A multi-attribute decision making procedure using fuzzy numbers and hybrid aggregators

The classical Analytical Hierarchy Process (AHP) has two limitations. Firstly, it disregards the aspect of uncertainty that usually embedded in the data or information expressed by human. Secondly, it ignores the aspect of interdependencies among attributes during aggregation. The application of fuzzy numbers aids in confronting the former issue whereas, the usage of Choquet Integral operator helps in dealing with the later issue. However, the application of fuzzy numbers into multi-attribute decision making (MADM) demands some additional steps and inputs from decision maker(s). Similarly, identification of monotone measure weights prior to employing Choquet Integral requires huge number of computational steps and amount of inputs from decision makers, especially with the increasing number of attributes. Therefore, this research proposed a MADM procedure which able to reduce the number of computational steps and amount of information required from the decision makers when dealing with these two aspects simultaneously. To attain primary goal of this research, five phases were executed. First, the concept of fuzzy set theory and its application in AHP were investigated. Second, an analysis on the aggregation operators was conducted. Third, the investigation was narrowed on Choquet Integral and its associate monotone measure. Subsequently, the proposed procedure was developed with the convergence of five major components namely Factor Analysis, Fuzzy-Linguistic Estimator, Choquet Integral, Mikhailov‘s Fuzzy AHP, and Simple Weighted Average. Finally, the feasibility of the proposed procedure was verified by solving a real MADM problem where the image of three stores located in Sabak Bernam, Selangor, Malaysia was analysed from the homemakers‘ perspective. This research has a potential in motivating more decision makers to simultaneously include uncertainties in human‘s data and interdependencies among attributes when solving any MADM problems

Fuzzy integral for rule aggregation in fuzzy inference systems

The fuzzy inference system (FIS) has been tuned and re-vamped many times over and applied to numerous domains. New and improved techniques have been presented for fuzzification, implication, rule composition and defuzzification, leaving one key component relatively underrepresented, rule aggregation. Current FIS aggregation operators are relatively simple and have remained more-or-less unchanged over the years. For many problems, these simple aggregation operators produce intuitive, useful and meaningful results. However, there exists a wide class of problems for which quality aggregation requires non- additivity and exploitation of interactions between rules. Herein, we show how the fuzzy integral, a parametric non-linear aggregation operator, can be used to fill this gap. Specifically, recent advancements in extensions of the fuzzy integral to \unrestricted" fuzzy sets, i.e., subnormal and non- convex, makes this now possible. We explore the role of two extensions, the gFI and the NDFI, discuss when and where to apply these aggregations, and present efficient algorithms to approximate their solutions

Проектування інформаційного забезпечення для оцінки якості ПЗ вбудованих систем

This article presents a system for evaluating the quality of embedded software using a decision system based on fuzzy logic. These approaches will improve the assessment of software quality, due to its features. This article defines the main criteria for software quality used in assessing the quality of the software. The main literature was examined, in which fuzzy logic was described, decision-making systems using fuzzy logic, as well as software quality assessment systems, including software for embedded systems. The main characteristics and properties of embedded syst ems were considered. Based on the considered characteristics and properties of embedded systems, the ranking of criteria was made, which will be further used in the software quality assessment methodology. The main criteria that are used to evaluate the quality of software were considered, and the criteria presented were distributed according to the degree of influence on the assessment of the quality of software of embedded systems. Fuzzy logic was considered, and more precisely: the basic properties of fuzzy logic and fuzzy numbers, the basic mathematical operators applied to fuzzy numbers. The system for constructing rules for the rule base, as well as the defuzzification process, built on the basis of the centroid method, is analyzed. An example of software evaluation for embedded systems was considered. In this example, linguistic variables were determined, as well as their numerical ranges, which were used for the initial assessment of the quality criteria of this software. Each range of ratings was distributed according to the influence of a criterion on software quality. The output linguistic variable and its numerical value were also determined. In the end, based on the set values, an estimate of the set software was derived. The theoretical result obtained in this article is the basis for constructing a system for evaluating software quality for embedded systems.У даній статті представлена система для оцінки якості програмного забезпечення вбудованих систем з використанням системи прийняття рішень на основі нечіткої логіки. Дані підхід дозволить поліпшити оцінку якості програмного забезпечення, за рахунок урахування його особливостей. У даній статті визначено основні критерії якості програмного забезпечення, використовувані при оцінці якості даного програмного забезпечення. Була оглянута основна література, в якій була описана нечітка логіка, системи прийняття рішень, що використовують нечітку логіку, а також системи оцінки якості програмного забезпечення, в тому числі і програмного забезпечення для вбудованих систем. Були розглянуті основні характеристики та властивості вбудованих систем. На підставі розглянутих характеристик і властивостей вбудованих систем виробилося ранжування критеріїв, які в подальшому будуть використовуватися в методиці оцінки якості програмного забезпечення. Були розглянуті основні критерії, які використовуються для оцінки якості програмного забезпечення, а також представлені критерії, які були розподілені за ступенем впливу на оцінку якості програмного забезпечення вбудованих систем. Була розглянута нечітка логіка, а точніше: основні властивості нечіткої логіки і нечітких чисел, основні математичні оператори, що застосовуються до нечітким числах. Розібрана система побудови правил для бази правил, а також процес дефазифікації, побудований на підставі центоїдного методу. Було розглянуто приклад оцінки програмного забезпечення для вбудованих систем. В даному прикладі були визначені лінгвістичні змінні, а також їх числові діапазони, які використовувалися для первісної оцінки критеріїв якості даного програмного забезпечення. Кожен діапазон оцінок був розподілений згідно впливу критерію на якість програмного забезпечення. Також була визначена вихідна лінгвістична змінна і її числове значення. В кінці, на основі заданих значень була виведена оцінка заданого програмного забезпечення. Отриманий теоретичний результат в даній статті є основою для побудови системи для оцінки якості програмного забезпечення для вбудованих системи

An equivalent condition to the Jensen inequality for the generalized Sugeno integral.

