Fuzzy Notion Research Articles

A study on intuitionistic fuzzy sets in Γ-semihypergroups

The notion of intuitionistic fuzzy sets was introduced by Atanassov as a generalization of the notion of fuzzy sets. In this paper, using Atanassov idea, we continue the study on intuitionistic fuzzy sets in Γ-semihypergroups initiated recently by Ersoy and Davvaz [25]. We give some further properties of intuitionistic fuzzy Γ-hyperideals and intuitionistic fuzzy bi-Γ-hyperideals in a Γ-semihypergroup and use the intuitionistic fuzzy left, right, two-sided and bi-Γ-hyperideals to characterize some classes of Γ-semihypergroups. We introduce and study λ, μ-intuitionistic fuzzy Γ-hyperideals. We also introduce the notion of an intuitionistic fuzzy M resp. N-hypersystem of a Γ-semihypergroup and some properties of them are investigated.

Ideals on fuzzy topological spaces

Fuzzy ideal set and fuzzy local function of fuzzy ideals with fuzzy topologies were introduced and studied by D. Sarker [10]. The purpose of this paper deals with new sort of fuzzy ideal and fuzzy local function namely fuzzy ideal and r-fuzzy open local function. Many of its characterizations, properties and connections between it and other corresponding fuzzy notions are studied. Also, we introduce r-fuzzy idealcompact, r-fuzzy ideal quasi H-closed and r-fuzzy compact modulo an fuzzy ideal in fuzzy ideal topological space in view of the definition of ˆ Sostak, and study some of their properties. Also, we investigate the behavior of r-fuzzy ideal-compact under several types of F-continuous mappings. In the last section, we define r-fuzzy I-open, r-fuzzy I-closed and F I-continuous. Also, we investigate some of their properties and the relationships between F-continuous and F I-continuous maps.

On the Mazur-Ulam Theorem in Non-Archimedean Fuzzy -Normed Spaces

The motivation of this paper is to present a new notion of non-Archimedean fuzzy -normed space over a field with valuation. We obtain a Mazur-Ulam theorem for fuzzy -isometry mappings in the strictly convex non-Archimedean fuzzy -normed spaces. We also prove that the interior preserving mapping carries the barycenter of a triangle to the barycenter point of the corresponding triangle. And then, using this result, we get a Mazur-Ulam theorem for the interior preserving fuzzy -isometry mappings in non-Archimedean fuzzy -normed spaces over a linear ordered non-Archimedean field.

“Cripping” Resilience: Contributions from Disability Studies to Resilience Theory

“Cripping” Resilience: Contributions from Disability Studies to Resilience Theory

Some new fixed point results in non-Archimedean fuzzy metric spaces

In this paper, we introduce the notions of fuzzy (α,β,ϕ)-contractive mapping, fuzzy α-φ-ψ-contractive mapping and fuzzy α-β-contractive mapping and establish some results of fixed point for this class of mappings in the setting of non-Archimedean fuzzy metric spaces. The results presented in this paper generalize and extend some recent results in fuzzy metric spaces. Also, some examples are given to support the usability of our results.

A fuzzy real-time temporal logic

High-level descriptions of real-time systems often use fuzzy notions of time that are left open to domain specific interpretations. In order to verify that a given implementation conforms to such loosely defined specifications, the typical approach is to verify the implementation to be correct within well defined limits of time tolerance. This approach determines whether the real-time requirements are met, but does not reflect how well it is met.Our goal in this paper is to prescribe the development of timed specifications using fuzzy notions of time, and to present a methodology for computing the quality of satisfaction of the specification on a given implementation using domain specific fuzzy membership functions. With this objective, we combine the notions of real-time interval temporal logic (like Metric Interval Temporal Logic) and fuzzy logic to derive FRTL, a fuzzy real-time temporal logic. The novelty of the proposed logic is in introducing the notion of fuzzy time intervals into the core fabric of conventional metric temporal logic. We present a method for evaluating the fuzzy truth of FRTL properties on finite traces. We discuss the motivation of computing the fuzzy truth towards evaluating the quality of control in time critical embedded control system applications. We also show that two important related problems from the domain of mixed-signal design verification, are subsumed by the proposed framework of analysis.

