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The grade of membership function for fuzzy monotone functions is defined and investigated. An algorithm for finding the membership value is presented. A minterm even function and minterm odd function are defined and studied. It is found that these two functions are the two most alternation functions. The relationships with threshold functions are also presented. In addition, three ways to implement a fuzzy monotone increasing function are investigated. Applications to function representation, data compression and error detection are illustrated. The results have useful applications in fuzzy logic, expert systems, fuzzy expert systems, and also management of uncertainty.

We develop new high‐order positive, monotone and convex interpolations, which are to be used in the multigrid context. This means that the value of the interpolant is calculated only at the midpoints lying between the locations of the given values. As a consequence, these interpolants can be calculated very efficiently. They are then tested in a time‐dependent very large scale integration process simulation application.

The purpose of this study is to develop two empirical models that predict the shear strength of exterior beam-column joints exposed to monotonic and cyclic loading using Gene expression programming (GEP).

The GEP model developed for the monotonic loading case is trained and validated using 81 data test points and that for cyclic loading case is trained and validated using 159 data test points that collected from different 9 and 39 experimental programs, respectively. The parameters that are selected to develop the cyclic GEP model are concrete compressive strength, joint aspect ratio, column axial load and joint transverse reinforcement. The monotonic GEP model is developed using concrete compressive strength, column depth, joint width and column axial load.

GEP models are proposed in this paper to predict the joint shear strength of beam-column joints under cyclic and monotonic loading. The predicted results obtained using the GEP models are compared to those calculated using the ACI-352 code formulations. A sensitivity analysis is also performed to further validate the GEP models.

The proposed GEP models provide an accurate prediction for joint shear strength of beam-column joints under cyclic and monotonic loading that is more fitting to the experimental database than the ACI-352 predictions where the GEP models have higher R² value than the code formulations.

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.

Fears over public accounting becoming increasingly concentrated have inspired several attempts to study the relationship between competition and audit quality. These studies have yielded conflicting results without a clear reason as to why. This paper aims to propose a new approach and empirically demonstrate a non-monotonic association between competition and audit quality.

Using metropolitan statistical area level data from the USA over the period of 2000–2014, the author shows that the effect that changes in the competition will have on audit quality depends upon the current competitive state of the market.

Audit quality is at its highest level when competition is neither too high nor too low. In addition, the point of inflection at which competition turns from being helpful to harmful is influenced by the saturation of the Big 4 auditors in the market.

These findings can help explain the mixed results of the literature and provide insight into the role that regulators can play in modulating competition.

This is the first paper to document a non-monotonic relationship between competition and audit quality. By introducing and exploring the validity of a non-monotonic component in the audit quality equation, the authors can better determine, which competitive structures generate desired levels of audit quality.

This paper applies a recently developed method of ranking socioeconomic inequality in health to ranking U.S. happiness from 1994 to 2012 using the GSS data. We also compare happiness between subgroups as decomposed by gender, race, and age. We establish and test a monotone condition of happiness – a richer person is likely to be happier. Under the monotone condition, standard tools of welfare and inequality ranking can be applied straightforwardly.

The purpose of this paper is to determine the relationship between indoor environmental quality (IEQ) and occupants’ productivity improvements in green buildings in order to propose probable enhancements of national green certification criteria.

Survey approach was selected under quantitative phenomenon. Hence, questionnaire survey was selected as a primary data collection technique. It was linked to semi-structured interviews to validate survey results. The survey data were analysed by using nonparametric statistical analysis techniques, such as significance testing and Spearman’s correlation. Statistical Package for the Social Science (SPSS) v.20 statistical analysis software was used in data analysis.

Seven factors were identified as significant factors which showed statistically significant monotonic correlation to major IEQ dimensions. Among those, air quality and acoustical partitioning factors confirmed a statistically significant weak positive monotonic correlation, whilst system control showed strongly positive monotonic correlation to occupants’ productivity in green buildings.

The findings can be practically implied as a basis to review the existing evaluation criteria of IEQ in national green certification system to propose probable enhancements.

