• International Journal of Fuzzy Logic and Intelligent Systems
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• v.5 no.2
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• pp.136-139
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• 2005

In this paper, we introduce the concepts of fuzzy (r,s)-preopen sets and fuzzy (r,s)-precontinuous mappings on intuitionistic fuzzy topological spaces in Sostak's sense and then we investigate some of their characteristic properties.

• International Journal of Fuzzy Logic and Intelligent Systems
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• v.11 no.4
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• pp.254-258
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• 2011

In this paper, we introduce the notion of fuzzy (r, s)-S1-pre-semicontinuous mappings on intuitionistic fuzzy topological spaces in $\check{S}$ostak'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.

• International Journal of Fuzzy Logic and Intelligent Systems
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• v.5 no.3
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• pp.179-182
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• 2005

A model of an assessment module has been created, using intuitionistic fuzzy estimations, which render account on the knowledge of the trained objects. The final mark is determined on the basis of a set of evaluation units. An opportunity is offered no only fur tracing the changes of the parameters of the trainer object, but there is also an opportunity of tracing the status of the already comprehended knowledge, as well as evaluating and changing the training themes and evaluation criteria.

• Journal of the Korean Mathematical Society
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• v.54 no.5
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• pp.1521-1536
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• 2017

This paper introduces a representation style of variable binding using dependent types when formalizing meta-theoretic properties. The style we present is a variation of the Coquand-McKinna-Pollack's locally-named representation. The main characteristic is the use of dependent families in defining expressions such as terms and formulas. In this manner, we can handle many syntactic elements, among which wellformedness, provability, soundness, and completeness are critical, in a compact manner. Another point of our paper is to investigate the roles of free variables and constants. Our idea is that fresh constants can entirely play the role of free variables in formalizing meta-theories of first-order predicate logic. In order to show the feasibility of our idea, we formalized the soundness and completeness of LJT with respect to Kripke semantics using the proof assistant Coq, where LJT is the intuitionistic first-order predicate calculus. The proof assistant Coq supports all the functionalities we need: intentional type theory, dependent types, inductive families, and simultaneous substitution.

• International Journal of Fuzzy Logic and Intelligent Systems
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• v.7 no.2
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• pp.120-126
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• 2007

In this paper, we investigate some of characteristic properties of fuzzy strongly (r, s)-semicontinuous, fuzzy strongly (r, s )-semiopen and fuzzy strongly (r, s )-semiclosed mappings on the intuitionistic fuzzy topological space in \check{S}ostak's$ sense.

• International Journal of Fuzzy Logic and Intelligent Systems
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• v.6 no.4
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• pp.299-303
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• 2006

In this paper, we introduce the concepts of fuzzy strongly (r, s)-semiopen sets and fuzzy strongly (r, s)-semicontinuous mappings on the intuitionistic fuzzy topological space in Sostak's sense and then we investigate some of their characteristic properties.

• International Journal of Fuzzy Logic and Intelligent Systems
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• v.12 no.2
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• pp.149-153
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• 2012

In this paper, we introduce the concept of fuzzy almost strongly (r, s)-semicontinuous mappings on intuitionistic fuzzy topological spaces in $\check{S}$ostak's sense. The relationships among fuzzy strongly (r, s)-semicontinuous, fuzzy almost (r, s)-continuous, fuzzy almost (r, s)-semicontinuous, and fuzzy almost strongly (r, s)-semicontinuous mappings are discussed. The characterization for the fuzzy almost strongly (r, s)-semicontinuous mappings is obtained.

• Korean Journal of Logic
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• v.17 no.1
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• pp.33-70
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• 2014

We still do not know against what histocial/philosophical background and motivation was Tarski's definition of logical consequence introduced, even if it has had such a strong influence. In view of the centrality of the notion of logical consequence in logic and philosophy of logic, it is rather shocking. There must be various intertwined reasons to blame for this uncomfortable situation. There has been remarkable progress achieved recently on the history of analytic philosophy and modern logic. In view of the recent developments of the controversies involved, however, we will have to wait years to resolve all this uneasiness. In this gloomy situation, Douglas Patterson's recent study of Tarski's philosophy of language and logic seems to have the potential to turn out to be a ground breaking achievement. [Patterson (2012)] This article aims at reporting the state-of-the-art in this problem area, and fathoming the future directions of research by examining critically some unclear components of Patterson's study.

• International Journal of Fuzzy Logic and Intelligent Systems
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• v.5 no.1
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• pp.35-39
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• 2005

We apply estimations of the intuitionistic fuzzy sets on the basis of which some amendments may be undertaken.