Medidas difusas e integrales difusas

This is a study of fuzzy measures and fuzzy inte-grals; it presents some of the phenomena wherethey are used. It exposes how the concept of fuzzymeasure is introduced and from it, the notion offuzzy integral is presented. Properties of fuzzymeasures are established and they are classifiedaccording to additive property and λ-measures,while the probability, plausibility, credibility, pos-sibility and necessity measures are observed asclassic examples of the classification completed.The two main fuzzy integrals were analyzed: theSugeno integral and the Choquet integral, giventhe application of these integrals is made on finitesets, a comparison between them for the finitecase is performed using the concept of equiorde-red functions. We present two examples in whichfuzzy measures and fuzzy integrals are used inthe classification of individuals and in qualityassessment. It also describes some phenomenawhere they are applied. Classic measures are usedin certain special cases of uncertainty based onrandomness. The use in certain contexts of fuzzymeasures (non-additive) and fuzzy integrals offera more flexible and realistic focus in modelinguncertainty

Denver Groups Classification of Human Chromosomes Using Fuzzy C-Means Clustering

Unbanded human chromosome can be classified into seven Denver Groups (A-G) based their lengths and the ratio of the length of the shorter arm to the whole length of the chromosome, which is called the centromere index (CI). In this article, the fuzzy c-means method will be used to perform the Denver Group classification of a given set of human chromosomes. The objective in clustering is to partition a given human chromosome set into homogeneous clusters; by homogeneous we mean that all points in the same cluster share similar attributes and they do not share similar attributes with points in other clusters. However, the separation of clusters and the meaning of similarity are fuzzy notions and can be described as such. It is found that the clusters iterations converge, highly depend on the initial partition matrix,

Fuzzy pricing, marketing and service planning in a fuzzy inventory model: A geometric programming approach

In the real world markets, demand is influenced by different parameters. Recently, many researchers have been interested in integrated production and marketing planning strategies in inventory models where demand depends on different parameters such as price and/or marketing expenditure. The quality of services that are offered to customers of a product is one of the most important parameters that affects demand in the real markets and has not been considered in development of inventory models. On the other hand, the cost parameters in real inventory systems and other parameters such as price, marketing and service elasticity to demand are imprecise and uncertain in nature. So, the notion of fuzziness can be applied to cope with this uncertainty. In this paper, a new fuzzy profit maximization inventory model with shortages is proposed. The demand is considered as a power function of price, marketing expenditure and service expenditure. Furthermore, unit cost is determined as a power function of order quantity. Since the proposed model is in a fuzzy environment, a fuzzy decision should be made to meet the decision criteria, and the results should be fuzzy. Therefore, the proposed model is formulated and solved using geometric programming and fuzzy optimization techniques to derive an approximation of the results’ membership functions. The model is illustrated with a numerical example and finally a case study is provided for evaluation and validation of the results of model.

A Wavelet Relational FuzzyC-Means Algorithm for 2D Gel Image Segmentation

One of the most famous algorithms that appeared in the area of image segmentation is the Fuzzy C-Means (FCM) algorithm. This algorithm has been used in many applications such as data analysis, pattern recognition, and image segmentation. It has the advantages of producing high quality segmentation compared to the other available algorithms. Many modifications have been made to the algorithm to improve its segmentation quality. The proposed segmentation algorithm in this paper is based on the Fuzzy C-Means algorithm adding the relational fuzzy notion and the wavelet transform to it so as to enhance its performance especially in the area of 2D gel images. Both proposed modifications aim to minimize the oversegmentation error incurred by previous algorithms. The experimental results of comparing both the Fuzzy C-Means (FCM) and the Wavelet Fuzzy C-Means (WFCM) to the proposed algorithm on real 2D gel images acquired from human leukemias, HL-60 cell lines, and fetal alcohol syndrome (FAS) demonstrate the improvement achieved by the proposed algorithm in overcoming the segmentation error. In addition, we investigate the effect of denoising on the three algorithms. This investigation proves that denoising the 2D gel image before segmentation can improve (in most of the cases) the quality of the segmentation.

Using a priori information in regression analysis

The paper considers the methods to evaluate regression parameters under indefinite a priori information of two types: fuzzy and stochastic. Fuzzy a priori information is assumed to be formulated on the basis of fuzzy notions of the model designer. Stochastic a priori information is systems of equations, which are linear in regression parameters and whose right-hand sides are random variables. Regression parameters may both be constant and vary in time. A classification of the evaluation methods using indefinite a priori information is proposed and used to generalize well-known methods. An evaluation method is developed, which combines the fuzzy and stochastic a priori information about regression parameters.

From interpersonal to international: two types of translation in the making of implicitness in diplomatic discourse

This article argues that constructing implicitness in diplomatic discourse involves intra-lingual translation in ST. It also argues that inter-lingually translating implicitness in diplomatic discourse sometimes involves a process of intra-lingual translation in TT. A review of implicitness in diplomatic discourse, which often demonstrates a scripted feature, shows that notions of ambiguity, fuzziness, generality, and vagueness put forward by Zhang (1998) can be employed to scrutinize the construction of implicitness via lexical choice. Viewed in terms of Hallidayian linguistics, the construction of implicitness, in both ST and TT, bears a strong interpersonal prominence. As shown in the analysis of the implicitness found in the diplomatic discourse around the 2001 Air-Collision Incident, the interpersonal prominence is governed by national interest concerns of the discourse producers. A tentative model of creating and translating lexical implicitness in diplomatic discourse is suggested. As illustrated in the model, the translation-engendered implicitness in diplomatic discourse is a textual manifestation of the interpersonal prominence in the international arena of foreign affairs.

