results illustrate the fast convergence speed of DE-NMR. [ABSTRACT FROM AUTHOR]

The extension of rough set model is an important research direction in the rough set theory. In this paper, based on the rough set model over two universes, we firstly propose the variable precision rough set model (VPRS-model) over two universes using the inclsion degree. Meantime, the concepts of the reverse lower and upper approximation operators are presented. Afterwards, the properties of the approximation operators are studied. Finally, the approximation operators with two parameters are introduced as a generalization of the VPRS-model over two universes, and the related conclusions are discussed. [ABSTRACT FROM AUTHOR]

Abstract  Hájek introduced the logic $$BL_{vt}$$ enriching the logic BL by a unary connective vt which is a formalization of Zadeh’s fuzzy truth value “very true”. $$\hbox{BL}_{vt}$$ algebras, i.e., BL-algebras with unary operations, called vt-operators, which are among others subdiagonal, are an algebraic counterpart of $$BL_{vt}.$$ Partially ordered commutative integral residuated monoids (pocrims) are common generalizations of both BL-algebras and Heyting algebras. The aim of our paper is to introduce and study algebraic properties of pocrims endowed by “very-true” and “very-false”-like operators. [ABSTRACT FROM AUTHOR]

Abstract  An MV-pair is a BG-pair (B; G) (where B is a Boolean algebra and G is a subgroup of the automorphism group of B) satisfying certain conditions. Recently, it was proved by Jenca that, given an MV-pair (B; G), the quotient $$(B/\!\sim_G),$$ where $$(\sim_G),$$ is an equivalence relation naturally associated with G, is an MV-algebra, and conversely, to every MV-algebra there corresponds an MV-pair. In this paper, we introduce a new definition of so called MV*-pair, and we show that $$(B/\!\sim_G),$$ is an effect algebra iff the first of the defining properties of the MV*-pair is satisfied, while the second property guarantees the MV-algebra structure of $$(B/\!\sim_G)$$. We also study some relations between states on MV-algebras and the corresponding R-generated Boolean algebras. [ABSTRACT FROM AUTHOR]

Abstract  This paper deals with the portfolio selection problem when the returns of assets obey LR-type possibility distributions and there exist the limits on holdings. A new possibilistic mean–variance model to portfolio selection is proposed based on the definitions of the possibilistic return and possibilistic risk, which can better integrate an uncertain decision environment with vagueness and ambiguity. This possibilistic mean–variance model can be regarded as extensions of conventional probabilistic mean–variance methodology and previous possibilistic approaches since it contains less parameter and has a more extensive application. A numerical example of a possibilistic fuzzy portfolio selection problem is given to illustrate our proposed effective means and approaches. [ABSTRACT FROM AUTHOR]

Abstract  This paper presents a new method for appraising the performance of high school teachers based on fuzzy number arithmetic operations. It uses fuzzy numbers to represent fuzzy grades. The fuzzy weights of criteria are automatically generated from the opinions of evaluators. The simplified fuzzy number arithmetic operations are used for calculating the average of fuzzy numbers. It can appraise the performance of high school teachers in a more flexible and more intelligent manner. [ABSTRACT FROM AUTHOR]

Abstract  A pervasive task in many forms of human activity is classification. Recent interest in the classification process has focused on ensemble classifier systems. These types of systems are based on a paradigm of combining the outputs of a number of individual classifiers. In this paper we propose a new approach for obtaining the final output of ensemble classifiers. The method presented here uses the Dempster–Shafer concept of belief functions to represent the confidence in the outputs of the individual classifiers. The combing of the outputs of the individual classifiers is based on an aggregation process which can be seen as a fusion of the Dempster rule of combination with a generalized form of OWA operator. The use of the OWA operator provides an added degree of flexibility in expressing the way the aggregation of the individual classifiers is performed. [ABSTRACT FROM AUTHOR]

Abstract  In this paper we deal with a generalization of the Quine–McCluskey method. We show that the generalized method can find a normal form for any finite-valued logical function. Moreover, this normal form is simpler than that found by the intuitive method using the table of values. The method has been successfully implemented and tested on examples. [ABSTRACT FROM AUTHOR]

Abstract  The present paper is a sequel to Paoli F, Ledda A, Giuntini R, Freytes H (On some properties of QMV algebras and $$\sqrt{^{\prime}}$$QMV algebras, submitted). We provide two representation results for quasi-MV algebras in terms of MV algebras enriched with additional structure; we investigate the lattices of subvarieties and subquasivarieties of quasi-MV algebras; we show that quasi-MV algebras, as well as cartesian and flat $$\sqrt{^{\prime}}$$ quasi-MV algebras, have the amalgamation property. [ABSTRACT FROM AUTHOR]

Abstract  In this paper, we describe the relationships between pseudo MV algebras and semirings. We also give definitions of automata on lattice ordered semirings, prove that the family of K-Languages is closed under union, and discuss the conditions for the closedness of families of K-languages under intersection, generalized intersection and reversal operations. [ABSTRACT FROM AUTHOR]

Abstract  The object of the present paper is the investigation and study of (fuzzy) hyperideals in H v - semigroups. Regular equivalence relations play in H v - semigroup theory a role analogous to congruences in semigroup theory, so we introduce fuzzy regular equivalence relations on H v -semigroups and then we study fuzzy Rees regular relations on H v -semigroups. Using this ideas, we establish a relation between fuzzy hyperideal of an H v -semigroup H and fuzzy hyperideal of a quotient H v -semigroup of H. Some characterizations of them are then shown. [ABSTRACT FROM AUTHOR]

Abstract??The class of bounded residuated lattice ordered monoidsRl-monoids) contains as proper subclasses the class of pseudoBL-algebras (and consequently those of pseudoMV-algebras,BL-algebras andMV-algebras) and of Heyting algebras. In the paper we introduce and investigate local boundedRl-monoids which generalize local algebras from the above mentioned classes of fuzzy structures. Moreover, we study and characterize perfect boundedRl-monoids. [ABSTRACT FROM AUTHOR]

Abstract Based on Jordan Curve Theorem, a universal classification method called hyper surface classification (HSC) has recently been proposed. Experimental results are exciting, which show that in three-dimensional space, this method works fairly well in both accuracy and efficiency even for large size data up to 107. However, designing a number of new classifiers is needed with the growing of feature dimension. To solve the problem, a kind of efficient dimension transposition method that is suitable for HSC and without losing any essential information is put forward in this paper. The dimension transposition method rearrange all of the numerals in the higher dimensional data to lower dimensional data without changing each numeral, but only change their position according to some orders. The experiment shows that the method can classify high dimension data with high accuracy. [ABSTRACT FROM AUTHOR]

Abstract  The notion of pseudo-BCK algebras was introduced by Georgescu and Iorgulescu Proceedings of DMTCS′01: Combinatorics, Computability and Logic, Springer, London, pp 97–114, 2001. It is so general that fleas, pseudo-hoops, psMTL, psBL, pseudo-MV et al., and so hoops, MTL, BL, MV et al. can be seen its extensions. In this paper, we extend the ideal and congruence theory to pseudo-BCK algebras, and investigate the connections between pseudo-BCK algebras and PD(GPD)-posets. [ABSTRACT FROM AUTHOR]