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The embedding of the formal concept analysis into the L-Fuzzy concept theory.

Ana Burusco Juandeaburre, Ramón Fuentes-González (1998)

Mathware and Soft Computing

In this work, we study the relation between the concept lattice of Wille ([5], [6]) and the L-Fuzzy concept lattice ([2]) developed by us. To do it, we have defined an application g that associates to each concept of Wille an L-Fuzzy concept. The main point of this work is to prove that if we are working with a crisp relation between an object set and an attribute set, the concept lattice of Wille is a sublattice of the L-Fuzzy concept lattice. At the end, we show a typical example in the formal...

The Formal Construction of Fuzzy Numbers

Adam Grabowski (2014)

Formalized Mathematics

In this article, we continue the development of the theory of fuzzy sets [23], started with [14] with the future aim to provide the formalization of fuzzy numbers [8] in terms reflecting the current state of the Mizar Mathematical Library. Note that in order to have more usable approach in [14], we revised that article as well; some of the ideas were described in [12]. As we can actually understand fuzzy sets just as their membership functions (via the equality of membership function and their set-theoretic...

The fuzzy hyperbolic inequality index of fuzzy random variables in finite populations.

Norberto Corral, María Angeles Gil, Hortensia López-García (1996)

Mathware and Soft Computing

This paper presents an approach to the problem of quantifying the inequality of a finite population with respect to a (social, economical, etc.) fuzzy-valued attribute. For this purpose, the fuzzy hyperbolic inequality index is introduced, and some properties extending the basic ones for real-valued attributes are examined.

The internal rate of return of fuzzy cash flows.

Loredana Biacino, M. Rosaria Simonelli (1992)

Stochastica

An internal rate of return (IRR) of an investment or financing project with cash flow (a0,a1,a2,...,an) is usually defined as a rate of interest r such thata0 + a1(1 + r)-1 + ... + an(1 + r)-n = 0.If the cash flow has one sign change then the previous equation has a unique solution r > -1.Generally the IRR technique does not extend to fuzzy cash flows, as it can be seen with examples (see [2]). In this paper we show that under suitable hypothesis a unique fuzzy IRR exists for a fuzzy cash...

The similarity of two strings of fuzzy sets

Gabriela Andrejková (2000)

Kybernetika

Let 𝒜 , ℬ be the strings of fuzzy sets over χ , where χ is a finite universe of discourse. We present the algorithms for operations on fuzzy sets and the polynomial time algorithms to find the string 𝒞 over χ which is a closest common subsequence of fuzzy sets of 𝒜 and ℬ using different operations to measure a similarity of fuzzy sets.

The stability of parameter estimation of fuzzy variables

Dug Hun Hong (2009)

Kybernetika

Recently, the parameter estimations for normal fuzzy variables in the Nahmias’ sense was studied by Cai [4]. These estimates were also studied for general T -related, but not necessarily normal fuzzy variables by Hong [10] In this paper, we report on some properties of estimators that would appear to be desirable, including unbiasedness. We also consider asymptotic or “large-sample” properties of a particular type of estimator.

The study of the L-fuzzy concept lattice.

Ana Burusco Juandeaburre, Ramón Fuentes-González (1994)

Mathware and Soft Computing

The L-Fuzzy concept theory that we have developed sets up classifications from the objects and attributes of a context through L-Fuzzy relations. This theory generalizes the formal concept theory of R. Wille. In this paper we begin with the L-Fuzzy concept definition that generalizes the definitions of the formal concept theory, and we study the lattice structure of the L-Fuzzy concept set, giving a constructive method for calculating this lattice. At the end, we apply this constructive method to...

The study on semicopula based implications

Zuming Peng (2020)

Kybernetika

Recently, Baczyński et al. (2017) proposed a new family of implication operators called semicopula based implications, which combines a given a priori fuzzy implication and a semicopula. In this paper, firstly, the relationship between the basic properties of the priori fuzzy implication and the semicopula based implication are analyzed. Secondly, the conditions such that the semicopula based implication is a fuzzy implication are studied, the study is carried out mainly in the case that the semicopula...