A note from the editor Hau: Year one

A note from the editor H<scp>au</scp>: Year one

Anti Fuzzy Deductive Systems of BL-Algebras

The aim of this paper is to introduce the notion of anti fuzzy (prime) deductive system in BL-algebra and to investigate their properties. It is shown that the set of all deductive systems (with the empty set) of a BL-algebra X is equipotent to a quotient of the set of all anti fuzzy deductive systems of X. The anti fuzzy prime deductive system theorem of BL-algebras is also proved.

Independence and mobility in later life

This paper explores independence in later life and its relations with mobility, or embodied movements through physical space on the basis of a review of a range of academic literature and in-depth interviews with community-dwelling adults aged 70 and more in the UK. We suggest that independence is a complex and fuzzy notion that is best thought of as a qualitative multiplicity and as an unstable achievement fabricated out of dependencies on bodies, technologies, infrastructures, social networks and other elements. Yet we also find that the study participants understand independent mobility as avoiding lifts provided by next of kin, friends or others for getting around. This is tied to the enactment of particular forms of embodiment and ageist subject positions for older people and implies that older adults are inadvertently complicit in the perpetuation of the connotations of dependency in later life with passivity, burden and undesirability. To counteract these tendencies, we end this paper by elaborating more inclusive and broader conceptualisations of dependence, independence and independent mobility in later life.

A Note From The Editor

A Note From The Editor

Policing the changing landscape of rural crime: a case study from Scotland

Although the notion of rural crime has an idyllic aura to it, crime occurs in a changing social landscape and is affected by demographic changes, changing crime trends and by the introduction of new policing practices. Similarly, exactly what constitutes rural crime is also open to debate and changes over time. Likewise, we only have a fuzzy notion of the stereotypical rural criminal and find it difficult to acknowledge the existence of a rural criminal underclass. As a result, crime in a rural context is more difficult to police than crime in an urban landscape because it requires a different set of skills and practices from policing the urban landscape. The closure of rural police stations and the reallocation of scarce policing resources to urban hotspots have inevitably led to a deskilling of the archetypal ‘country bobby’. Consequently, this quasi-longitudinal case study examines changes in policing practices in a (fictionalised) subdivision in rural Scotland over a 40-year period. This enables consideration of the changing rural landscape of crime and from this mapping process implications and conclusions in relation to good practice on rural policing can emerge.

Fuzzy (r, s)-S1-pre-semicontinuous mappings

In this paper, we introduce the notion of fuzzy (r, s)-S 1/SUB>-pre-semicontinuous mappings on intuitionistic fuzzy topological spaces in Sostak’s sense, which is a generalization of S 1 -pre-semicontinuous mappings by Shi-Zhong Bai. The relationship between fuzzy (r, s)-pre-semicontinuous mapping and fuzzy (r, s)-S 1 -pre-semicontinuous mapping is discussed. The characterizations for the fuzzy (r, s)-S 1 -pre-semicontinuous mappings are obtained.

Fuzzy Implication in the Area of Policy and Policy Making; a Short Non- Mathematical Introduction for Policy Makers

Between selecting and not selecting policy, there are other selections. The history of Fuzzy logic and fuzzy method do not go very beyond. But the implementation of fuzzy and its logic in different disciplines are getting increased. This paper aims to study the notion of fuzzy and policy and importance of fuzzy in today's chaotic environment for policy makers in national and international era. Also there are a lot of books and papers published on the methods on fuzzy but this paper is somehow different with them because has non-mathematical look on fuzzy and it just makes familiar the policy makers with the notion of non-mathematical fuzzy.

The problem with spatial identity: revisiting the “sense of place”

PurposeThe purpose of this paper is twofold: on the one hand, it is to contribute to a sound conceptualization of the notion of place identity in the context of geographical spatial approaches; on the other, it is to show the implications this has in place branding research.Design/methodology/approachFirst, the paper draws from place branding literature to point out the lack of a conceptualization of place identity, second, it presents the case study of Prenzlauer Berg to show how place identity is constituted. Finally, these findings are linked to literature about the constitution of space and place.FindingsThe concept of spatial identity suffers under the anthropomorphism of the term identity. Only in a sound conceptual framework and through a method mix it is possible to understand how the specificity of space is constituted.Research limitations/implicationsThe case study that is the base of this conceptual paper is a neighbourhood. There is a need to further discuss the issue of scale, i.e. whether the same rules apply for cities, regions or nations.Practical implicationsPlace branding/marketing is often based on a fuzzy notion of place identity. The above non‐essentialist approach of this identity deeply questions both the legitimacy and the efficiency of any place branding strategy. It thus asks for more sophisticated analytical methods by policy makers and consultants alike.Originality/valueConceptualization of spatial identity is a rather vague concept and, though it is often used as a point of departure for several issues, it is usually taken for granted. This paper offers a new systematic approach to the disambiguation of the concept.