MV-Partitions and MV-Powers

Advances in Computational Intelligence and Robotics - Mathematics of Uncertainty Modeling in the Analysis of Engineering and Science Problems ◽

10.4018/978-1-4666-4991-0.ch011 ◽

2014 ◽

pp. 217-238

Author(s):

C. Drossos ◽

P. L. Theodoropoulos

Keyword(s):

Boolean Power ◽

Power Construction ◽

Mv Algebras

In this chapter, the authors generalize the Boolean partition to semisimple MV-algebras. MV-partitions together with a notion of refinement is tantamount a construction of an MV-power, analogous to Boolean power construction (Mansfield, 1971). Using this new notion we introduce the corresponding theory of MV-powers.

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Towards a calculus of algorithms

Bulletin of the Australian Mathematical Society ◽

10.1017/s000497270000959x ◽

1994 ◽

Vol 50 (1) ◽

pp. 81-89 ◽

Cited By ~ 2

Author(s):

M. Bulmer ◽

D. Fearnley-Sander ◽

T. Stokes

Keyword(s):

Universal Algebra ◽

Function Composition ◽

Boolean Power ◽

Power Construction ◽

Abstract Operation

We develop a generalised polynomial formalism which captures the concept of an algebra of piece-wise denned polynomials. The formalism is based on the Boolean power construction of universal algebra. A generalisation of the theory of substitution homomorphisms is developed. The abstract operation of composition of generalised polynomials in one variable is denned and shown to correspond to function composition.

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Semi-simple and complete MV-algebras

Algebra Universalis ◽

10.1007/bf01190751 ◽

1992 ◽

Vol 29 (1) ◽

pp. 1-9 ◽

Cited By ~ 37

Author(s):

L. P. Belluce

Keyword(s):

Mv Algebras

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Residuated Structures and Orthomodular Lattices

Studia Logica ◽

10.1007/s11225-021-09946-1 ◽

2021 ◽

Author(s):

D. Fazio ◽

A. Ledda ◽

F. Paoli

Keyword(s):

Algebraic Logic ◽

Residuated Lattices ◽

Quantum Structures ◽

Heyting Algebras ◽

Quantum Algebras ◽

Orthomodular Lattices ◽

Lattice Of Subvarieties ◽

Residuated Structures ◽

Common Framework ◽

Mv Algebras

AbstractThe variety of (pointed) residuated lattices includes a vast proportion of the classes of algebras that are relevant for algebraic logic, e.g., $$\ell $$ ℓ -groups, Heyting algebras, MV-algebras, or De Morgan monoids. Among the outliers, one counts orthomodular lattices and other varieties of quantum algebras. We suggest a common framework—pointed left-residuated $$\ell $$ ℓ -groupoids—where residuated structures and quantum structures can all be accommodated. We investigate the lattice of subvarieties of pointed left-residuated $$\ell $$ ℓ -groupoids, their ideals, and develop a theory of left nuclei. Finally, we extend some parts of the theory of join-completions of residuated $$\ell $$ ℓ -groupoids to the left-residuated case, giving a new proof of MacLaren’s theorem for orthomodular lattices.

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Priestley duality for MV-algebras and beyond

Forum Mathematicum ◽

10.1515/forum-2020-0115 ◽

2021 ◽

Vol 0 (0) ◽

Author(s):

Wesley Fussner ◽

Mai Gehrke ◽

Samuel J. van Gool ◽

Vincenzo Marra

Keyword(s):

Large Class ◽

Order Conditions ◽

Enriched Environment ◽

Priestley Duality ◽

Distributive Lattices ◽

First Order ◽

Dual Spaces ◽

Binary Operations ◽

New Perspective ◽

Mv Algebras

Abstract We provide a new perspective on extended Priestley duality for a large class of distributive lattices equipped with binary double quasioperators. Under this approach, non-lattice binary operations are each presented as a pair of partial binary operations on dual spaces. In this enriched environment, equational conditions on the algebraic side of the duality may more often be rendered as first-order conditions on dual spaces. In particular, we specialize our general results to the variety of MV-algebras, obtaining a duality for these in which the equations axiomatizing MV-algebras are dualized as first-order conditions.

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Riesz–McNaughton functions and Riesz MV-algebras of nonlinear functions

Fuzzy Sets and Systems ◽

10.1016/j.fss.2016.03.003 ◽

2017 ◽

Vol 311 ◽

pp. 1-14 ◽

Cited By ~ 5

Author(s):

Antonio Di Nola ◽

Giacomo Lenzi ◽

Gaetano Vitale

Keyword(s):

Nonlinear Functions ◽

Mv Algebras ◽

Mcnaughton Functions

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Research in Geological Environmental Evaluation System of Transmission Line

Applied Mechanics and Materials ◽

10.4028/www.scientific.net/amm.641-642.1238 ◽

2014 ◽

Vol 641-642 ◽

pp. 1238-1245

Author(s):

Zi Xia Feng ◽

Bin Bin Zhao ◽

Lei He ◽

Chen Fang

Keyword(s):

Transmission Lines ◽

Evaluation System ◽

Evaluation Method ◽

Rapid Development ◽

Evaluation Research ◽

Planning Period ◽

Environmental Evaluation ◽

Life Cycle Design ◽

Power Construction ◽

Whole Life Cycle

With the rapid development of electric power construction , transmission lines and the surrounding geological environment influence each other that has become increasingly serious, however, there is not formed yet a set of complete and more scientific geological environmental evaluation system in transmission lines at present. In this paper, on the basis of using the experience of other industries of geological environmental evaluation research , study and put forward the geological environmental evaluation method specifically for transmission lines. Evaluation system is established for transmission lines in planning period and construction period , and also put forward the corresponding evaluation index. The research conclusion can provides theoretical support and maintenance for transmission lines of the whole life cycle design,and it also provides reference in designing transmission lines plan and preventing, and controlling geological environmental problems of transmission lines for the decision-making department.

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