Constructing an Objective Function for Aggregating Incomplete Preferences

Today, the evidence of the Eskov–Zinchenko effect is becoming increasingly widespread. In this case, it is proved that any set of human body parameters is unique (statistically unique). Now we are also applying this effect to the neural networks of the brain. An analysis of electroencephalograms shows that brain biopotentials are not statistically stable. For the electroencephalograms analysis, it is proposed to create paired sample comparison matrices and find numbers k of the sample pairs that can have one (common) general population. It was found that these numbers k depend on the physiological state of the test subject. For example, for epileptic patients, number k increases dramatically, and it usually does not exceed 30-45% of all 105 pairs in each of such paired comparison matrices.

Effects of sudden changes in temperature on the general state of functional systems of the body can be assessed by the effects of local cold expesure on the neuromuscular system. Aim: to study electromyograms of the retracting muscle flexor of the little finger with weak static muscle tension (F1 = 50 N) during cold exposure. Methods. Altogether, 15 men aged 20-27 years participated in the study. We used one of the stochastic methods in the form of calculation of matrices of paired comparisons of electromyogram samples as an indicator of k pairs of matches of samples. Matrices of paired comparisons of samples were calculated for each test subject at a static voltage F1 = 50 N before and after local cold exposure. At the same time built a quasi-attractor dynamics, the behavior of x(t) and determined area of the quasi-attractor. In the end, the analysis of the state of the muscles of the subjects in the development of static force F was carried out on the basis of a comparison of the area of quasi-attractors in the form of S. Results. With weak (F1 = 50 N) static force after cold exposure, the area of quasi-attractor increased by 2.5 times, while in the matrices of paired comparisons of samples after local cold exposure, the number of matches of pairs of samples increased from 8 to 14. Conclusion: the regularities of changes in the number of matches of pairs of samples k in the matrices of paired comparisons with changes in the static force and under the influence of local cold exposure were revealed; statistically significant differences were found for such samples k and S before and after hypothermia.

Preference fusion when the number of alternatives exceeds two: indirect scoring procedures

Contributors

In the paper we deal with lower bounds constructed for the asymptotic competitive ratio of semi-online bin packing and batched bin packing algorithms.We determine the bounds as the solutions of a related nonlinear optimization problem using theoretical analysis and a reliable numerical global optimization method. Our results improve the lower bounds given in Gutin et al. (Discrete Optim 2:71–82, 2005) for some special cases of the batched bin packing problem.

A general concept of majority rule

In this paper, we establish a relation-theoretic set-valued version of the fixed point result of Ćirić and Prešić (Acta Math. Univ. Comen. LXXVI(2):143–147, 2007) on metric spaces endowed with an arbitrary binary relation. The results of this paper, generalize and unify the fixed point results of Ćirić and Prešić (Acta Math. Univ. Comen. LXXVI(2):143–147, 2007), Shukla and López (Quaest. Math. 45(3):1–16, 2019), and Shukla and Radenović (An. Ştiinţ. Univ. ‘Al.I. Cuza’ Iaşi, Mat. 63(2):339–350, 2017) in product spaces. Some examples are provided that justify and establish the importance of our results. As applications of our main result, we have established the existence of solutions to differential inclusion problems and the weak asymptotical stability and a global attractivity of the equilibrium point of a difference inclusion problem. The use of arbitrary binary relations in our results permits us to apply the results to the differential inclusion problems and difference inclusion problems with weaker assumptions than those used in the papers mentioned above.

The aim of this paper is to introduce a concept of quasiconvexity for set-valued maps in a general framework, by only considering an abstract convexity structure in the domain and an arbitrary binary relation in the codomain. It is shown that this concept can be characterized in terms of usual quasiconvexity of certain real-valued functions. In particular, we focus on cone-quasiconvex set-valued maps with values in a partially ordered vector space.

In this study, we consider a non-linear matrix equation of the formwhere Q is a Hermitian positive definite matrix, A * i stands for the conjugate transpose of an n n matrix A i and F j are order-preserving continuous mappings from the set of all Hermitian matrices to the set of all positive definite matrices such that F (O) = O.We discuss sufficient conditions that ensure the existence of a unique positive definite solution of the given matrix equation.For this, we derive some fixed point results for Suzuki-implicit type mappings on metric spaces (not necessarily complete) endowed with arbitrary binary relation (not necessarily a partial order).We provide adequate examples to validate the fixed-point results and the importance of related work, and the convergence analysis of non-linear matrix equations.

The Elementary Theory of Well-Odering—A Metamathematical Study—

In this paper, we prove coincidence and common fixed points results under nonlinear contractions on a metric space equipped with an arbitrary binary relation. Our results extend, generalize, modify and unify several known results especially those are contained in Berzig [J. Fixed Point Theory Appl. 12, 221-238 (2012))] and Alam and Imdad [To appear in Filomat (arXiv:1603.09159 (2016))]. Interestingly, a corollary to one of our main results under symmetric closure of a binary relation remains a sharpened version of a theorem due to Berzig. Finally, we use examples to highlight the accomplished improvements in the results of this paper.

Communicating between information systems

We extend the notion of generalized weakly contraction mappings due to Choudhury et al. (2011) to generalized α-β-weakly contraction mappings. We show with examples that our new class of mappings is a real generalization of several known classes of mappings. We also establish fixed point results for such mappings in metric spaces. Applying our new results, we obtain fixed point results on ordinary metric spaces, metric spaces endowed with an arbitrary binary relation, and metric spaces endowed with graph.

The idea of neighborhood systems is induced from the geometric idea of “near,” and it is primitive in the topological structures. Now, the idea of neighborhood systems has been extensively applied in rough set theory. The master contribution of this manuscript is to generate various topologies by means of the concepts of j -adhesion neighborhoods and ideals. Then, we define a new rough set model derived from these topologies and discussed main features. We show that these topologies are finer than those given in the previous ones under arbitrary binary relations. In addition, we elucidate that these topologies are finer than those topologies initiated based on different neighborhoods and ideals under reflexive relations. Several examples are provided to validate that our model is better than the previous ones.

In this paper the continuous utility representation problem will be discussed in arbitrary concrete categories. In particular, generalizations of the utility representation theorems of Eilenberg, Debreu and Estevez and Herves will be presented that also hold if the codomain of a utility function is an arbitrary totally ordered set and not just the real line. In addition, we shall prove and apply a general result on the characterization of structures that have the property that every continuous total preorder has a continuous utility representation. Finally, generalizations of the utility representation theorems of Debreu and Eilenberg will be discussed that are valid if we consider arbitrary binary relations and allow a utility function to have values in an arbitrary totally ordered set.