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In the course of development of human communities towards industrially advanced societies of today, there have been changes not only in economic conditions in the majority of fields of human activity but also in the ways of providing for food, which went hand in hand with changes in living conditions. Large‐scale industrial production has brought about major changes in the way of life of the population. The development of industrial agglomerations results in a growing number of city dwellers, most of whom have no chance of producing foodstuffs of their own in kind. The distance between residential and industrial areas has been growing, the number of employed women has risen considerably. These are but a few factors affecting the way of boarding, particularly in households.

Buffer operators can be utilized to improve the smooth degree of the raw data sequence, and to increase the simulation accuracy of the model. The purpose of this paper is to analyze the cause of increase in the simulation accuracy of the buffer operator.

This paper probed into the modeling mechanism of several typical buffer operators such as the arithmetic buffer operators, the buffer operators with monotonic function and weighted buffer operators. The paper also gives an example of the buffer operator sequence.

The results indicate that after applying an infinite buffer operator, whether the authors adopt a weakening buffer operator or a strengthen buffer operator, the raw sequence can be changed into a constant sequence. Because the discrete GM(1,1) model can completely simulate constant sequence, the simulation accuracy is 100 percent. Because the discrete GM(1,1) model is the accurate form of the GM(1,1) model, after applying an infinite buffer operator, the GM(1,1) model can have a very high simulation accuracy. The buffer operator model can increase the simulation accuracy of both the GM(1,1) model and the discrete GM(1,1) model.

The paper analyses the cause of increasing simulation accuracy of the buffer operator model. The paper may indicate that possible results can be studied in the future. All the buffer operator models have similar properties. After applying an infinite buffer operator, the raw sequence can be changed into a constant sequence. A fixed-point axiom may be the basic cause.

Based on some of the results and definitions provided in the paper “system linkage: structural functions and hierarchies” and adding new definitions that are in keeping with the spirit of the same paper, new results have been obtained that explore the utility of the structural input‐output function.

Our approach is based principally on the application of graph theory to the study of relationships between variables using specific set theory concepts.

A result such as the fact that A covers B, for example, can be interpreted in terms of the latter set being formed of direct influences from elements in the former set in relation to one or more than one relationships. Analogously, the invariant set concept may be interpreted as the set maintaining its structure and status, remaining constant with respect to any possible relationships.

From a practical point of view, in the context of the study of networks within an ecosystem, authors (such as Patten et al. and Patten) have demonstrated that indirect effects between the variables of an ecosystem outweigh direct effects. This is the notion that the present authors have borne in mind in order to extend previous results to indirect influences from a discrete perspective.

The papers in this issue were given at the 25th Annual Conference, held at Bristol University from 22nd to 25th September, 1950. Some 230 delegates from the British Isles, the Commonwealth and Europe were welcomed to dinner on Friday evening by Sir Philip Morris, C.B.E., M.A., Vice‐Chancellor of the University, and Lady Morris. No papers were given on Friday evening, Mr. J. E. Wright arranging an informal dance after dinner.

A number of U.S. studies have documented an optimistic bias in analysts’ forecasts of earnings. This study investigates whether the optimistic bias and asymmetric behavior of forecast errors found in most U.S. studies exists in Japan. We find that for firms reporting profits, Japanese analysts’ forecasts have much greater accuracy and exhibit a small pessimistic bias in comparison to firms reporting losses, where analysts’ forecasts exhibit extremely poor accuracy and an extremely significant optimistic bias. The lack of ability to forecast losses is due to their transitory nature and not due to earnings management. Forecast accuracy and bias are not related to firm size, but are related to the magnitude of reported lossess and profits.

The purpose of this paper is to study free L‐fuzzy left R‐module, using the language of categories and functors for the general description of L‐fuzzy left R‐modules generated by L‐fuzzy set. In the language of categories and functors, an L‐fuzzy left R‐modules generated by L‐fuzzy set is called a free object in the category of L‐fuzzy left R‐modules determined by L‐fuzzy set.

Category theory is used to study the existent quality, unique quality and material structure of L‐fuzzy left R‐modules generated by L‐fuzzy set.

The paper gives the uniqueness, structure and existence theorems of free object in the category of L‐fuzzy left R‐modules determined by L‐fuzzy set, and the authors prove that the fuzzy free functor is left adjoint to the fuzzy underlying functor.

Some property of free L‐fuzzy left R‐modules will need to be further researched.

The paper defines a new class of L‐fuzzy left R‐modules, i.e. free L‐fuzzy left R‐modules, research and explore free L‐fuzzy left R‐modules in theory.

Entropy measures of fuzzy events of a set X with a (not necessary finite) positive measure µ defined on a σ‐algebra of subsets of X are studied. Using fuzzy measures and fuzzy integrals, a theorem is presented, which gives a sufficient condition for the existence of entropy measures under a list of reasonable axioms. The result is used to define entropy measures for fuzzy numbers.

It is obvious that an inventory item's lead time demand is affected by the length of the lead time as well as the actual demand on each day during the lead time. In a situation where the lead time and the daily demand are both stochastic, the probability distribution of an item's lead time demand is then determined by the probability distributions of the item's daily demand and lead time. This article presents a computationally simple method for determining the lead time demand's probability distribution from estimations of the item's daily demand and lead time probability distributions; no restriction is placed on the distribution forms of the daily demand, the lead time and the lead time demand. After obtaining the lead time demand distribution, this article illustrates the computation of “reorder points” and “protection levels” for an inventory item.

In this chapter, we advance an understanding of identity theory (IT) as originally created by Sheldon Stryker and developed over the past 50 years. We address misunderstandings of IT concepts and connections. We provide definitions of key ideas in IT, propositions that identify important relationships, and scope conditions that outline the circumstances to which IT applies. Our goal is to provide scholars with an accurate view of IT so that it can continue to advance the science of human behavior in sociology and beyond.