On migrative means and copulas

In this short work we extend the results of J.Fodor and I.J. Rudas [6] characterizing migrative triangular norms, to quasi-arithmetic means. We use idempotisation construction to obtain quasi-arithmetic means migrative with respect to fixed parameter a. We also obtain the necessary and sufficient condition for a migrative triangular norm to be a copula. <br /

Migrativity properties of 2-uninorms over semi-t-operators

summary:In this paper, we analyze and characterize all solutions about $\alpha$-migrativity properties of the five subclasses of 2-uninorms, i. e. $C^{k}$, $C^{0}_{k}$, $C^{1}_{k}$, $C^{0}_{1}$, $C^{1}_{0}$, over semi-t-operators. We give the sufficient and necessary conditions that make these $\alpha$-migrativity equations hold for all possible combinations of 2-uninorms over semi-t-operators. The results obtained show that for $G\in C^{k}$, the $\alpha$-migrativity of $G$ over a semi-t-operator $F_{\mu,\nu}$ is closely related to the $\alpha$-section of $F_{\mu,\nu}$ or the ordinal sum representation of t-norm and t-conorm corresponding to $F_{\mu,\nu}$. But for the other four categories, the $\alpha$-migrativity over a semi-t-operator $F_{\mu,\nu}$ is fully determined by the $\alpha$-section of $F_{\mu,\nu}$

Fuzzy implications: alpha migrativity and generalised laws of importation

In this work, we discuss the law of α-migrativity as applied to fuzzy implication functions in a meaningful way. A generalisation of this law leads us to Pexider-type functional equations connected with the law of importation, viz., the generalised law of importation I(C(x,α),y)=I(x,J(α,y)) (GLI) and the generalised cross-law of importation I(C(x,α),y)=J(x,I(α,y)) (CLI), where C is a generalised conjunction. In this article we investigate only (GLI). We begin by showing that the satisfaction of law of importation by the pairs (C, I) and/or (C, J) does not necessarily lead to the satisfaction of (GLI). Hence, we study the conditions under which these three laws are related

Funciones t-migrativas t-overlap: una generalización de migratividad en funciones t-overlap

Este artículo introduce una generalización de funciones migrativas por extensión de la condición de la operación producto aplicada en las variables. Más específicamente, en lugar de exigir multiplicar la variable x por un número real alfa; en este trabajo se trabaja este número alfa con las variables de acuerdo a una t-norma. Se denomina a esta generalización función t-migrativa con respecto a tal tnorma. Luego se analizan las propiedades principales de funciones t-migrativas en funciones t-overlap y se introducen algunos métodos de construcción de este tipo de funciones.This paper introduces a generalization of migrative functions by extending the conditions of the product operation applied in the variables. We operate a number with the variables according to a t-norm instead of multiplying the variable x by this number. Such generalization, whenever it occurs, is called a t-migrative function with respect to such t-norm. Furthermore, we analyse the main properties of t-migrative and t-overlap functions. We introduce some interesting methods of construction of such functions

On Some Functional Equations Related to Alpha Migrative t-conorms

In this contribution, we analyse in details the recently introduced definition of migrative tconorms [see Fuzzy implications: alpha migrativity and generalised laws of importation, M. Baczy´nski, B. Jayaram, R. Mesiar, 2020]. We also focus on some general functional equations, which might be obtained from such a notion. We concentrate on some particular well-known families of fuzzy implications and show solutions of those equations among this kind of fuzzy implication functions

Funciones t-migrativas t-overlap: una generalización de migrtividad en funciones t-overlap

Este artículo introduce una generalización de funciones migrativas por extensión de la condición de la operación producto aplicada en las variables. Más específicamente, en lugar de exigir multiplicar la variable x por un número real α, en este trabajo se trabaja este número α con las variables de acuerdo a una t-norma. Se denomina a esta generalización función t-migrativa con respecto a tal tnorma. Luego se analizan las propiedades principales de funciones t-migrativas en funciones t-overlap y se introducen algunos métodos de construcción de este tipo de funcionesThis paper introduces a generalization of migrative functions by extending the conditions of the product operation applied in the variables. More specifically, instead of requiring to multiply the variable x by a real number α, in this work we operate this α number with the variables according to a t-norm. We call such generalization as a t-migrative function with respect to such t-norm. Then we analyze the main properties of t-migrative t-overlap functions and introduce some construction method

Solution to an open problem: A characterization of conditionally cancellative t-subnorms

In this work we solve an open problem of U. Höhle (Klement et al. Fuzzy Sets Syst 145:471-479, 2004, Problem 11). We show that the solution gives a characterization of all conditionally cancellative t-subnorms. Further, we give an equivalence condition under which a conditionally cancellative t-subnorm has 1 as its neutral element and hence show that conditionally cancellative t-subnorms whose natural negations are strong are, in fact, t-norms

Invariability, orbits and fuzzy attractors

In this paper, we present a generalization of a new systemic approach to abstract fuzzy systems. Using a fuzzy relations structure will retain the information provided by degrees of membership. In addition, to better suit the situation to be modelled, it is advisable to use T-norm or T-conorm distinct from the minimum and maximum, respectively. This gain in generality is due to the completeness of the work on a higher level of abstraction. You cannot always reproduce the results obtained previously, and also sometimes different definitions with different views are obtained. In any case this approach proves to be much more effective when modelling reality

Mathematical Modeling of Secondary Malignancies and Associated Treatment Strategies

Several scientific and technological advancements in radiation oncology have resulted in dramatic improvements in dose conformity and delivery to the target volumes using external beam radiation therapy (EBRT). However, radiation therapy acts as a double-edged sword leading to drastic side-effects, one of them being secondary malignant neoplasms in cancer survivors. The latency time for the occurrence of second cancers is around $10$-$20$ years. Therefore, it is very important to evaluate the risks associated with various types of clinically relevant radiation treatment protocols, to minimize the second cancer risks to critical structures without impairing treatment to the primary tumor volume. A widely used biologically motivated model (known as the initiation-inactivation-proliferation model) with heterogeneous dose volume distributions of Hodgkin's lymphoma survivors is used to evaluate the excess relative risks (ERR). There has been a paradigm shift in radiation therapy from purely photon therapy to other particle therapies in cancer treatments. The extension of the model to include the dependence of linear energy transfer (LET) on the radio-biological parameters and mutation rate for charged particle therapy is discussed. Due to the increase in the use of combined modality regimens to treat several cancers, it is extremely important to evaluate the second cancer risks associated with these anti-cancer therapies. The extension of the model to include chemotherapy induced effects is also discussed. There have been several clinical studies on early and late relapses of cancerous tumors. A tumor control probability (TCP) model with recurrence dynamics in conjunction with the second cancer model is developed in order to enable design of efficient radiation regimens to increase the tumor control probability and relapse time, and at the same time decrease secondary cancer risks. Evolutionary dynamics has played an important role in modeling cancer progression of primary cancers. Spatial models of evolutionary dynamics are considered to be more appropriate to understand cancer progression for obvious reasons. In this context, a spatial evolutionary framework on lattices and unstructured meshes is developed to investigate the effect of cellular motility on the fixation probability. In the later part of this work, this model is extended to incorporate random fitness distributions into the lattices to explore the dynamics of invasion probability in the presence and absence of migration.1 yea