Soft Computing

Soft computing is used where a complex problem is not adequately specified for the use of conventional math and computer techniques. Soft computing has numerous real-world applications in domestic, commercial and industrial situations. This book elaborates on the most recent applications in various fields of engineering

Equilibrium linguistic computation method for fuzzy group decision making

This paper proposes an equilibrium computation method using linguistic variables based on the conflicting bifuzzy sets. The linguistic terms were defined and associated with the triangular fuzzy number as well as the labeling system in the early stages. Then, the negation operator was introduced and the bifuzzy approaches were employed to derive the aggregation equilibrium linguistic judgement for evaluation process

Soft Computing

Soft computing is used where a complex problem is not adequately specified for the use of conventional math and computer techniques. Soft computing has numerous real-world applications in domestic, commercial and industrial situations. This book elaborates on the most recent applications in various fields of engineering

Some results associated with the max–min and min–max compositions of bifuzzy matrices

AbstractIn this paper, we define some kinds of bifuzzy matrices, the max–min (○) and the min–max (*) compositions of bifuzzy matrices are defined. Also, we get several important results by these compositions. However, we construct an idempotent bifuzzy matrix from any given one through the min–max composition

New fuzzy preference relations and its application in group decision making

Decision making preferences to certain criteriabusually focus on positive degrees without considering the negative degrees. However, in real life situation, evaluation becomes morebcomprehensive if negative degrees are considered concurrently. Preference is expected to be more effective when considering both positive and negative degrees of preference to evaluate the best selection. Therefore, the aim of this paper is to propose the conflicting bifuzzy preference relations in group decision making by utilization of a novel score function. The onflicting bifuzzy preference relation is obtained by introducing some modifications on intuitionistic fuzzy preference relations. Releasing the intuitionistic condition by taking into account positive and negative degrees simultaneously and utilizing the novel score function are the main modifications to establish the proposed preference model. The proposed model is tested with a numerical example and proved to be simple and practical. The four-step decision model shows the efficiency of obtaining preference in group decision making

Level subsets and translations of QFST(G)

First, we introduce level subsets and translations of  QFST(G)  and study their properties.  Secondly,  we prove that the union and intersection of two-level subsets of QTST(G)  are subgroups of G. Also we prove that translations of  QTST(G)  are also  QFST(G).  Finally,  we define  fuzzy image and fuzzy pre-image of translations of  QFST(G)  under group homomorphisms and anti group homomorphisms and investigate properties of them

Sequence of image enhancement of flat electroencephalography using intuitionistic fuzzy set

v ABSTRACT This study focused on contrast enhancement of Flat Electroencephalography (fEEG) image during epileptic seizure. The main interest is in visualizing the path of brainstorm in the brain that occur during seizure. Selected techniques that are involved ranging from classical, ordinary fuzzy, and advanced fuzzy namely the intuitionistic fuzzy sets (IFS). Different techniques may result in different output of fEEG image. The methods in classical approach are Power Law Transformation, Histogram Equalization, and Image Size Dependent Normalization. The intensifier operator is implemented in the fuzzy contrast enhancement technique. For the IFS approach, the Window Based Enhancement Scheme (WBES) and its revised version (RWBES) are applied. The RWBES gives better results compared to the WBES whereby the vague boundary of the cluster centres are reduced resulting in a smaller area of the vague boundary. The vague boundary represents the strength of the electrical potential of the foci of seizure. Next, the quality of the output image is measured via the objective measure such as mean squared error (MSE), peak-signalto- noise-ratio (PSNR), universal image quality index (UIQI), and structural similarity index measure (SSIM). In IFS, the sum of membership and non-membership is not necessarily equal to one. Thus, there exists hesitancy in deciding the degree to which an element satisfies a particular property. Moreover, the sequence of enhanced fEEG images are demonstrated by varying the value of parameter, namely λ, that also influence the hesitation value π. In addition, the Sugeno type intuitionistic fuzzy generator which is used to compute the non-membership value v has been extended to the concept of fuzzy limit. Hence, by implementing the definition of fuzzy limit, different values of ∈ will be tested in obtaining the values of integer N that will determine the value of λ and hence the value of hesitation π. The relationship between membership, non-membership, and hesitation values are also demonstrated graphically

Sequence of image enhancemant of flat electroencephalography using intuitionistic fuzzy set

This study focused on contrast enhancement of Flat Electroencephalography (fEEG) image during epileptic seizure. The main interest is in visualizing the path of brainstorm in the brain that occur during seizure. Selected techniques that are involved ranging from classical, ordinary fuzzy, and advanced fuzzy namely the intuitionistic fuzzy sets (IFS). Different techniques may result in different output of fEEG image. The methods in classical approach are Power Law Transformation, Histogram Equalization, and Image Size Dependent Normalization. The intensifier operator is implemented in the fuzzy contrast enhancement technique. For the IFS approach, the Window Based Enhancement Scheme (WBES) and its revised version (RWBES) are applied. The RWBES gives better results compared to the WBES whereby the vague boundary of the cluster centres are reduced resulting in a smaller area of the vague boundary. The vague boundary represents the strength of the electrical potential of the foci of seizure. Next, the quality of the output image is measured via the objective measure such as mean squared error (MSE), peak-signalto- noise-ratio (PSNR), universal image quality index (UIQI), and structural similarity index measure (SSIM). In IFS, the sum of membership and non-membership is not necessarily equal to one. Thus, there exists hesitancy in deciding the degree to which an element satisfies a particular property. Moreover, the sequence of enhanced fEEG images are demonstrated by varying the value of parameter, namely �, that also influence the hesitation value π. In addition, the Sugeno type intuitionistic fuzzy generator which is used to compute the non-membership value � has been extended to the concept of fuzzy limit. Hence, by implementing the definition of fuzzy limit, different values of � will be tested in obtaining the values of integer N that will determine the value of � and hence the value of hesitation �. The relationship between membership, non-membership, and hesitation values are also demonstrated graphically

