Attributes Inequality in Multidimensional Poverty MeasuresFuzzy Modeling

Poverty is recently considered to be a multidimensional one. That is to say the poor can suffer multiple disadvantages at the same time. This paper aims to further develop and refine the multidimensional poverty measure using Fuzzy Sets Theory (FST). The application of FST starts with the choice of membership functions and the rules to manipulate to integrate attributes inequality in multidimensional poverty measure. An application based on individual well-being data from Tunisian households in 2015 is presented to illustrate use proposed concepts. JEL classification: P46; I32; D81; C00;

Note on one inequality and its application in intuitionistic fuzzy sets theory. Part 2

In the paper, the inequality \frac{\mu^{\frac{1}{\nu}}}{\nu} + \frac{\nu^{\frac{1}{\mu}}}{\mu} \leq \frac{1}{2\mu\nu} - 1 is introduced and proved. The same inequality is valid for \mu = \mu_A(x), \nu = \nu_A(x), where \mu_A and \nu_A are the membership and the non-membership functions of an arbitrary intuitionistic fuzzy set A over a fixed universe E and x \in E.

Fuzzy modelling of the transportation logistics processes

The relevance of mechanisms and fuzzy modeling methods used in transport and logistics processes is justified. The logic of the transport and logistics chains study by their decomposition into separate economic entities with subsequent synthesis, with taking into account their conflicting interests, is presented. The task of managing transport and logistics processes is set within the framework of the conceptual positions of the fuzzy sets theory: the use of linguistic variables, the concept of a fuzzy set, fuzzy inference, implemented on the basis of fuzzy sets operations. In this study, the fuzzy modeling on the bottom-up conclusions from the premises to the conclusion was used. Various methods of implication and defuzzification have been analyzed. An iterative procedure for managing transport and logistics chains and their links has been proposed, which ensures the adaptation of the process to the specified performance indicators. A calculated example is given for a marshalling yard as a link in the transport and logistics chain.

FUZZY AGGREGATION FOR RANKING IN BUSINESS

Today, businesses depend strongly on data and the opinion of customers or the experience of managers or experts. The large databases contain non-heterogeneous data, which is the ground for further decisions. Business uses multicriterial decisions in more areas (e.g., customer care, marketing, product development, risk management, HR, etc.) and often it is based on assessment. One of the assessment methods is the ranking, which can be done by crisp values of data where the sharp borders between evaluated entities do not give the adequate ranking result. On the other hand, the ranking process is based on the qualitative assessment, which has linguistic expression. It is more familiar and understandable for people. The article shows how to treat non-heterogeneous data to prepare them for a ranking process using fuzzy sets theory. The article aims at offering several types of ranking methods based on different inputs and preferences of the user and describes appropriate fuzzy aggregations for solving the ranking problem.

New Applications of Sălăgean and Ruscheweyh Operators for Obtaining Fuzzy Differential Subordinations

The present paper deals with notions from the field of complex analysis which have been adapted to fuzzy sets theory, namely, the part dealing with geometric function theory. Several fuzzy differential subordinations are established regarding the operator Lαm, given by Lαm:An→An, Lαmf(z)=(1−α)Rmf(z)+αSmf(z), where An={f∈H(U),f(z)=z+an+1zn+1+…,z∈U} is the subclass of normalized holomorphic functions and the operators Rmf(z) and Smf(z) are Ruscheweyh and Sălăgean differential operator, respectively. Using the operator Lαm, a certain fuzzy class of analytic functions denoted by SLFmδ,α is defined in the open unit disc. Interesting results related to this class are obtained using the concept of fuzzy differential subordination. Examples are also given for pointing out applications of the theoretical results contained in the original theorems and corollaries.

A Fuzzy Cooperative Approach to Resolve the Image Segmentation Problem

The image segmentation problem is one of the most studied problems because it helps in several areas. In this paper, the authors propose new algorithms to resolve two problems, namely cluster detection and centers initialization. The authors opt to use statistical methods to automatically determine the number of clusters and the fuzzy sets theory to start the algorithm with a near optimal configuration. They use the image histogram information to determine the number of clusters and a cooperative approach involving three metaheuristics, genetic algorithm (GA), firefly algorithm (FA). and biogeography-based optimization algorithm (BBO), to detect the clusters centers in the initialization step. The experimental study shows that, first, the proposed solution determines a near optimal initial clusters centers set leading to good image segmentation compared to well-known methods; second, the number of clusters determined automatically by the proposed approach contributes to improve the image segmentation quality.

Fuzzy sets theory and applications in engineering economy: A literature review

Engineering economics is an essential issue in investments and can be quietly difficult to make decisions especially in indefinite, vague and incomplete environments because of human thought. Usage of fuzzy sets gives better solutions in vagueness. Fuzzy sets could be an agreeable tool when no probabilities are accessible for states of nature and decisions are given under incompleteness. In this study, fuzzy engineering economics studies are summarized for showing fuzzy sets usage in engineering economics applications and finding gaps for future studies. The possible suggested are given in conclusion.

Note on one inequality and its application in intuitionistic fuzzy sets theory. Part 1

The inequality \mu^{\frac{1}{\nu}} + \nu^{\frac{1}{\mu}} \leq 1 is introduced and proved, where \mu and \nu are real numbers, for which \mu, \nu \in [0, 1] and \mu + \nu \leq 1. The same inequality is valid for \mu = \mu_A(x), \nu = \nu_A(x), where \mu_A and \nu_A are the membership and the non-membership functions of an arbitrary intuitionistic fuzzy set A over a fixed universe E and x \in E. Also, a generalization of the above inequality for arbitrary n \geq 2 is proposed and proved.

Four Distances for Circular Intuitionistic Fuzzy Sets

In the paper, for the first time, four distances for Circular Intuitionistic Fuzzy Sets (C-IFSs) are defined. These sets are extensions of the standard IFS that are extensions of Zadeh’s fuzzy sets. As it is shown, the distances for the C-IFS are different than those for the standard IFSs. At the moment, they do not have analogues in fuzzy sets theory. Examples, comparing the proposed distances, are given and some ideas for further research are formulated.

Condition Assessment Framework for Facility Management Based on Fuzzy Sets Theory

Condition information is essential to develop effective facility management (FM) strategies. Visual inspections and walk-through surveys are common practices of condition assessment (CA), generally resulting in qualitative and subjective outcomes such as “poor”, “good”, etc. Furthermore, limited resources of the FM process demand that CA practices be efficient. Given these, the purpose of this study is to develop a resource efficient quantitative CA framework that can be less subjective in establishing a condition rating. The condition variables of the study—mean time between failures, age-based obsolescence, facility condition index, occupant feedback, and preventive maintenance cycle—are identified through different sources, such as a computerized maintenance management system, expert opinions, occupants, and industry standards. These variables provide proxy measures for determining the condition of equipment with the implementation example for heating, ventilating, and air conditioning equipment. Fuzzy sets theory is utilized to obtain a quantitative condition rating while minimizing subjectivity, as fuzzy sets theory deals with imprecise, uncertain, and ambiguous judgments with membership relations. The proposed CA framework does not require additional resources, and the obtained condition rating value supports decision-making for building maintenance management and strategic planning in FM, with a comprehensive and less subjective understanding of condition.