Axiomatization and construction of orness measures for aggregation functions

Abstract

The notion of an orness measure for aggregation functions has been a relevant study subject whose history can be traced back to the early works of Dujmović in 1973. Intuitively, an orness measure quantifies the similarity of an aggregation function to the “or” function and results in an essential tool for decision engineering, field in which the choice of aggregation function is sometimes restricted to a desired value of orness (orness‐directed aggregation). In 1988, Yager presented a particular example of orness measure for ordered weighted averaging (OWA) functions and initiated a series of contributions aiming at proposing an axiomatic definition of orness measure for OWA functions. In this paper, we go much further and present an axiomatic definition of orness measure for the whole family of aggregation functions. We end by proposing two natural construction methods for an orness measure for aggregation functions. The particular examples of the (discrete) Choquet integral and uninorms are studied in detail.

Bi-Objective Optimization: A Pareto Method with Analytical Solutions

“…For instance, Zhou et al [1], Kukkonen and Deb [2], Pinto-Varela et al [3], Lath et al [4], Pereyra et al [5], Garg [6], Futrell et al [7], Hirpa et al [8], Liu et al [9], Wang et al [10], Cheraghalipour et al [11], Ho-Huu et al [12], Yeh [13], Liu et al [14], Nagamanjula and Pethalakshmi [15], Xu et al [16], Diao et al [17], Mohammadi et al [18], Kparib et al [19], Kparib et al [20], Gulben and Orhan [21], Zaninudin and Paputungan [22], and Stutzle and Hoos [23]. Studies proposing multi-objective optimization techniques and solution can be found in Messac [24], Das and Dennis [25], Deb [26], Messac et al [27], Messac and Mattson [28], Kim and Weck [29], Zhang and Li [30], Chinchuluun and Pardalos [31], Mueller-Gritschneder et al [32], Pereyra et al [5], Pérez-Fernández et al [33], Marler and Arora [34], Gunantara [35], Orths et al [36], Collette and Siarry [37], Ehrgott [38], Eskelinen et al [39], Fonseca and Fleming [40], Alaa et al [41], Subhamoy and Sugata…”

Recursive Aggregation and Its Fusion Process for Intuitionistic Fuzzy Numbers Based on Non-Additive Measure

“…Fortunately, fuzzy measure, defined by Sugeno in 1974, can be utilized to depict the correlations of attribute indexes [7][8][9][10]. Meanwhile, aggregation functions and aggregation operators are investigated by many researchers recently [11][12][13][14]. Because of the fuzziness and uncertainty of actual decision issues, the evaluation values involved in the decision process are not always expressed as crisp numbers.…”