The Compromise Ratio Method With Intuitionistic Fuzzy Distance for FMAGDM

The compromise ratio method (CRM) is an effective method to solve multiple attribute group decision making (MAGDM). Distance measure of intuitionistic fuzzy (IF) numbers (IFNs) is important for CRM. In this paper, according to the IF distance of IFNs, an extended compromise ratio method (CRM) is developed for (MAGDM) problems which attribute weights and evaluation values of alternatives on attributes are expressed in linguistic variables parameterized using TIFNs. Finally, the effectiveness and practicability of the extended CRM with IF distance are demonstrated by solving a software selection problem.

Some properties of integration of real-valued function over a fuzzy interval

One of the most fundamental concepts in fuzzy set theory is the extension principle. It gives a generic way of dealing with fuzzy quantities by extending non-fuzzy mathematical concepts. There are a few examples, including the concept of fuzzy distance between fuzzy sets. The extension approach is then methodically applied to real algebra, with considerable development of fuzzy number operations. These operations are computationally appealing and generalized interval analysis. Although the set of real fuzzy numbers with extended addition or multiplication is no longer a group, it retains many structural qualities. The extension concept is demonstrated to be particularly beneficial for defining set-theoretic operations for higher fuzzy sets. We need some definitions related to our properties before we can create the properties of integration of a crisp real-valued function over a fuzzy interval. It is our goal in this article to develop and demonstrate certain characteristics of a real-valued function over a fuzzy interval in order to broaden the scope of the notion of integration of a real-valued function over a fuzzy interval. Some of these characteristics are linked to the operations of extended addition and extended subtraction, while others are not.

Picture Hesitant Fuzzy Clustering Based on Generalized Picture Hesitant Fuzzy Distance Measures

Certain scholars have generalized the theory of fuzzy set, but the theory of picture hesitant fuzzy set (PHFS) has received massive attention from distinguished scholars. PHFS is the combination of picture fuzzy set (PFS) and hesitant fuzzy set (HFS) to cope with awkward and complicated information in real-life issues. The well-known characteristic of PHFS is that the sum of the maximum of the membership, abstinence, and non-membership degree is limited to the unit interval. This manuscript aims to develop some generalized picture hesitant distance measures (GPHDMs) as a generalization of generalized picture distance measures (GPDMs). The properties of developed distance measures are investigated, and the generalization of developed theory is proved with the help of some remarks and examples. A clustering problem is solved using GPHDMs and the results obtained are explored. Some advantages of the proposed work are discussed, and some concluding remarks based on the summary of the proposed work and as well as future directions, are added.

A Novel Filter-Wrapper Algorithm on Intuitionistic Fuzzy Set for Attribute Reduction From Decision Tables

Attribute reduction from decision tables is one of the crucial topics in data mining. This problem belongs to NP-hard and many approximation algorithms based on the filter or the filter-wrapper approaches have been designed to find the reducts. Intuitionistic fuzzy set (IFS) has been regarded as the effective tool to deal with such the problem by adding two degrees, namely the membership and non-membership for each data element. The separation of attributes in the view of two counterparts as in the IFS set would increase the quality of classification and reduce the reducts. From this motivation, this paper proposes a new filter-wrapper algorithm based on the IFS for attribute reduction from decision tables. The contributions include a new instituitionistics fuzzy distance between partitions accompanied with theoretical analysis. The filter-wrapper algorithm is designed based on that distance with the new stopping condition based on the concept of delta-equality. Experiments are conducted on the benchmark UCI machine learning repository datasets.

Distance-Based Knowledge Measure for Intuitionistic Fuzzy Sets with Its Application in Decision Making

Much attention has been paid to construct an applicable knowledge measure or uncertainty measure for Atanassov’s intuitionistic fuzzy set (AIFS). However, many of these measures were developed from intuitionistic fuzzy entropy, which cannot really reflect the knowledge amount associated with an AIFS well. Some knowledge measures were constructed based on the distinction between an AIFS and its complementary set, which may lead to information loss in decision making. In this paper, knowledge amount of an AIFS is quantified by calculating the distance from an AIFS to the AIFS with maximum uncertainty. Axiomatic properties for the definition of knowledge measure are extended to a more general level. Then the new knowledge measure is developed based on an intuitionistic fuzzy distance measure. The properties of the proposed distance-based knowledge measure are investigated based on mathematical analysis and numerical examples. The proposed knowledge measure is finally applied to solve the multi-attribute group decision-making (MAGDM) problem with intuitionistic fuzzy information. The new MAGDM method is used to evaluate the threat level of malicious code. Experimental results in malicious code threat evaluation demonstrate the effectiveness and validity of proposed method.

Dhouib-Matrix-TSP1 Method to Optimize Octagonal Fuzzy Travelling Salesman Problem Using α-Cut Technique

This paper proposes the optimization of the fuzzy travel salesman problem by using the α-Cut technique as a ranking function and the Dhouib-Matrix-TSP1 as an approximation method. This method is enhanced by the standard deviation metric and obtains a minimal tour in fuzzy environment where all parameters are octagonal fuzzy numbers. Fuzzy numbers are converted into a crisp number thanks to the ranking function α-Cut. The proposed approach in details is discussed and illustrated by a numerical example. This method helps in designing successfully the tour to a salesman on navigation through the distance matrix so that it minimizes the total fuzzy distance.

Fuzzy Balanced Allocation Problem with Efficiency on Servers

This paper deals with the problem of allocation customers to servers with regards to some fuzzy parameters. In this problem each customer is allocated to the nearest server, and assignment of a customer to a server involves the cost to the customer, which is due to the customer's fuzzy distance to the server. Each server has a fuzzy efficiency which is calculated by the data envelopment analysis method with fuzzy parameters. The higher efficiency of the server to which a customer is assigned, cause more profit for the customer. The goal is allocation of all customers to the servers such that the profitability of the least profits for the customers is maximized. In addition, to prevent queuing in some servers, we consider the balancing on allocation customers to the servers. Therefore, the second goal is minimizing the difference between the maximum and minimum number of customers that are assigned to different servers. A fuzzy bi-objective programming model is presented for the problem, then two fuzzy approaches are proposed for solving this model.

Students’ Admission Process based on a Novel Fermatean Fuzzy Distance Measure Algorithm

Fermatean fuzzy set is a competent tool in curbing indeterminacy embedded in soft computing. Fermatean fuzzy set generalizes both intuitionistic fuzzy sets and Pythagorean fuzzy sets in an effective way to handle imprecision by expanding the spatial scope of Pythagorean/intuitionistic fuzzy sets. Distance measure has become an integral aspect of utilizing generalized fuzzy sets in soft computing. In this paper, a novel distance measure between Fermatean fuzzy sets is introduced with a better and reliable output. Some properties of the proposed distance measure are characterized. It is demonstrated that the new distance measure between Fermatean fuzzy sets is more reliable than the existing Fermatean fuzzy distance measure. In addition, it is shown that Fermatean fuzzy set is more equipped to curb imprecision than Pythagorean/intuitionistic fuzzy sets. In terms of application, the new Fermatean fuzzy distance measure is utilized in executing students’ admission process using an algorithmic approach implemented by a programming language to enhance accuracy and ease of computations.