This paper summarizes the basic concepts of Graded Logic (GL) and the use of GL in professional decision making.Our goal is to contrast two approaches to the development of a continuum-valued propositional logic: (1) the human-centric approach based on observing and modeling human commonsense logical reasoning in the context of decision making, and (2) the theoretical approach where logic is developed as a formal axiomatic deductive system.We show the basic advantages of human-centric approach and the applicability of this approach in the area of professional decision making.

Personalizing hotel recommendations for tourists is challenging because it needs to model a logical aggregation of multiple criteria in terms of the user’s decision process and preferences. In this paper, we propose a hierarchical multi-criteria hotel evaluation model that includes important hotel properties as well as hotel ratings by previous customers. The recommender system proposed, called HR.LSP, applies different graded logic aggregation operators following the method of Logic Scoring of Preference (LSP). Asymmetric aggregation is used for some of the criteria, where the user can not only define the importance of inputs, but also indicate if they are mandatory or optional. This is the first recommender system based on graded logic and the first non-professional use of LSP. The application of graded logic operators significantly improves the decision-making process of hotel selection for each user. The case of Riohacha (an emerging tourist destination in Colombia) is studied. In addition to quality and location criteria, some security information is included in the model as it is of utmost importance to provide to travelers a secure experience at the destination.

Decision making is a mental process of evaluation of existing alternatives and selection of the best among sufficiently suitable alternatives. The motivation is to attain desired goals of specific stakeholder/decision-maker. This is a natural process based on intuitive evaluation criteria. The criteria include the aggregation of graded logic values that are degrees of truth or fuzzy membership. The logic properties of this decision process are observable, measurable, modellable, and explainable. In decision engineering, such models are necessary for development of decision support systems. In this paper we present experiments designed for investigating and modeling mental aggregation in the case of conjunctive criteria. We use all versions of the graded conjunction/disjunction and include experimental analysis of wider spectrum of aggregators than the models previously investigated in the literature. Two forms of conjunctive aggregation are identified and investigated: (1) the logic aggregation used for modeling the simultaneity of properties of analyzed objects, and (2) the logic aggregation of degrees of realization of simultaneous goals of decision-maker. These two types of graded logic functions have different characteristic properties that are identified, modelled, and analyzed in the paper.

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.

Logic Scoring of Preference (LSP) is a soft computing decision method for evaluation and selection of complex objects and alternatives using logic criteria. LSP criteria are based on graded logic aggregation structures that in most cases have a canonical form of tree. Such trees aggregate degrees of truth or degrees of fuzzy membership. The aggregators are graded logic functions. Each node in the tree of logic aggregators has a specific semantic identity - it has the interpretation, role, meaning, and importance for the decision maker. The semantic identity of all arguments can be used to develop explainable LSP criteria, and to provide explanation of all results generated in the process of evaluation, comparison, and selection of complex objects and alternatives. In this paper we propose explainability parameters and use them in decision making to provide the explainability of both the results of evaluation of a single object, and the results of comparison and selection of multiple competitive alternatives.

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.

Logic aggregators are defined as graded aggregators that aggregate degrees of truth, suitability, preference, and fuzzy membership. In this paper we present necessary and sufficient logic aggregators. In particular, we study logic aggregators that generalize classical Boolean logic and model observable properties of human reasoning in the area of soft computing evaluation logic. This paper introduces restrictive conditions that logic aggregators must satisfy.

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.

Generalized conjunction/disjunction (GCD) is a fundamental idempotent logic function that enables a continuous transition from conjunction to disjunction. GCD is a building block for all idempotent compound aggregation structures. In this paper we investigate various implementations of GCD. Our goals are to provide justifiable andness/orness rating scales, to propose GCD implementations that have adjustable granularity, sufficient precision, adjustable threshold andness and threshold orness and the ultimate computational simplicity. The proposed GCD implementations are sufficient for building compound criteria that have high expressive power and are suitable for a wide spectrum of applications in computational intelligence.

