Credibility Hypothesis Testing of Variance of Fuzzy Normal Distribution

This paper considers the problem of developing test procedures for testing credibility hypotheses about the variance of fuzzy normal distribution assuming the expected values of the distributions mentioned under null and alternative credibility hypotheses are known and equal. The cases where the underlying hypothesis is simple and composite (one sided) are considered. Tests have been derived with the help of the membership ratio criterion. Properties possessed by the developed tests, like best credibility rejection region and uniformly best rejection region have been studied. Examples are also given to illustrate the usage of the derived tests.

MAGDM Problems with Correlation Coefficient of Triangular Fuzzy IFS

Correlation coefficient of Intuitionistic Fuzzy Set (IFS), Interval valued IFS, Triangular IFS and Trapezoidal IFS are already present in the literature. This paper proposes the correlation coefficient for Triangular Fuzzy Intuitionistic Fuzzy set (TrFIFS). The method on uncertain Multiple Attribute Group Decision Making (MAGDM) problems based on aggregating intuitionistic fuzzy information is investigated for TrFIFSs. The Triangular Fuzzy Intuitionistic Fuzzy Ordered Weighted Averaging (TrFIFOWA) operator is proposed for TrFIFSs and the Triangular Fuzzy Intuitionistic Fuzzy Ordered Weighted Geometric (TrFIFOWG) operator is utilized for decision making models where expert weights are completely unknown. Based on these operators and the correlation coefficient defined for the TrFIFSs, new decision making models are proposed with numerical illustrations. Some comparisons are also made with existing ranking methods for validity.

Performance Estimation of Firms by G-L-A Supply Chain under Imperfect Data

Amongst various proposed SC philosophies, Lean, Green and Agile strategies of SC worked seminal to solve many problems of firms. Performance measurement acts as a tool to quantify overall efficiency via G-L-A SC activities of firm, where Green SC agenda is to control and diminish pollution and Lean SC helps to reduce waste of firm, while Agile SC target to manage SC more cum quick responding to clients. This chapter proposed a MCDM performance appraisement module (module constituted by mixing the segregated chain of green-lean-agile logistic activities and corresponding their interrelated metrics) conjunctive with Fuzzy Performance Index model in purpose to estimation the overall performance of individual firm. Furthermore, a centroid method coupled with fuzzy number set is proposed for classifying ill and strong G-L-A metrics of firm, so that managers could escalate their firms performance in case of non desirable performance. A hypothetical case research of two firms i.e. gear and shaft manufacturing firms are shown to measure their performance under G-LA supply chain.

Application of Fuzzy Soft Set in Patients' Prioritization

Based on studies, access to healthcare services and long waiting time is one of the main issues in many countries including Canada and United States. Healthcare organizations can't increase their limited resources nor treat all patients simultaneously. Then, patients' access to these services should be prioritized in a way that best uses the scarce resources and insures patients' safety. Prioritization is essential and inevitable not only because of resource shortage, which have not been improved during years, but also because it is a crucial issue that could contribute to the capability and stability of the healthcare systems, and most importantly to patients' safety. On the other hand, inappropriate prioritization of patients waiting for treatment, could affect directly on inefficiencies in healthcare delivery, quality of care, and most importantly on patients' safety and their quality of life and satisfaction. Inspired by these facts, in this chapter the importance of patients' prioritization and using fuzzy logic in this area will be discussed, and a novel hybrid framework using fuzzy soft sets for patients' prioritization will be proposed. The proposed framework may have a significant impact on patients' safety, and on both medical community and the public's faith in justice and equity.

Some Recent Defuzzification Methods

Defuzzification is a process that converts a fuzzy set or fuzzy number into a crisp value or number. Defuzzification is used in fuzzy modeling and in fuzzy control system to convert the fuzzy outputs from the systems to crisp values. This process is necessary because all fuzzy sets inferred by fuzzy inference in the fuzzy rules must be aggregated to produce one single number as the output of the fuzzy model.There are numerous techniques for defuzzifying a fuzzy set; some of the more popular techniques are included in fuzzy logic system. In the present chapter some recent defuzzification methods used in the literature are discussed with examples.

Prediction of Solar and Wind Energies by Fuzzy Logic Control

Nowadays, the use of renewable energy has become increasingly significant, and cost-effective. Between all existing sources of energy, solar and wind energies are the highly exploited. However, solar and wind energies are not available all the time and their performance is affected by unpredictable weather changes, therefore, it is not always feasible to obtain an accurate mathematical model of the controlled system. Various mathematical modeling methods were used to predict wind and solar powers using natural parameters but considering multiple parameters in equations makes the solution more complex. In addition to complexity, some coefficients are uncertain and based on probability. Fuzzy logic is a perfect tool to model any kind of uncertainty related to vagueness. This chapter presents a computer algorithm based on fuzzy logic control (FLC) to estimate the wind and solar energies using natural factors. As input parameters, the wind speed was used to predict the wind power and the temperature and the lightening were used to estimate the solar power.