The significant IEQ factors influencing occupants’ productivity were determined as the focal point of this research. Accordingly, new provisions were proposed to enhance the national green certification criteria.

The purpose of this paper is to discuss the necessary condition of the relative error between continuous function transformation after inverse transformation and original sequence is not larger than the relative error between transformed sequence and its corresponding simulation sequence.

First, explore the function transformation feature of after inverse transformation the relative error not enlarged, then combine this feature with the function transformation feature of not enlarge the class ratio dispersion, not reduce the smoothness which author have got, and obtain a kind of special transformation that not enlarge class ratio dispersion, not reduce the smoothness and after inverse transformation keep the relative not enlarged. Meanwhile, offer the concrete form of this special function type to monotone increasing continuous function transformation and monotone decreasing continuous function transformation, respectively, and study its properties.

This paper finds the concise and important feature of monotonically increasing function transformation after inverse transformation whether the relative error enlarge or not is at first, the concise and important feature of monotonically decreasing function transformation after inverse transformation relative error not enlarged is. And find that the ideal function transformation which both reduces class ratio dispersion strictly and keeps error of inverse transformation not enlarged is non-exist for monotone increasing function transformation and monotone decreasing function transformation.

Use the necessary condition given by this paper, it may use to judge whether function transformation can keep relative error of inverse transformation not enlarged by easy data calculation before build modeling, therefore, choose the best function transformation. These results tell the authors: the paper cannot treat any functions as the same that whether the relative error of inverse transformation will not enlarge (or not reduced), but the authors should divide them into two parts to discuss that it will be expanded in some range or be reduced in some range. It will affect the future direction of the research, not to find the function transform both satisfies the class ratio dispersion reduced and keep the relative error of inverse transformation not enlarged, but to study which kind of function transform will narrow class ratio dispersion in some range, after the modeling accuracy improvement, but after the inverse transformation the relative error enlarged, and at this time the simulation accuracy is still higher than the simulation accuracy of original data modeling directly. Which kind of function transform will expand class ratio dispersion in some range, after the modeling accuracy diminution, but after the inverse transformation the relative error not enlarged, and now the simulation accuracy is still higher than the simulation accuracy of original data modeling directly, too.

Let peers no longer spend energy in seeking the function transformation which both reduce class ratio dispersion and keep relative error of inverse transformation not enlarged. At the same time, also remind peers that even if a function transformation reduces class ratio dispersion greatly, the data modeling accuracy improves a lot after transformation, but the error of inverse transformation is may quite large, still. Besides, even if function transformation increases class ratio dispersion, the data modeling accuracy is not good after transformation, the ideal situation after inverse transformation would occur, and the possibility cannot be excluded.

The purpose of this paper is to investigate whether a non-monotonic relationship may exist between financial distress and foreign exchange (FX) exposure. The authors hypothesize that firms with higher FX exposures are those with the lowest levels of financial distress because the costs of hedging exceed the benefits and those with highest levels of financial distress due to the conflict of interest between shareholders and bondholders.

The methodology allows for the possibility of a non-monotonic relation between financial distress and FX exposure for firms known to have ex-ante exposures. The approach is to include a Black-Scholes-Merton financial distress measure and standard accounting-based financial distress measures.

The results support the hypothesis of a non-monotonic relationship between financial distress and exposure; companies with the lowest and highest levels of financial distress are willing to bear greater FX exposures.

The authors examine whether a non-monotonic relationship may exist between distress and FX exposure. Intuition for this non-monotonic relationship is provided by Stulz (1996) as he describes the risk management practices of firms with low, medium, and high default probabilities.

Many engineering and scientific problems require the filling of a two‐dimensional region with scan lines of finite width. The number of contiguous scan line segments required for the filling depends on the direction used for scanning. When the cost of the filling operation increases with the number of scan line segments, as is the case in numerically controlled machining, layered fabrication and computer graphics applications, then it is desirable to select a direction that minimizes this number. In this paper we provide a method for efficiently computing such an optimal direction when the region to be filled is bounded by straight‐line segments and/or circular arcs.