INTUITIONISTIC FUZZY I-CONVERGENT DIFFERENCE SEQUENCE SPACES DEFINED BY COMPACT OPERATOR

In this paper, we introduce and study the intuitionistic fuzzy $I$-convergent difference sequence spaces  ${I}^{(\mu,\upsilon)}(T,\Delta)$ and  ${I^{0}}^{(\mu,\upsilon)}(T,\Delta)$ using by compact operator. Also we introducce a new concept, called closed ball in these spaces. By the helping of these notions, we establish a new topological space and investigate some topological properties in intuitionistic fuzzy $I$-convergent difference sequence spaces  ${I}^{(\mu,\upsilon)}(T,\Delta)$ and  ${I^{0}}^{(\mu,\upsilon)}(T,\Delta)$ using by compact operator

Approximate fixed point property in IFNS

In this paper, we define concept of approximate fixed point property of a function and a set in intuitionistic fuzzy normed space. Furthermore, we give intuitionistic fuzzy version of some class of maps used in fixed point theory and investigate approximate fixed point property of these maps.This work has been supported by Yildiz Technical University Scientific Research Projects Coordination Unit under the project number BAPK 2012-07-03-DOP03.Publisher's Versio

A systematic review on multi-criteria group decision-making methods based on weights: analysis and classification scheme

Interest in group decision-making (GDM) has been increasing prominently over the last decade. Access to global databases, sophisticated sensors which can obtain multiple inputs or complex problems requiring opinions from several experts have driven interest in data aggregation. Consequently, the field has been widely studied from several viewpoints and multiple approaches have been proposed. Nevertheless, there is a lack of general framework. Moreover, this problem is exacerbated in the case of experts’ weighting methods, one of the most widely-used techniques to deal with multiple source aggregation. This lack of general classification scheme, or a guide to assist expert knowledge, leads to ambiguity or misreading for readers, who may be overwhelmed by the large amount of unclassified information currently available. To invert this situation, a general GDM framework is presented which divides and classifies all data aggregation techniques, focusing on and expanding the classification of experts’ weighting methods in terms of analysis type by carrying out an in-depth literature review. Results are not only classified but analysed and discussed regarding multiple characteristics, such as MCDMs in which they are applied, type of data used, ideal solutions considered or when they are applied. Furthermore, general requirements supplement this analysis such as initial influence, or component division considerations. As a result, this paper provides not only a general classification scheme and a detailed analysis of experts’ weighting methods but also a road map for researchers working on GDM topics or a guide for experts who use these methods. Furthermore, six significant contributions for future research pathways are provided in the conclusions.The first author acknowledges support from the Spanish Ministry of Universities [grant number FPU18/01471]. The second and third author wish to recognize their support from the Serra Hunter program. Finally, this work was supported by the Catalan agency AGAUR through its research group support program (2017SGR00227). This research is part of the R&D project IAQ4EDU, reference no. PID2020-117366RB-I00, funded by MCIN/AEI/10.13039/ 501100011033.Peer ReviewedPostprint (published version

Fuzzy Sets, Fuzzy Logic and Their Applications

The present book contains 20 articles collected from amongst the 53 total submitted manuscripts for the Special Issue “Fuzzy Sets, Fuzzy Loigic and Their Applications” of the MDPI journal Mathematics. The articles, which appear in the book in the series in which they were accepted, published in Volumes 7 (2019) and 8 (2020) of the journal, cover a wide range of topics connected to the theory and applications of fuzzy systems and their extensions and generalizations. This range includes, among others, management of the uncertainty in a fuzzy environment; fuzzy assessment methods of human-machine performance; fuzzy graphs; fuzzy topological and convergence spaces; bipolar fuzzy relations; type-2 fuzzy; and intuitionistic, interval-valued, complex, picture, and Pythagorean fuzzy sets, soft sets and algebras, etc. The applications presented are oriented to finance, fuzzy analytic hierarchy, green supply chain industries, smart health practice, and hotel selection. This wide range of topics makes the book interesting for all those working in the wider area of Fuzzy sets and systems and of fuzzy logic and for those who have the proper mathematical background who wish to become familiar with recent advances in fuzzy mathematics, which has entered to almost all sectors of human life and activity

