Defining Bonferroni means over lattices

In the face of mass amounts of information and the need for transparent and fair decision processes, aggregation functions are essential for summarizing data and providing overall evaluations. Although families such as weighted means and medians have been well studied, there are still applications for which no existing aggregation functions can capture the decision makers\u27 preferences. Furthermore, extensions of aggregation functions to lattices are often needed to model operations on L-fuzzy sets, interval-valued and intuitionistic fuzzy sets. In such cases, the aggregation properties need to be considered in light of the lattice structure, as otherwise counterintuitive or unreliable behavior may result. The Bonferroni mean has recently received attention in the fuzzy sets and decision making community as it is able to model useful notions such as mandatory requirements. Here, we consider its associated penalty function to extend the generalized Bonferroni mean to lattices. We show that different notions of dissimilarity on lattices can lead to alternative expressions.<br /

Using linear programming for weights identification of generalized bonferroni means in R

The generalized Bonferroni mean is able to capture some interaction effects between variables and model mandatory requirements. We present a number of weights identification algorithms we have developed in the R programming language in order to model data using the generalized Bonferroni mean subject to various preferences. We then compare its accuracy when fitting to the journal ranks dataset

On extending generalized Bonferroni means to Atanassov orthopairs in decision making contexts

Extensions of aggregation functions to Atanassov orthopairs (often referred to as intuitionistic fuzzy sets or AIFS) usually involve replacing the standard arithmetic operations with those defined for the membership and non-membership orthopairs. One problem with such constructions is that the usual choice of operations has led to formulas which do not generalize the aggregation of ordinary fuzzy sets (where the membership and non-membership values add to 1). Previous extensions of the weighted arithmetic mean and ordered weighted averaging operator also have the absorbent element 〈1,0〉, which becomes particularly problematic in the case of the Bonferroni mean, whose generalizations are useful for modeling mandatory requirements. As well as considering the consistency and interpretability of the operations used for their construction, we hold that it is also important for aggregation functions over higher order fuzzy sets to exhibit analogous behavior to their standard definitions. After highlighting the main drawbacks of existing Bonferroni means defined for Atanassov orthopairs and interval data, we present two alternative methods for extending the generalized Bonferroni mean. Both lead to functions with properties more consistent with the original Bonferroni mean, and which coincide in the case of ordinary fuzzy values.<br /

Hesitant Triangular Fuzzy Information Aggregation Operators Based on Bonferroni Means and Their Application to Multiple Attribute Decision Making

We investigate the multiple attribute decision-making (MADM) problems with hesitant triangular fuzzy information. Firstly, definition and some operational laws of hesitant triangular fuzzy elements are introduced. Then, we develop some hesitant triangular fuzzy aggregation operators based on Bonferroni means and discuss their basic properties. Some existing operators can be viewed as their special cases. Next, we apply the proposed operators to deal with multiple attribute decision-making problems under hesitant triangular fuzzy environment. Finally, an illustrative example is given to show the developed method and demonstrate its practicality and effectiveness

Using Ordered Weighted Average for Weighted Averages Inflation

This paper presents the ordered weighted average weighted average inflation (OWAWAI) and some extensions using induced and heavy aggregation operators and presents the generalized operators and some of their families. The main advantage of these new formulations is that they can use two different sets of weighting vectors and generate new scenarios based on the reordering of the arguments with the weights. With this idea, it is possible to generate new approaches that under- or overestimate the results according to the knowledge and expertise of the decision-maker. The work presents an application of these new approaches in the analysis of the inflation in Chile, Colombia, and Argentina during 2017

A method to multi-attribute decision making with picture fuzzy information based on Muirhead mean

The recently proposed picture fuzzy set (PFS) is a powerful tool for handling fuzziness and uncertainty. PFS is character-ized by a positive membership degree, a neutral membership degree, and a negative membership degree, making it more suitable and useful than the intuitionistic fuzzy set (IFS) when dealing with multi-attribute decision making (MADM). The aim of this paper is to develop some aggregation operators for fusing picture fuzzy information. Considering the Muirhead mean (MM) is an aggregation technology which can consider the interrelationship among all aggregated ar-guments, we extend MM to picture fuzzy context and propose a family of picture fuzzy Muirhead mean operators. In addition, we investigate some properties and special cases of the proposed operators. Further, we develop a novel meth-od to MADM in which the attribute values take the form of picture fuzzy numbers (PFNs). Finally, a numerical example is provided to illustrate the validity of the proposed method

