Unidefiners

Year 2025, Volume: 29 Issue: 1, 220 - 227, 25.04.2025

Selim Çetin

https://doi.org/10.19113/sdufenbed.1666339

Abstract

In this study, we examine the concept of a unidefiner, defined on the interval [0,∞], which provides a unified framework for both t-definer and t-codefiner structures. Similar to the approach of uninorms on [0,1], a unidefiner is a binary operation on [0,∞], with a neutral element e∈[0,∞],, which is associative, commutative, and monotonic. Consequently, when e = 0, it yields a t-definer, and when e =∞, it yields a t-codefiner. This paper discusses the theoretical properties of unidefiners and explores their relationship with t-definer and t-codefiner examples. In conclusion, it emphasizes that unidefiners can serve as a “generalized connective” analogous to uninorms for a “proper” identity value (i.e., e ≠ 0, e≠∞) in the [0,∞] range.

Keywords

Unidefiner, t-definer, t-codefiner, identity element, monoid

Unibelirleyici

Abstract

Bu çalışmada, hem t-belirleyici (t-definer) hem de t-eşbelirleyici (t-codefiner) yapılarını kapsayan birleşik bir çerçeve sağlayan ve [0,∞]aralığında tanımlanan unibelirleyici (unidefiner) kavramını incelemekteyiz. [0,1]aralığında tanımlanan uninormlara benzer bir yaklaşımla, unibelirleyici, [0,∞] üzerinde tanımlı, değişmeli (komütatif), birleşmeli (assosiatif) ve monoton olan bir ikili işlemdir ve e∈[0,∞] olmak üzere birim (nötr) elemana sahiptir. Buna bağlı olarak, e=0 durumunda bir t-belirleyici, e=∞ durumunda ise bir t-eşbelirleyici elde edilir. Bu çalışma, unibelirleyicilerin teorik özelliklerini ele almakta ve t-belirleyici ile t-eşbelirleyici yapılarla olan ilişkilerini incelemektedir. Sonuç olarak, unibelirleyicilerin, [0,∞] aralığında uygun bir birim değeri (e ≠ 0,e ≠ ∞) seçildiğinde, uninormlara benzer şekilde "genelleştirilmiş bir bağlayıcı" olarak işlev görebileceği vurgulanmaktadır.

Keywords

Unibelirleyici, t-belirleyici, t-eşbelirleyici, birim eleman, monoid

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