Bipolar picture fuzzy sets and relations with applications

The notions of both the bipolar fuzzy sets and picture fuzzy sets have been studied by many authors, the bipolar picture fuzzy set is the nice combination of these two notions. Basically, the concepts we present in our study are the direct extensions of both the bipolar fuzzy sets and picture fuzzy sets. In this study, we add few more operations and results in the theory of the bipolar picture fuzzy sets. We also initiate the notion of bipolar picture fuzzy relations along with their applications. We present numerous basic operations along with the algebraic sums, bounded sums, algebraic product, bounded difference on bipolar picture fuzzy sets. Different types of distances between two bipolar picture fuzzy sets are also addressed. We provide the application of bipolar picture fuzzy sets towards decision making theory along with its algorithm. Afterward, we introduce different types of bipolar picture fuzzy relations like bipolar picture fuzzy reflexive, symmetric and transitive relations. Subsequently, we introduce the concepts of the bipolar picture fuzzy equivalence relation and partition. We also produce numerous interesting results based on these relations. Finally, we establish the criteria for the detection of covid-19 at the base of bipolar picture fuzzy relations

Lattice-valued intuitionistic preference structures and applications

Intuicionistički rasplinuti skupovi su već proučavani i definisani u kontekstu mrežnovrednosnih struktura, ali svaka od postojećih definicija imala je odgovarajuće nedostatke. U ovom radu razvijena je definicija intuicionističkog poset-vrednosnog rasplinutog skupa, kojom se poset predstavlja kao podskup distributivne mreže. Na ovaj način možemo ispitivati funkcije pripadanja i nepripadanja i njihove odnose bez upotrebe komplementiranja na posetu. Takođe, u ovako postavljenim okvirima, svaki poset (a samim tim i mreža) može biti kodomen intuicionističkog rasplinutog skupa (čime se isključuje uslov ograničenosti poseta). Primenom uvedene definicije razmatrane su IP-vrednosne rasplinute relacije, x-blokovi ovih relacija i familije njihovih nivoa.Razvijene su jake poset vrednosne relacije reciprociteta koje  predstavljaju uopštenje relacija reciprociteta sa intervala [0,1]. Pokazano je da ovakve relacije imaju svojstva slična poset-vrednosnim relacijama preferencije. Međutim, postoje velika ograničenja za primenu ovakvih relacija jer su zahtevi dosta jaki. Uvedene su IP-vrednosne relacije reciprociteta koje se mogu definisati za veliku klasu poseta.Ovakve relacije pogodne su za opisivanje preferencija. Posmatrana je intuicionistička poset-vrednosna relacija preferencije, koja je refleksivna rasplinuta relacija, nad skupom alternativa. U samom procesu višekriterijumskog odlučivanja može se pojaviti situacija kada alternative nisu međusobno uporedive u odnosu na relaciju preferencije, kao i nedovoljna određenost samih alternativa. Da bi se prevazišli ovakvi problemi uvodi se intuicionistička poset-vrednosna relacija preferencije kao intuicionistička rasplinuta relacija na skupu alternativa sa vrednostima u uređenom skupu. Analizirana su neka njena svojstva. Ovakav model pogodan je za upoređivanje alternativa koje nisu, nužno, u linearnom poretku. Dato je nekoliko opravdanja za uvodjenje oba tipa definisanih relacija. Jedna od mogućnosti jeste preko mreže intervala elemenata iz konačnog lanca S, a koji predstavljaju ocene određene alternative. Relacije preferencije mogu uzimati vrednosti sa ove mreže i time se može prevazići nedostatak informacija ili neodlučnost donosioca odluke.Intuitionistic fuzzy sets have already been explored in depth and defined in the context of lattice-valued intuitionistic fuzzy sets, however, every existing definition has certain drawbacks. In this thesis, a definition of poset-valued intuitionistic fuzzy sets is developed, which introduces a poset as a subset of a distributive lattice. In this manner, functions of membership and non-membership can be examined as well as  their relations without using complement in the poset. Also, in such framework, each poset (and the lattice) can be a co-domain of an intuitionistic fuzzy set (which excludes the condition of the bounded poset). Introduced definition defines IP-valued fuzzy relations, x-blocks of these relations andfamilies of their levels. Strong IP-valued  reciprocialy relations have been developed as a generalization of reciprocal relations from interval [0,1]. It has been shown that these relations have properties similar to the P-valued preferences relations. However, there are great constraints on the application of these relations because the requirements are quite strong.IP- valued reciprocial relations have been introduced, which can be defined for a large class of posets. Such relations are suitable for describing preferences.An intuitionistic poset-valued preference relation, which is a reflexive fuzzy relation, over the set of  alternatives, has been examined. In the process of a multi-criteria decision making, a situation can occur that the alternatives cannot be compared by the preference relation, as well as insufficient determination of the mentioned alternatives. In order to overcome similar problems, we have introduced an intuitionistic poset-valued preference relation as an intuitionistic fuzzy set over the set of alternatives with values in a certain poset. We have analyzed some its performances. This model is suitable for comparing alternatives which are not necessarily linearly ordered. There are several justifications for the introduction of  both types of defined relations. One of the possibilities is via the lattice of the intervals  of elements from the finite chain S, which represent the preference of a particular alternative. Preferences relations can take values from this lattice and this can overcome the lack of informations or the decisiveness of the decision maker