For the classical Jensen inequality of convex functions, i.e., [Formula: see text] an equivalent condition is proved in the framework of the generalized Sugeno integral. Also, the necessary and sufficient conditions for the validity of the discrete form of the Jensen inequality for the generalized Sugeno integral are given

Data-informed fuzzy measures for fuzzy integration of intervals and fuzzy numbers

The fuzzy integral (FI) with respect to a fuzzy measure (FM) is a powerful means of aggregating information. The most popular FIs are the Choquet and Sugeno, and most research focuses on these two variants. The arena of the FM is much more populated, including numerically derived FMs such as the Sugeno λ-measure and decomposable measure, expert-defined FMs, and data-informed FMs. The drawback of numerically derived and expert-defined FMs is that one must know something about the relative values of the input sources. However, there are many problems where this information is unavailable, such as crowdsourcing. This paper focuses on data-informed FMs, or those FMs that are computed by an algorithm that analyzes some property of the input data itself, gleaning the importance of each input source by the data they provide. The original instantiation of a data-informed FM is the agreement FM, which assigns high confidence to combinations of sources that numerically agree with one another. This paper extends upon our previous work in datainformed FMs by proposing the uniqueness measure and additive measure of agreement for interval-valued evidence. We then extend data-informed FMs to fuzzy number (FN)-valued inputs. We demonstrate the proposed FMs by aggregating interval and FN evidence with the Choquet and Sugeno FIs for both synthetic and real-world data

Application of Generalized Choquet Fuzzy Integral Method in the Sustainability Rating of Green Buildings based on the BSAM scheme

The need to reduce the impact of building projects on the sustainability of the built environment and improve the use of resources necessitated several interventions such as the development of methods to assess building impacts and improve the sustainability performance of buildings. Using the BSAM scheme – a green building rating system developed specifically for the sub-Saharan region of Africa, the generalized Choquet fuzzy integral method was employed to determine the importance weights of the sustainability assessment criteria. Data collected from industry experts form the base inputs for the impact of the various sustainability criteria based on the local variations. Consequently, the building sustainability evaluation index and grading scheme were developed to measure and evaluate the sustainability performance of buildings. The developed sustainability rating model was validated in four real-world case studies to demonstrate its usefulness and robustness in practice. The findings revealed that the conventional approach of aggregation of points used by the existing green rating tools is less effective in dealing with criteria that have interactive characteristics. Also, assessment criteria such as sustainable construction practices, transportation, and energy have a significant impact on the sustainability of buildings. The study provides substantial contributions to the existing body of knowledge about green building assessment systems for built environment stakeholders, both from the theoretical and practical perspectives

Hazardous Materials Warehouse Selection as a Multiple Criteria Decision making Problem

Abstract. Radioactive, toxic, smother, flammable, and explosive materials in solid, liquid or gas states which can negatively impact goods, organisms, and most importantly humans are called as “Hazardous Materials”. Hazardous material transportation and storage carry risk factors in addition to their other types of transportation operations. Furthermore, selection of a suitable warehouse becomes a problematic issue in which multiple criteria are evaluated as paying attention to risky circumstances. In this context, hazardous material warehouse selection is considered as a multiple criteria decision problem in our study. In particularly, for the explosives storage among other hazardous materials, necessary criteria are determined according to expert’s consultant. The determined criteria are weighted according to decision makers’ consultancy and the alternatives are evaluated by fuzzy MULTIMOORA under uncertainty throughout the decision making process in the study.. The proposed approach is discussed on a case study.Keywords. Fuzzy MULTIMOORA, Warehouse Selection, Hazardous Materials.JEL. D81, R53, C40, C44

Modeling of Characteristics on Artificial Intelligence IQ Test: a Fuzzy Cognitive Map-Based Dynamic Scenario Analysis

This research article uses a Fuzzy Cognitive Map (FCM) approach to improve an earlier proposed IQ test characteristics of Artificial Intelligence (AI) systems. The defuzzification process makes use of fuzzy logic and the triangular membership function along with linguistic term analyses. Each edge of the proposed FCM is assigned to a positive or negative influence type associated with a quantitative weight. All the weights are based on the defuzzified value in the defuzzification results. This research also leverages a dynamic scenario analysis to investigate the interrelationships between driver concepts and other concepts. Worst and best-case scenarios have been conducted on the correlation among concepts. We also use an inference simulation to examine the concepts importance order and the FCM convergence status. The analysis results not only examine the FCM complexity, but also draws insightful conclusions

Application of an automatically designed fuzzy logic decision support system to connection admission control in ATM networks

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