Sezgisel bulanık normlu uzaylarda tanımlanan bazı yakınsaklık çeşitleri

06.03.2018 tarihli ve 30352 sayılı Resmi Gazetede yayımlanan “Yükseköğretim Kanunu İle Bazı Kanun Ve Kanun Hükmünde Kararnamelerde Değişiklik Yapılması Hakkında Kanun” ile 18.06.2018 tarihli “Lisansüstü Tezlerin Elektronik Ortamda Toplanması, Düzenlenmesi ve Erişime Açılmasına İlişkin Yönerge” gereğince tam metin erişime açılmıştır.Sezgisel bulanık normlu uzaylarda tanımlanan bazı yakınsaklık çeşitleri isimli bu tez çalışması beş bölümden oluşmaktadır. Birinci bölümde, normlu lineer uzaylarda tanımlanan bazı yakınsaklık çeşitleri hakkında kısa bir özet verildi. İkinci bölümde, diğer bölümlerde kullanılacak olan temel tanım ve teoremlere değinildi. Üçüncü bölümde, ilk olarak, sezgisel bulanık normlu lineer uzaylarda (N, p)- toplanabilirlik ve ağırlıklı istatistiksel yakınsaklık kavramları verildi ve bu kavramlar arasındaki bağıntılar incelendi. Ardından, sezgisel bulanık normlu lineer uzaylarda (Nl , p)- toplanabilme ve genelleştirilmiş ağırlıklı istatistiksel yakınsaklık kavramları tanımlandı ve bu kavramlarla ilgili bazı teoremler ispat edildi. Son olarak, sezgisel bulanık normlu lineer uzaylarda ( )- r N, p ,q toplanabilirlik ve ağırlıklı lacunary istatistiksel yakınsaklık kavramları tanımlandı ve bu kavramların bazı özellkler" incelendi. Dördüncü bölümde ise fark dizisi ve lacunary istatistiksel yakınsaklık kavramları birleştirilerek sezgisel bulanık n- normlu lineer uzaylarda lacunary D- istatistiksel yakınsak dizi ve lacunary D- istatistiksel Cauchy dizi tanımları verildi ve bu kavramlarla ilgili bazı teoremler ispat edildi. Son bölümde ise bazı genel sonuçlar ve araştırma problemleri verildi.This thesis which is entitled "Some convergence types defined in intuitionistic fuzzy normed spaces"consists of five sections. In the first section, a short abstract is given about some convergence types defined in normed linear spaces. In the second section, some basic definitions and theorems which will be used in the later sections are given. In the third section, firstly, definitions of (N, p)- summmability and weighted statistical convergence in intuitionistic fuzzy normed linear spaces are given and some relations between these concepts are investigated. After, concepts of (Nl , p)- summmability and generalized weighted statistical convergence in intuitionistic fuzzy normed linear spaces are introduced and some theorems related to these concepts are proved. Lastly, the concepts of ( N, p r ,q)- summmability and weighted lacunary statistical convergence in intuitionistic fuzzy normed linear spaces are introduced and some properties of these concepts are investigated. In the fourth sect on, by combining the concepts of difference sequence and lacunary statistical convergence, defnitions of lacunary D- statistical convergence sequence and lacunary D- statistical Cauchy sequence are given in intuitionistic fuzzy n- normed linear spaces and some theorems related to these concepts are given. In the last section, some general conclusions and some investigation problems were given

ON LACUNARY CONVERGENCE IN CREDIBILITY SPACE

In this paper, we present the notions of lacunary statistically convergent sequence for fuzzy variables, lacunary statistically Cauchy sequence in credibility space, and present a kind of lacunary statistical completeness for credibility space. Also, we present lacunary strong convergence concepts of sequences of fuzzy variables of different types

Improved multi-objective optimization model for policy design of rental housing market

Renting is, like owning a house, a way to realize residence rights, playing an important role in maintaining the equilibrium of the housing market. The lack of attention paid to policy design of the rental housing market causes low effectiveness in the housing resource flow and allocation at both local and national levels. Thus, we propose a novel design framework and process of public policy, in particular the development policy for the rental housing market. This innovative approach abstracts the policy design process into a solution-formation process for a high-dimensional and multi-objective optimization problem. First, based on opinion mining, using co-occurrence networks, text mining and other methods, in addition to authoritative literature and expert opinions from the Chinese Social Sciences Citation Index (CSSCI) as data sources, the objective function and the constraint function coefficients were determined to construct a multi-objective function of rental housing market policy. Second, this paper proposes a two-stage evolutionary high-dimensional multi-objective optimization algorithm based on the Pareto dominance relationship to solve high-dimensional multi-objective functions. Finally, we designed a rental housing policy tool-mix selection system-modeling process and obtained six sets of feasible solutions and objectives after 300,000 simulations. Therefore, the policy tool-mix selection system presented in this study effectively supports the policymaking process.</jats:p

Dieudonné-type theorems for lattice group-valued kk-triangular set functions

summary:Some versions of Dieudonné-type convergence and uniform boundedness theorems are proved, for $k$-triangular and regular lattice group-valued set functions. We use sliding hump techniques and direct methods. We extend earlier results, proved in the real case. Furthermore, we pose some open problems