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An extension method for t-norms on subintervals to t-norms on bounded lattices

Funda Karaçal, Ümit Ertuğrul, M. Nesibe Kesicioğlu (2019)

Kybernetika

In this paper, a construction method on a bounded lattice obtained from a given t-norm on a subinterval of the bounded lattice is presented. The supremum distributivity of the constructed t-norm by the mentioned method is investigated under some special conditions. It is shown by an example that the extended t-norm on L from the t-norm on a subinterval of L need not be a supremum-distributive t-norm. Moreover, some relationships between the mentioned construction method and the other construction...

An extension of the ordering based on nullnorms

Emel Aşıcı (2019)

Kybernetika

In this paper, we generally study an order induced by nullnorms on bounded lattices. We investigate monotonicity property of nullnorms on bounded lattices with respect to the F -partial order. Also, we introduce the set of incomparable elements with respect to the F-partial order for any nullnorm on a bounded lattice. Finally, we investigate the relationship between the order induced by a nullnorm and the distributivity property for nullnorms.

An inquiry-based method for Choquet integral-based aggregation of interface usability parameters

Miguel-Ángel Sicilia, Elena García Barriocanal, Tomasa Calvo (2003)

Kybernetika

The concept of usability of man-machine interfaces is usually judged in terms of a number of aspects or attributes that are known to be subject to some rough correlations, and that are in many cases given different importance, depending on the context of use of the application. In consequence, the automation of judgment processes regarding the overall usability of concrete interfaces requires the design of aggregation operators that are capable of modeling approximate or ill-defined interactions...

An investigation on the n -fold IVRL-filters in triangle algebras

Saeide Zahiri, Arsham Borumand Saeid (2020)

Mathematica Bohemica

The present study aimed to introduce n -fold interval valued residuated lattice (IVRL for short) filters in triangle algebras. Initially, the notions of n -fold (positive) implicative IVRL-extended filters and n -fold (positive) implicative triangle algebras were defined. Afterwards, several characterizations of the algebras were presented, and the correlations between the n -fold IVRL-extended filters, n -fold (positive) implicative algebras, and the Gödel triangle algebra were discussed.

Automatic risk control based on FSA methodology adaptation for safety assessment in intelligent buildings

Jerzy Mikulik, Mirosław Zajdel (2009)

International Journal of Applied Mathematics and Computer Science

The main area which Formal Safety Assessment (FSA) methodology was created for is maritime safety. Its model presents quantitative risk estimation and takes detailed information about accident characteristics into account. Nowadays, it is broadly used in shipping navigation around the world. It has already been shown that FSA can be widely used for the assessment of pilotage safety. On the basis of analysis and conclusion on the FSA approach, this paper attempts to show that the adaptation of this...

BL-algebras of basic fuzzy logic.

Esko Turunen (1999)

Mathware and Soft Computing

BL-algebras [Hajek] rise as Lindenbaum algebras from certain logical axioms familiar in fuzzy logic framework. BL-algebras are studied by means of deductive systems and co-annihilators. Duals of many theorems known to hold in MV-algebra theory remain valid for BL-algebras, too.

Cauchy-like functional equation based on a class of uninorms

Feng Qin (2015)

Kybernetika

Commuting is an important property in any two-step information merging procedure where the results should not depend on the order in which the single steps are performed. In the case of bisymmetric aggregation operators with the neutral elements, Saminger, Mesiar and Dubois, already reduced characterization of commuting n -ary operators to resolving the unary distributive functional equations. And then the full characterizations of these equations are obtained under the assumption that the unary...

Classes of fuzzy filters of residuated lattice ordered monoids

Jiří Rachůnek, Dana Šalounová (2010)

Mathematica Bohemica

The logical foundations of processes handling uncertainty in information use some classes of algebras as algebraic semantics. Bounded residuated lattice ordered monoids (monoids) are common generalizations of BL -algebras, i.e., algebras of the propositional basic fuzzy logic, and Heyting algebras, i.e., algebras of the propositional intuitionistic logic. From the point of view of uncertain information, sets of provable formulas in inference systems could be described by fuzzy filters of the corresponding...

Considering uncertainty and dependence in Boolean, quantum and fuzzy logics

Mirko Navara, Pavel Pták (1998)

Kybernetika

A degree of probabilistic dependence is introduced in the classical logic using the Frank family of t -norms known from fuzzy logics. In the quantum logic a degree of quantum dependence is added corresponding to the level of noncompatibility. Further, in the case of the fuzzy logic with P -states, (resp. T -states) the consideration turned out to be fully analogous to (resp. considerably different from) the classical situation.

Construction methods for implications on bounded lattices

M. Nesibe Kesicioğlu (2019)

Kybernetika

In this paper, the ordinal sum construction methods of implications on bounded lattices are studied. Necessary and sufficient conditions of an ordinal sum for obtaining an implication are presented. New ordinal sum construction methods on bounded lattices which generate implications are discussed. Some basic properties of ordinal sum implications are studied.

Construction methods for uni-nullnorms and null-uninorms on bounded lattice

Ümit Ertuğrul, M. Nesibe Kesicioğlu, Funda Karaçal (2019)

Kybernetika

In this paper, two construction methods have been proposed for uni-nullnorms on any bounded lattices. The difference between these two construction methods and the difference from the existing construction methods have been demonstrated and supported by an example. Moreover, the relationship between our construction methods and the existing construction methods for uninorms and nullnorms on bounded lattices are investigated. The charactertics of null-uninorms on bounded lattice L are given and a...

Construction of uninorms on bounded lattices

Gül Deniz Çaylı, Funda Karaçal (2017)

Kybernetika

In this paper, we propose the general methods, yielding uninorms on the bounded lattice ( L , ≤ , 0 , 1 ) , with some additional constraints on e ∈ L ∖ { 0 , 1 } for a fixed neutral element e ∈ L ∖ { 0 , 1 } based on underlying an arbitrary triangular norm T e on [ 0 , e ] and an arbitrary triangular conorm S e on [ e , 1 ] . And, some illustrative examples are added for clarity.

Declarative and procedural semantics of fuzzy similarity based unification

Peter Vojtáš (2000)

Kybernetika

In this paper we argue that for fuzzy unification we need a procedural and declarative semantics (as opposed to the two valued case, where declarative semantics is hidden in the requirement that unified terms are syntactically – letter by letter – identical). We present an extension of the syntactic model of unification to allow near matches, defined using a similarity relation. We work in Hájek’s fuzzy logic in narrow sense. We base our semantics on a formal model of fuzzy logic programming extended...

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