The σ-complete MV-algebras which have enough states

Antonio Di Nola, Mirko Navara (2005)

Colloquium Mathematicae

We characterize Łukasiewicz tribes, i.e., collections of fuzzy sets that are closed under the standard fuzzy complementation and the Łukasiewicz t-norm with countably many arguments. As a tool, we introduce σ-McNaughton functions as the closure of McNaughton functions under countable MV-algebraic operations. We give a measure-theoretical characterization of σ-complete MV-algebras which are isomorphic to Łukasiewicz tribes.

Tietze extension theorem for pairwise ordered fuzzy extremally disconnected spaces

Mallasamudram Kuppusamy Uma, Elango Roja, Ganesan Balasubramanian (2008)

Mathematica Bohemica

In this paper a new class of fuzzy topological spaces called pairwise ordered fuzzy extremally disconnected spaces is introduced. Tietze extension theorem for pairwise ordered fuzzy extremally disconnected spaces has been discussed as in the paper of Kubiak (1987) besides proving several other propositions and lemmas.

Towards an extension of the 2-tuple linguistic model to deal with unbalanced linguistic term sets

Mohammed-Amine Abchir, Isis Truck (2013)

Kybernetika

In the domain of Computing with words (CW), fuzzy linguistic approaches are known to be relevant in many decision-making problems. Indeed, they allow us to model the human reasoning in replacing words, assessments, preferences, choices, wishes... by ad hoc variables, such as fuzzy sets or more sophisticated variables. This paper focuses on a particular model: Herrera and Martínez' 2-tuple linguistic model and their approach to deal with unbalanced linguistic term sets. It is interesting since the...

Towards the properties of fuzzy multiplication for fuzzy numbers

Alexandru Mihai Bica, Dorina Fechete, Ioan Fechete (2019)

Kybernetika

In this paper, by using a new representation of fuzzy numbers, namely the ecart-representation, we investigate the possibility to consider such multiplication between fuzzy numbers that is fully distributive. The algebraic and topological properties of the obtained semiring are studied making a comparison with the properties of the existing fuzzy multiplication operations. The properties of the generated fuzzy power are investigated.

Transitive decomposition of fuzzy preference relations: the case of nilpotent minimum

Susana Díaz, Susana Montes, Bernard De Baets (2004)

Kybernetika

Transitivity is a fundamental notion in preference modelling. In this work we study this property in the framework of additive fuzzy preference structures. In particular, we depart from a large preference relation that is transitive w.r.t. the nilpotent minimum t-norm and decompose it into an indifference and strict preference relation by means of generators based on t-norms, i. e. using a Frank t-norm as indifference generator. We identify the strongest type of transitivity these indifference and...

Una introducción a la W-calculabilidad: Operaciones básicas.

Buenaventura Clares Rodríguez (1983)

Stochastica

Our purpose is to introduce the W-composition, W-minimalization and W-primitive recursion operations as operations between W-valued functions, where W denotes the ordered semiring ([0,1],+,≤). We prove that: 1) the set of W-calculable functions is closed under the W-composition and W-primitice recursion operations, and 2) the set of the partially W-calculable functions is closed under the W-minimalization operation.

Una nueva definición de aplicación difusa.

Miguel Delgado Calvo-Flores (1980)

Stochastica

If X, Y are universes of discourse, a fuzzy mapping f: X --> Y is defined as a classical mapping f: X x [0,1] --> P(Y). Their basic properties are studied as well as their relations with the classical model of fuzzy mapping.

Una visión unificada de los operadores en la teoría de la evidencia.

Luis Miguel de Campos Ibáñez, María Teresa Lamata Jiménez, Serafín Moral Callejón (1988)

Stochastica

The aim of this paper is to review the different operators defined in the Theory of Evidence. All of them are presented from the same point of view. Special attention is given to the logical operators: conjunction (Dempster's Rule), disjunction and negation (defined by Dubois and Prade), and the operators changing the level of granularity on the set of possible states (partitions, fuzzy partitions, etc.).

Upper and lower set formulas: restriction and modification of the Dempster-Pawlak formalism

Ismail Türkşen (2002)

International Journal of Applied Mathematics and Computer Science

A modification of Dempster's and Pawlak's constructs forms a new foundation for the identification of upper and lower sets formulas. Also, in this modified Dempster-Pawlak construct we require that subsets of the power set be restricted to the well-known information granules of the power set. An aggregation of upper information granules amongst each other and lower information granules amongst each other determine upper and lower set formulas for both crisp and fuzzy sets. The results are equivalent...

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