Benchmarking of Advanced Manufacturing Machines Based on Fuzzy-TOPSIS Method

The evaluation of the most appropriate Computer Numerical Control (CNC) machine tool is found foremost issue for sustaining the advanced manufacturing production units at competitive global market place. In last years, many evaluation parameter/ criteria/ issues (i.e. Cost [C], Tool Length [TL], Tool Diameter [TD], Metal Removal Rate [MRR], X-Y-Z-Axis Movement of Tool [AMT], etc.) carried out into account besides productivity, precision, accuracy, reliability etc prior to purchasing/electing CNC machine tools amongst preferred alternatives. This chapter exhibited a hypothetical case research pertaining to election of CNC machine tool under the qualitative parameter/criteria/issues excluding quantitative, where, subjective (qualitative) criteria are considered beside objective (quantitative) criteria and complexity to elect the best CNC machine tool is solved via subjective assessments of expert's panel also called the group decision making. In present research, TOPSIS algorithmic technique conjunction with Trapezoidal Fuzzy Number set (TFNs) is explored for appraising and benchmarking the preferable CNC machine tool options/ alternatives. Finally, a hypothetical case research is carried out to check the validity of proposed algorithmic technique for proposed module and exhibit the path for benchmarking alternative machine tools. The preferences orders are carried out in accordance with descending value of the ‘collective index'. Higher value of ‘collective index' reflects higher degree of performance.

Fuzzy-AHP

Logistics activities are performed in order to balance the operational chains of firms. The selection of the Third Party Logistics (3PL) is a challenging task for each organization, which involves various factors and attributes. The presented methodology acts as a boon and aids the decision makers for effectively choosing the appropriate Third Party Logistics (3PL) network. In the revealed work, the authors explored fuzzy sets theory and presented a fuzzy AHP model to facilitate the managers of organizations to deal with the Third Party Logistics (3PL) decision making problems. The overall performance of defined Third Party Logistics (3PL) Service Providers are greatly influenced by many significant parameters: quality, reliability, service assurance, shipment cost, customer relationship, etc. The authors have considered various significant parameters: service level, financial security capabilities, location, global presence, relationship management, and client fulfillment representing first level indices. These parameters have chain of various sub-parameters, represented as second level indices, whose importance is affecting the judgment of the decision makers. Various researches have constraint their work up to first level indices and have not considered the second level indices, which is a crucial part of today's practical decision making process. The authors have considered this issue as research gap and transformed this research gap into research agenda. The authors applied an AHP (Analytical Hierarchy Process) accompanied with fuzzy set theory in order to solve industrial Logistics problems. The objective of chapter is to propose a fuzzy based AHP method towards solve benchmarking (preference orders of defined alternatives under criteria) problems. The presented method facilitates the managers of firms to make the verdict towards choosing the best Third Party Logistics (3PL) service provider. A numerical illustration is provided to validate the method application upon module.

Intuitionistic Fuzzy Distance-Based Intuitionistic Fuzzy TOPSIS Method and Application to MADM

In this paper, an intuitionistic fuzzy (IF) distance measure between two triangular intuitionistic fuzzy numbers (TIFNs) is developed. The metric properties of the proposed IF distance measures are also studied. Then, based on the IF distance, an extended TOPSIS is developed to solve multi-attribute decision making (MADM) problems with the ratings of alternatives on attributes of TIFNs. In this methodology, the IF distances between each alternative and the TIFN positive ideal-solution are calculated as well as the TIFN negative ideal-solution. Then the relative closeness degrees obtained of each alternative to the TIFN positive ideal solution are TIFNs. Based on the ranking methods of TIFNs the alternatives are ranked. A numerical example is examined to the validity and practicability of the method proposed in this paper.

Interval-Valued Intuitionistic Fuzzy Multi-Attribute Decision Making Based on Satisfactory Degree

The aim of this paper is to propose a satisfactory degree method by using nonlinear programming for solving multi-attribute decision making (MADM) problems in which ratings of alternatives on attributes is expressed via interval-valued intuitionistic fuzzy (IVIF) sets and preference information on attributes is incomplete. Concretely, a nonlinear programming model is firstly explored to determine the satisfactory degree which is the ratio of the square of the weight Euclidean distance between an alternative and the IVIF negative ideal solution (IVIFNIS) to the sum of the square of the weight Euclidean distance between the IVIF negative ideal solution (IVIFNIS) and the IVIF positive ideal solution (IVIFPIS). Another nonlinear programming model is also developed to obtain satisfactory intuitionistic fuzzy sets, and then the general satisfactory degrees of the satisfactory intuitionistic fuzzy sets are used to generate the ranking order of the alternatives. Finally, a real example is employed to verify the applicability of the proposed approach and illustrate its practicality and effectiveness.