Logic aggregators are all aggregators characterized by andness/orness. In this paper we present necessary properties of logic aggregators and use them to compare major implementations of andness-characterized aggregators: means, t-norms/conorms, ordered weighted average family, fuzzy integrals, and graded conjunction/disjunction. Our goal is to provide methodology for justifiable selection of the most suitable aggregator for various information fusion problems. When aggregating arguments from [0, 1], such arguments are regularly interpreted as degrees of truth or degrees of fuzzy membership. In such cases we deal with logic aggregators that must have appropriate logic properties. Our analysis identifies 10 necessary properties that are critical for decision support applications and must be satisfied by logic aggregators. Then, we evaluate and compare five families of logic aggregators that offer different levels of support to desired logic properties.

We present the soft computing graded logic (GL) as a mathematical infrastructure for a soft computing propositional calculus, and GL aggregation. The GL aggregation of degrees of truth (or fuzzy membership) is a crucial component of complex criterion functions used in decision support systems. In the context of GL we propose aggregation functions that integrate means and t-norms/conorms, combining logic and probabilistic reasoning. We also propose a set of necessary and sufficient basic logic functions (models of simultaneity, substitutability, and complementing of degrees of truth) and their analytic forms. GL is developed as a seamless soft computing generalization of classical Boolean logic. The proposed generalizations include: (1) the continuous parameterized transition from drastic conjunction to drastic disjunction, integrating the regions of hyperconjunction, hard and soft partial conjunction, logic neutrality, soft and hard partial disjunction, and hyperdisjunction and (2) semantic generalization where we assign a degree of importance to each degree of truth, in a way that is consistent with observable properties of human intuitive reasoning. These generalizations reflect the fact that degrees of truth are not anonymous real numbers, but values that have semantic identity derived from goals and requirements of decision-maker. The basic goal of GL is to provide humancentric mathematical models of logic aggregators that can be used in the decision process of comparison and selection of alternatives based on the evaluation of each alternative. This paper is structured to present the characteristic properties of entire GL in a way that is both concise and complete.

We propose weighted aggregation algorithms for creating general idempotent weighted aggregators of n variables derived from related symmetric idempotent aggregators of two variables. This computational method, together with interpolative aggregation, can be used for the development of general idempotent logic aggregators that satisfy a variety of conditions necessary for building decision models in the area of weighted compensative logic.

In this paper, we identify and describe fundamental logic properties of multicriteria methods for land-use suitability analysis and the design of suitability maps. The existing multicriteria methods can be evaluated from the standpoint of their ability to support the necessary logic properties that affect the expressive power of evaluation methods. The paper investigates and compares simple additive scoring, multiattribute value technique, multiattribute utility technique, analytic hierarchy process, ordered weighted average, outranking methods, and logic scoring of preference (LSP). We introduce canonical forms of logic aggregation in suitability maps and show how to use canonical aggregation structures to design LSP suitability maps that evaluate distributions of points of interests (POIs) in urban areas. © 2011 Wiley Periodicals, Inc.

This paper describes a general cost-benefit decision model that is applicable to the evaluation, comparison, and selection of alternative products with a multiplicity of features, such as complex computer systems. The application of this model is explained and illustrated using the selection of data management systems as an example. The model has the following features: (1) it is mathematically based on an extended continuous logic and a theory of complex criteria; (2) the decision-making procedure is very general yet systematic, well-structured, and quantitative; (3) the technique is based on a comprehensive cost analysis and an elaborate analysis of benefits expressed in terms of the decision maker's preferences. The decision methodology, when applied to the problem of selecting a data management system, takes into consideration the life cycle of a DMS and the objectives and goals for the new systems under evaluation. It allows the cost and preference analyses to be carried out separately using two different models. The model for preference analysis makes use of comprehensive performance (or preference) parameters and allows what we call a “logic scoring of preferences” using continuous values between zero and one, to express the degree with which candidate systems satisfy stated requirements. It aggregates preference parameters based on their relative weights and logical relationships to compute a global performance (preference) score for each system. The cost model incorporates an aggregation of costs which may be estimated over different time horizons and discounted at appropriate discount rates. A procedure to establish an overall ranking of alternative systems based on their global preference scores and global costs is also discussed.