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Our purpose of this study is to construct an algorithm for finding a zero of the sum of two maximally monotone mappings in Hilbert spaces and discus its convergence. The assumption that one of the mappings is α-inverse strongly monotone is dispensed with. In addition, we give some applications to the minimization problem. Our method of proof is of independent interest. Finally, a numerical example which supports our main result is presented. Our theorems improve and unify most of the results that have been proved for this important class of nonlinear mappings.

This paper deals with the theoretical analysis of the notion of interval valued fuzzy sets (IVFS) applied to possibility measures. This permits to provide interval valued possibility measure (IVPM) and interval valued necessity measure (IVNM) as well as interval valued possibility distribution (IVPD). Particularly, two kinds of IVPM will be provided. The first one assumes a conjunctive normal form and a disjunctive normal form pertaining to a logical assertion. While the second one considers a logical AND and a logical OR as an essence to construct the underlying interval. The properties of both representations are investigated. Also, some basic mode operations involving conjunction and disjunction combinations are examined. Conditioning in the setting of IVPM is introduced considering either a canonical extension of well established rules, or more interestingly by solving the underlying Cox's axiomatic equation. Finally, some further extensions using general class of t‐norms operators are discussed.

This paper aims to initiate a new, formal theory of sociocultural physics.

Its intended scope is limited to predicting either long‐term, large‐scale or short‐term, small‐scale sociocultural events. The theory that the authors develop, called sociohistory, links three independent but relatable approaches: part of Sorokin's epistemological theory of sociocultural dynamics, Frieden's epistemological theory of extreme physical information (EPI), and Yolles's social viable systems (SVS) theory.

Although not all of Sorokin's ideas are universally accepted, a subset of them is found to be extremely useful for describing the conceptual context of complex systems. This includes how sociocultural processes link closely into political processes.

The theory that develops helps explain how opposing, cultural enantiomers or yin‐yang forces (represented, for instance, by the polar mindsets represented in Islamic fundamentalism and global enterprise) can result in violent conflict, or in either viable or non‐viable social communities. The informations I and J of EPI theory are regarded, respectively, as sensate and ideational enantiomers.

While the resulting sociocultural physics is in its infancy, an illustrative application to the developmental dynamics of post‐colonial Iran demonstrates its potential utility.

This study updates the literature review of Jones (1987) published in this journal. The study pays particular attention to two important themes that have shaped the field over the past 35 years: (1) the development of a range of innovative new statistical learning methods, particularly advanced machine learning methods such as stochastic gradient boosting, adaptive boosting, random forests and deep learning, and (2) the emergence of a wide variety of bankruptcy predictor variables extending beyond traditional financial ratios, including market-based variables, earnings management proxies, auditor going concern opinions (GCOs) and corporate governance attributes. Several directions for future research are discussed.

This study provides a systematic review of the corporate failure literature over the past 35 years with a particular focus on the emergence of new statistical learning methodologies and predictor variables. This synthesis of the literature evaluates the strength and limitations of different modelling approaches under different circumstances and provides an overall evaluation the relative contribution of alternative predictor variables. The study aims to provide a transparent, reproducible and interpretable review of the literature. The literature review also takes a theme-centric rather than author-centric approach and focuses on structured themes that have dominated the literature since 1987.

There are several major findings of this study. First, advanced machine learning methods appear to have the most promise for future firm failure research. Not only do these methods predict significantly better than conventional models, but they also possess many appealing statistical properties. Second, there are now a much wider range of variables being used to model and predict firm failure. However, the literature needs to be interpreted with some caution given the many mixed findings. Finally, there are still a number of unresolved methodological issues arising from the Jones (1987) study that still requiring research attention.

The study explains the connections and derivations between a wide range of firm failure models, from simpler linear models to advanced machine learning methods such as gradient boosting, random forests, adaptive boosting and deep learning. The paper highlights the most promising models for future research, particularly in terms of their predictive power, underlying statistical properties and issues of practical implementation. The study also draws together an extensive literature on alternative predictor variables and provides insights into the role and behaviour of alternative predictor variables in firm failure research.

Provides an overview of major developments pertaining to generalized information theory during the lifetime of Kybernetes. Generalized information theory is viewed as a collection of concepts, theorems, principles, and methods for dealing with problems involving uncertainty‐based information that are beyond the narrow scope of classical information theory. Introduces well‐justified measures of uncertainty in fuzzy set theory, possibility theory, and Dempster‐Shafer theory. Shows how these measures are connected with the classical Hartley measure and Shannon entropy. Discusses basic issues regarding some principles of generalized uncertainty‐based information.

The main purpose of this paper is first to discern the overwhelming influence of Kantian thought in the development of mainstream political economic doctrines. In this we will show that the Kantian philosophical influence has introduced an abiding element of duality in all matters of the western liberal theory of social contract and political economy. The nature of Kantian moral philosophy will be shown to have left the study of political economy by and large ethically neutral by treating the role of morals, ethics and values exogenously to the economic system. We will then introduce some substantive elements of an alternative approach to the treatment of ethics and values in the socio‐economic system. We will show that in the alternative approach to the study of social contract theory and political economy the ethical considerations appear as endogenous elements and strongly negate the Kantian principle of duality and individualistic rationalism.

Results are given which establish a computational foundation for simplicial approximation and design centering of a convex body. A simplicial polyhedron is used to approximate the convex body and the “design center”, i.e. the point inside the body furthest in some norm from its exterior, is approximated by the point in the polyhedron furthest from its exterior. A point representation of the polyhedron is used, so that there is no necessity for computing or storing the faces of the approximation. Since in N space there can be factorially more faces than points, we are able to achieve significant efficiencies in both operation count and storage requirements, compared to previously reported methods. We give results for the 2 norm and the max norm, and demonstrate that our new method is operable in the nonconvex case, and can handle a mixed basis of faces and points as well.