Environmental and genetic factors influencing the development of belly nosing in the early-weaned pig

This study investigated environmental and genetic factors influencing the development of belly nosing in the early-weaned pig. The first experiment investigated the effects of gender, duration of liquid milk replacer supplementation, breed line and environmental enrichment designed to simulate components of a sow's udder, on the incidence of belly nosing and its associated behaviours in pigs weaned at 7 days-of-age. Both breed line and environmental enrichment were found to affect the incidence of oralnasal behavioural vices related to belly nosing. Differences between breed lines were found in the types of behavioural vices performed and whether these vices were generally focused or directed at specific regions of the body of penmates. Enrichment devices, designed for nosing, rooting, sucking, and biting were also found to be specific in the types of behavioural vices they effectively alleviated. Significant breed line by environmental enrichment interactions were found, with Yorkshire pigs more responsive to environmental enrichment than Duroc pigs. The second study documented the ontogeny of belly nosing from weaning into the grow-finish period in pigs weaned at 12-14 days-of-age and determined whether early belly nosing correlated with behavioural vices observed during the grow-finish period. The results of the study suggest that after belly nosing subsides, a number of other oralnasal behaviours take its place. Pigs that progressed from belly nosing to belly sucking, tended to continue to perform belly sucking behaviour into the grow-finish phase. In contrast, piglets which exhibited generalized nosing and sucking behaviours during the grow-finish period were more likely to tail bite and to engage in generalized biting of penmates. A direct correlation between belly nosing during the nursery phase and tail biting during the grow-finish period was not found. The third study investigated the effects of sire breed and individual sires within breed on belly nosing. Breed of sire affected whether nosing and sucking behaviours were generally focused or directed towards the belly of penmates. Specifically, Large White-sired pigs performed more belly nosing and belly sucking behaviour, while Duroc-sired pigs performed more generally directed nosing and sucking behaviours. The fourth study investigated the use of 'relevant' environmental enrichment devices to further clarify the underlying motivation for belly nosing. A second objective was to investigate the provision of such enrichment at two different developmental stages to determine whether a sensitive period exists for the introduction of environmental enrichment. While providing any type of environmental enrichment during the nursery phase reduced belly nosing, providing nosing enrichment in particular had the most significant effect, despite it being the least utilized. The sensitive period for providing environmental enrichment to reduce belly nosing was found to be during the early nursery phase, within the first two weeks following weaning. The final study investigated the thermal preference of early-weaned pigs as it relates to activity levels, huddling and belly nosing. Early-weaned pigs preferred cooler temperatures during the night, when they huddled to keep warm, and warmer temperatures during the day. Activity levels and belly nosing also demonstrated a diurnal pattern, with the highest incidence of belly nosing occurring during the transition from piglets being more active during the day to spending more time lying at night. Belly nosing is influenced by both environmental and genetic factors. Recognizing the circumstances in which belly nosing occurs will help in designing strategies to reduce the incidence of the behaviour, while still keeping the practice of early weaning as a viable option in disease eradication programs

A novel approach to multi-attribute group decision-making based on interval-valued intuitionistic fuzzy power Muirhead mean

This paper focuses on multi-attribute group decision-making (MAGDM) course in which attributes are evaluated in terms of interval-valued intuitionistic fuzzy (IVIF) information. More explicitly, this paper introduces new aggregation operators for IVIF information and further proposes a new IVIF MAGDM method. The power average (PA) operator and the Muirhead mean (MM) are two powerful and effective information aggregation technologies. The most attractive advantage of the PA operator is its power to combat the adverse effects of ultra-evaluation values on the information aggregation results. The prominent characteristic of the MM operator is that it is flexible to capture the interrelationship among any numbers of arguments, making it more powerful than Bonferroni mean (BM), Heronian mean (HM), and Maclaurin symmetric mean (MSM). To absorb the virtues of both PA and MM, it is necessary to combine them to aggregate IVIF information and propose IVIF power Muirhead mean (IVIFPMM) operator and the IVIF weighted power Muirhead mean (IVIFWPMM) operator. We investigate their properties to show the strongness and flexibility. Furthermore, a novel approach to MAGDM problems with IVIF decision-making information is introduced. Finally, a numerical example is provided to show the performance of the proposed method