We have had the following papers accepted for presentation at FUZZIEEE (part of WCCI) in Beijing in July and Modeling Decisions for Artificial Intelligence (MDAI) in Tokyo in October. We received particularly positive feedback for all of these which is nice. The first and third (submitted to FUZZIEEE and MDAI respectively) relate to our project on the relationship between ecology indices and aggregation functions. We still have a lot of analysis and data to extract from that project so it is nice to have the work viewed positively in its initial stages. The second paper (submitted to FUZZIEEE) is based on a paper presented by R.R. Yager at IFSA in Canada last year.
Title: Can Indices of Ecological Evenness Be Used to Measure Consensus?
Authors: G. Beliakov, S. James and D. Nimmo
In the context of group decision making with fuzzy preferences, consensus measures are employed to provide feedback and help guide automatic or semi-automatic decision reaching processes. These measures attempt to capture the intuitive notion of how much inputs, individuals or groups agree with one another. Meanwhile, in ecological studies there has been an ongoing research effort to define measures of community evenness based on how evenly the proportional abundances of species are distributed. The question hence arises as to whether there can be any cross-fertilization from developments in these fields given their intuitive similarity. Here we investigate some of the models used in ecology toward their potential use in measuring consensus. We found that although many consensus characteristics are exhibited by evenness indices, lack of reciprocity and a tendency towards a minimum when a single input is non-zero would make them undesirable for inputs expressed on an interval scale. On the other hand, we note that some of the general frameworks could still be useful for other types of inputs like ranking profiles and that in the opposite direction consensus measures have the potential to provide new insights in ecology.
Title: Averaging Aggregation Functions for Preferences Expressed as Pythagorean Membership Grades and Fuzzy Orthopairs
Authors: G. Beliakov and S. James
Rather than denoting fuzzy membership with a single value, orthopairs such as Atanassov’s intuitionistic membership and non-membership pairs allow the incorporation of uncertainty, as well as positive and negative aspects when providing evaluations in fuzzy decision making problems. Such representations, along with interval-valued fuzzy values and the recently introduced Pythagorean membership grades, present particular challenges when it comes to defining orders and constructing aggregation functions that behave consistently when summarizing evaluations over multiple criteria or experts. In this paper we consider the aggregation of pairwise preferences denoted by membership and non-membership pairs. We look at how mappings from the space of Atanassov orthopairs to more general classes of fuzzy orthopairs can be used to help define averaging aggregation functions in these new settings. In particular, we focus on how the notion of `averaging’ should be treated in the case of Yager’s Pythagorean membership grades and how to ensure that such functions produce outputs consistent with the case of ordinary fuzzy membership degrees.
Title: Single-Preference Consensus Measures Based on Models of Ecological Evenness
Authors: G. Beliakov, S. James and L. Smith
We investigate the relationship between consensus measures used in different settings depending on how voters or experts express their preferences. We propose some new models for single-preference voting, which we derive from the evenness concept in ecology, and show that some of these can be placed within the framework of existing consensus measures using the discrete distance. Finally, we suggest some generalizations of the single-preference consensus measures allowing the incorporation of more general notions of distance.