The threshold andness is a border between soft and hard partial conjunction (similarly, the threshold orness is a border between soft and hard partial disjunction). This paper presents a weighted compensative logic based on aggregators that use adjustable threshold andness and orness. The adjustability of threshold andness/orness is a new degree of freedom in weighted logics, which is suitable for increasing the precision of evaluation criteria developed by evaluation experts. We investigate the distribution of threshold andness and present a new form of interpolative aggregators that provide adjustable threshold andness and orness. Our goal is to use a new verbalized approach, based on decomposing the perception of overall importance, for designing the generalized conjunction/disjunction (GCD) aggregators. The verbalized approach helps specify parameters that affect both the formal logic properties and the semantic properties of GCD, facilitating the use of soft computing evaluation logic and corresponding evaluation methods.

This paper investigates the structure and properties of interpolative generalized conjunction/disjunction (GCD) aggregators. The main advantage of interpolative aggregators is the possibility to include suitable properties and to exclude inconvenient properties of aggregators. Using this method we can create new forms of logic aggregators by interpolating between heterogeneous base aggregators, i.e. aggregators that belong to different families and have different logic properties. The resulting interpolative aggregators then extend the desirable properties inherited from the base aggregator classes. We propose a general interpolative GCD aggregator (IGCD) and its important uniform special case. I GCD can be used to build compound aggregators and complex logic aggregation structures with suitable logic properties.

This paper investigates basic semantic aspects of evaluation logic. We propose a verbalized approach to the design and use of the Generalized Conjunction/disjunction (GCD) aggregators. The main goals of verbalized approach are to help in specifying semantic components of GCD, and to facilitate the use of soft computing evaluation logic and corresponding evaluation methods (such as LSP), making those more accessible to general nonprofessional decision makers.

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.

In this paper we investigate the effects of using LSP logic aggregators in spatially-explicit suitability maps and compare logic aggregation with aggregation based on aggregators that use fixed andness. In particular, we analyze differences between the LSP aggregators and the additive aggregators that are currently predominant in GIS suitability maps. This analysis shows that the LSP logic aggregators are indispensable for correct expression of justifiable requirements of decision makers. We propose a method for evaluation of the suitability of locations with respect to a given distribution of points of interest in an urban area using logic aggregation to create spatially-explicit suitability maps.

In this paper, we propose a benchmarking technique and performance indicators that can be used to evaluate and compare programming languages and language processors in the area of efficiency of array processing. The proposed subscript permutation technique is used to develop a matrix multiplication benchmark (MMB). MMB is used to evaluate language processors and provide insight into performance levels attainable by scripting languages, virtual machine based languages, and languages that compile to the native machine language.

In this paper we investigate seven special cases and nine characteristic forms of generalized conjunction/disjunction. They include the concepts of hard and soft partial conjunction and hard and soft partial disjunction, and their combinations. We analyze the threshold values of andness and orness that define the border between the hard and soft partial conjunction and partial disjunction. In addition, we propose new forms of aggregators that have adjustable values of andness and orness thresholds.

In this paper, we investigate mathematical models that are suitable for modeling decisions in the area of system evaluation, comparison, and selection. Our interest is focused on soft computing models that can be directly related to observable properties of human reasoning, and have a record of use in system evaluation practice. We analyze various approaches to defining andness and orness, and use a generalized conjunction/disjunction (GCD) to build compound preference logic functions and logic models for system evaluation. We also present applications of the continuous preference logic in decision models based on the LSP method.

This paper presents NPME/NT, a tool for performance measurement of networks that work under the Windows NT operating system. The tool is organized as a network performance measurement environment (NPME) that includes a network workload generator, and a control system that automatically distributes the workload to each node of the network and generates files containing performance indicators. We present the concepts of NPME, the implementation of NPME/NT, and experimental results of using the tool.

We present theoretical concepts, design, and use of universal benchmark suites. Such suites consist of benchmark programs that represent all relevant characteristic types of workload. The execution times of individual benchmarks and appropriate weights can be used to compute global performance indicators that reflect a spectrum of specific compound workloads. All such global indicators can be obtained from the same universal benchmark suite. This approach substantially reduces the cost of benchmarking.

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.

Computer evaluation, comparison, and selection is essentially a decision process. The decision making is based on a number of worth indicators, including various computer performance indicators. The performance indicators are obtained through the computer performance measurement procedure. Consequently, this procedure should be completely conditioned by the decision process.