• International Journal of Fuzzy Logic and Intelligent Systems
• /
• 제3권2호
• /
• pp.200-205
• /
• 2003

In this paper, we generally introduce some of the terminology of Yalvac [10] and Azad [4] in intuitionistic fuzzy topological spaces. In addition to the fundamental concepts of intuitionistic fuzzy sets, we emphasize the usefulness of the concepts of intuitionistic fuzzy points intuitionistic fuzzy elementhood. Mainly, this paper is devoted to the study of intuitionistic fuzzy topological spaces with specific attention to the weaker forms of fuzzy continuity.

• 대한수학회보
• /
• 제37권1호
• /
• pp.63-76
• /
• 2000

In this paper, we introduce the concept of intuitionistic fuzzy points and intuitionistic fuzzy neighborhoods. We investigate the properties of continuous, open and closed maps in the intuitionistic fuzzy topological spaces, and show that the category of Chang's fuzzy topological spaces is a bireflective full subcategory of that of intuitionistic fuzzy topological spaces.

• 한국지능시스템학회:학술대회논문집
• /
• 한국퍼지및지능시스템학회 1998년도 The Third Asian Fuzzy Systems Symposium
• /
• pp.225-230
• /
• 1998

In this paper, we introduce the concepts of intuitionistic fuzzy points and intuitionistic fuzzy neighborhoods. We investigate properties of continuous, open and closed maps in the intuitionistic fuzzy topological spaces, and show that the category of Chang's fuzzy topological spaces is a bireflective full subcategory of that of intuitionistic fuzzy topogical spaces.

• International Journal of Fuzzy Logic and Intelligent Systems
• /
• 제13권2호
• /
• pp.147-153
• /
• 2013

Previously, Park et al. (2005) defined an intuitionistic fuzzy metric space and studied several fixed-point theories in this space. This paper provides definitions and describe the properties of type(${\beta}$) compatible mappings, and prove some common fixed points for four self-mappings that are compatible with type(${\beta}$) in an intuitionistic fuzzy metric space. This paper also presents an example of a common fixed point that satisfies the conditions of Theorem 4.1 in an intuitionistic fuzzy metric space.

• Kyungpook Mathematical Journal
• /
• 제45권1호
• /
• pp.87-87
• /
• 2005

Using the belongs to relation $({\in})$ and quasi-coincidence with relation (q) between intuitionistic fuzzy points and intuitionistic fuzzy sets, the concept of (${\Phi},\;{\Psi}$)-intuitionistic fuzzy subgroup where ${\Phi},\;{\Psi}$ are any two of {${\in},\;q,\;{\in}{\vee}q,\;{\in}{\wedge}q$} with ${\Phi}\;{\neq}\;{\in}{\wedge}q$ is introduced, and related properties are investigated.

• International Journal of Fuzzy Logic and Intelligent Systems
• /
• 제7권3호
• /
• pp.159-164
• /
• 2007

Park, Park and Kwun[6] is defined the intuitionistic fuzzy metric space in which it is a little revised from Park[5]. According to this paper, Park, Kwun and Park[11] Park and Kwun[10], Park, Park and Kwun[7] are established some fixed point theorems in the intuitionistic fuzzy metric space. Furthermore, Park, Park and Kwun[6] obtained common fixed point theorem in the intuitionistic fuzzy metric space, and also, Park, Park and Kwun[8] proved common fixed points of maps on intuitionistic fuzzy metric spaces. We prove a fixed point for pair of maps with another method from Park, Park and Kwun[7] in intuitionistic fuzzy metric space defined by Park, Park and Kwun[6]. Our research are an extension of Vijayaraju and Marudai's result[14] and generalization of Park, Park and Kwun[7], Park and Kwun[10].

• 대한수학회논문집
• /
• 제24권2호
• /
• pp.197-214
• /
• 2009

In this paper, we formulate the definition of compatible mappings of type (I) and (II) in intuitionistic fuzzy metric spaces and prove a common fixed point theorem by using the conditions of compatible mappings of type (I) and (II) in complete intuitionistic fuzzy metric spaces. Our results intuitionistically fuzzify the result of Cho, Sedghi, and Shobe [4].

• International Journal of Fuzzy Logic and Intelligent Systems
• /
• 제7권1호
• /
• pp.49-57
• /
• 2007

Using the idea of degree of openness and degree of nonopenness, Coker and Demirci [5] defined intuitionistic fuzzy topological spaces in Sostak's sense as a generalization of smooth topological spaces and intuitionistic fuzzy topological spaces. M. N. Mukherjee and S. P. Sinha [10] introduced the concept of fuzzy irresolute maps on Chang's fuzzy topological spaces. In this paper, we introduce the concepts of fuzzy (r,s)-irresolute, fuzzy (r,s)-presemiopen, fuzzy almost (r,s)-open, and fuzzy weakly (r,s)-continuous maps on intuitionistic fuzzy topological spaces in Sostak's sense. Using the notions of fuzzy (r,s)-neighborhoods and fuzzy (r,s)-semineighborhoods of a given intuitionistic fuzzy points, characterizations of fuzzy (r,s)-irresolute maps are displayed. The relations among fuzzy (r,s)-irresolute maps, fuzzy (r,s)-continuous maps, fuzzy almost (r,s)-continuous maps, and fuzzy weakly (r,s)-cotinuous maps are discussed.

• 대한수학회논문집
• /
• 제31권4호
• /
• pp.729-743
• /
• 2016

In the current work, the intuitionistic fuzzy version of Hyers-Ulam stability for a nonic functional equation by applying a fixed point method is investigated. This way shows that some fixed points of a suitable operator can be a nonic mapping.

• KSII Transactions on Internet and Information Systems (TIIS)
• /
• 제12권7호
• /
• pp.3128-3149
• /
• 2018

A number of effective methods for multiple-attribute group decision making (MAGDM) with interval-valued intuitionistic fuzzy numbers (IVIFNs) have been proposed in recent years. However, the different methods frequently yield different, even sometimes contradictory, results for the same problem. In this paper a novel criterion to determine the advantages and disadvantages of different methods is proposed. First, the decision-making process is divided into three parts: translation of experts' preferences, aggregation of experts' opinions, and comparison of the alternatives. Experts' preferences aggregation is considered the core step, and the quality of the collective matrix is considered the most important evaluation index for the aggregation methods. Then, methods to calculate the similarity measure, correlation, correlation coefficient, and energy of the intuitionistic fuzzy matrices are proposed, which are employed to evaluate the collective matrix. Thus, the optimal method can be selected by comparing the collective matrices when all the methods yield different results. Finally, a novel approach for aggregating experts' preferences with IVIFN is presented. In this approach, experts' preferences are mapped as points into two-dimensional planes, with the plant growth simulation algorithm (PGSA) being employed to calculate the optimal rally points, which are inversely mapped to IVIFNs to establish the collective matrix. In the study, four different methods are used to address one example problem to illustrate the feasibility and effectiveness of the proposed approach.