Issues on adjointness in multiple-valued logics

Morsi, Nehad N.; Roshdy, Elewa M.

doi:10.1016/j.ins.2005.08.005

Cited by 11 publications

(10 citation statements)

References 43 publications

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“…Implication triples and adjointness algebras were introduced in [42] and a lot of properties were studied in [1,46]. Moreover, an extension, the logic of tied implications, was presented in [43][44][45].…”

Section: Implication Triplesmentioning

confidence: 99%

Multi-adjoint algebras versus non-commutative residuated structures

Cornejo

Medina

Ramírez‐Poussa

2015

International Journal of Approximate Reasoning

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Adjoint triples and pairs are basic operators used in several domains, since they increase the flexibility in the framework in which they are considered. This paper introduces multiadjoint algebras and several properties; also, we will show that an adjoint triple and its "dual" cannot be considered in the same framework. Moreover, a comparison among general algebraic structures used in different frameworks, which reduce the considered mathematical requirements, such as the implicative extendedorder algebras, implicative structures, the residuated algebras given by sup-preserving aggregations and the conjunctive algebras given by semi-uninorms and u-norms, is presented. This comparison shows that multi-adjoint algebras generalize these structures in domains which require residuated implications, such as in formal concept analysis, fuzzy rough sets, fuzzy relation equations and fuzzy logic.

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Section: Implication Triplesmentioning

confidence: 99%

Multi-adjoint algebras versus non-commutative residuated structures

Cornejo

Medina

Ramírez‐Poussa

2015

International Journal of Approximate Reasoning

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“…With the essentially same assumptions as presented by Zhao (1987) and Wang (2001) characterized the solution set of a system of sup-T M equations on a complete Brouwerian lattice. Drewniak (1984), Miyakoshi and Shimbo (1985), Izumi et al (1986), Di Nola and Lettieri (1989), Pedrycz (1991), Gottwald (2001), and Morsi and Roshdy (2006) discussed the role of adjointness, i.e., the existence of a pair of residual operators, in the resolution of fuzzy relational equations. De Baets (1995aBaets ( , 1998 extended the work of Zhao (1987) to sup-T equations on a complete lattice.…”

Section: Basic Inequalities and Equationsmentioning

confidence: 99%

A survey on fuzzy relational equations, part I: classification and solvability

Fang

2009

Fuzzy Optim Decis Making

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Fuzzy relational equations play an important role in fuzzy set theory and fuzzy logic systems, from both of the theoretical and practical viewpoints. The notion of fuzzy relational equations is associated with the concept of "composition of binary relations." In this survey paper, fuzzy relational equations are studied in a general lattice-theoretic framework and classified into two basic categories according to the duality between the involved composite operations. Necessary and sufficient conditions for the solvability of fuzzy relational equations are discussed and solution sets are characterized by means of a root or crown system under some specific assumptions.

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“…In Zadeh's composition rule of fuzzy inference (fuzzy modus ponens, fuzzy modus tollens, etc. ), a fuzzy implication represents the fuzzy relation between two variables [9,Chapter 5,12,13,16,20]. In image processing, a fuzzy implication is used to define the subsethood measure between two fuzzy sets [5, Theorem 1].…”

Section: Definitions and Propertiesmentioning

confidence: 99%

“…According to (13), a QL-implication I is generated by a t-conorm S, a t-norm T and a strong fuzzy negation n. In this section, let n denote any strong fuzzy negation. We suppose both S and T are continuous and intend to investigate all possible combinations of S and T and find the sufficient and necessary conditions for I to satisfy (1).…”

Section: Ql-implicationsmentioning

confidence: 99%