On t-Conorm Based Fuzzy (Pseudo)metrics

Abstract

<jats:p>We present an alternative approach to the concept of a fuzzy (pseudo)metric using t-conorms instead of t-norms and call them t-conorm based fuzzy (pseudo)metrics or just CB-fuzzy (pseudo)metrics. We develop the basics of the theory of CB-fuzzy (pseudo)metrics and compare them with “classic” fuzzy (pseudo)metrics. A method for construction CB-fuzzy (pseudo)metrics from ordinary metrics is elaborated and topology induced by CB-fuzzy (pseudo)metrics is studied. We establish interrelations between CB-fuzzy metrics and modulars, and in the process of this study, a particular role of Hamacher t-(co)norm in the theory of (CB)-fuzzy metrics is revealed. Finally, an intuitionistic version of a CB-fuzzy metric is introduced and applied in order to emphasize the roles of t-norms and a t-conorm in this context.</jats:p>

Some Remarks on Strong Fuzzy Metrics and Strong Fuzzy Approximating Metrics with Applications in Word Combinatorics

“…Thus, if we restrict to the situation when t > 0, each GV-fuzzy metric is a KM-fuzzy metric, but not the converse. See also Remark 3.8 in [24] in this concern.…”

The First Rational Type Revised Fuzzy-Contractions in Revised Fuzzy Metric Spaces with an Applications

“…In the year 2018, Alexander Sostak [1][2][3] introduced the idea of revised fuzzy metrics, which allow for the progressive evaluation of an element's inclusion in a collection. Revised fuzzy contraction mappings were described by Muraliraj and Thangathamizh [4][5][6][7], and the existence of fixed points was established for it.…”

“…On the other hand, function N, which in some sense complements function M, is based on a t-conorm (that is, probably, unrelated to the t-norm *). In contrast to the case of an intuitionistic fuzzy metric, we, when defining an RGV-fuzzy metric, started with a "classic" GV-metric and just reformulated the axioms from [3] by using involution. So, in our approach, a t-conorm ⊕ in the definition of a fuzzy metric is used to evaluate the degree of nearness of two points, and hence, it is opposite to the role of a t-conorm in the definition of an intuitionistic fuzzy metric.…”

“…The following articles [2][3][4][5][8][9][10][11][12][13][14][15][16][17][18][19][20][21] contain some triangular characteristic and integral type application findings in the theory of fixed point.…”

New Relation-Theoretic Fixed Point Theorems in Revised Fuzzy Metric Spaces With an Application to Fractional Differential Equations

“…Šostak [20] improved on George and Veeramani's notion of revised fuzzy metric spaces, which they introduced in 2018. Grigorenko [6] developed the class of fuzzy (pseudo) metric spaces in 2020 to exploit this notion in topology. Muraliraj and Thangathamizh [11,12] and Muraliraj et al [13] went on to develop fuzzy mapping and come up with a fixed point result for it.…”