Fuzzy Arithmetic and Extension Principle

Fuzzy arithmetic is an extensively used instrument for dealing with uncertainty in a computationally competent method, recently and much better in the upcoming years. This thesis aims to investigate the basic properties of fuzzy arithmetic as its title implies. The properties of fuzzy arithmetic definitions, examples are discussed. Here we investigates the properties of fuzzy sets, properties of fuzzy number, performing arithmetic operations on fuzzy number, properties of L-R fuzzy number, performing operations on L-R fuzzy number, properties of fuzzy interval and properties of L-R fuzzy interval. Also, the extension principle and fuzzy arithmetic operations using extension principle are investigated. The fuzzy equation is solved by using the method o

Fuzzy algebras of concepts

Preconcepts are basic units of knowledge that form the basis of formal concepts in formal concept analysis (FCA). This paper investigates the relations among different kinds of preconcepts, such as protoconcepts, meet and join-semiconcepts and formal concepts. The first contribution of this paper, is to present a fuzzy powerset lattice gradation, that coincides with the preconcept lattice at its 1-cut. The second and more significant contribution, is to introduce a preconcept algebra gradation that yields different algebras for protoconcepts, semiconcepts, and concepts at different cuts. This result reveals new insights into the structure and properties of the different categories of preconcepts.Partial funding for open access charge: Universidad de Málag

Generalising KAT to verify weighted computations

Kleene algebra with tests (KAT) was introduced as an algebraic structure to model and reason about classic imperative programs, i.e. sequences of discrete transitions guarded by Boolean tests. This paper introduces two generalisations of this structure able to express programs as weighted transitions and tests with outcomes in non necessarily bivalent truth spaces: graded Kleene algebra with tests (GKAT) and a variant where tests are also idempotent (I-GKAT). In this context, and in analogy to Kozen's encoding of Propositional Hoare Logic (PHL) in KAT we discuss the encoding of a graded PHL in I-GKAT and of its while-free fragment in GKAT. Moreover, to establish semantics for these structures four new algebras are de ned: FSET (T ), FREL(K; T ) and FLANG(K; T ) over complete residuated lattices K and T , and M(n;A) over a GKAT or I-GKAT A. As a nal exercise, the paper discusses some program equivalence proofs in a graded context.POCI-01-0145-FEDER-03094, NORTE-01-0145-FEDER-000037. ERDF – European Regional Development Fund through the Operational Programme for Competitiveness and Internationalisation - COMPETE 2020 Programme and by National Funds through the Portuguese funding agency, FCT - Fundação para a Ciência e a Tecnologia, within project POCI-01-0145-FEDER-030947. This paper is also a result of the project SmartEGOV, NORTE-01-0145-FEDER-000037. The second author is supported in the scope of the framework contract foreseen in the numbers 4, 5 and 6 of the article 23, of the Decree-Law 57/2016, of August 29, changed by Portuguese Law 57/2017, of July 19, at CIDMA (Centro de Investigação e Desenvolvimento em Matemática e Aplicações) UID/MAT/04106/2019

NORTH- HOIJ-AND Development and Evaluation of Five Fuzzy Multiattribute Decision-Making Methods

We present the development of five fuzzy multiattribute decision-making methods. These methods are based on the analytic hierarchy process (original and ideal mode), the weighted-sum model, the weighted-product model, and the TOPSlS method. Moreover, these methods are examined in terms of two evaluative criteria. Computational results on test problems suggest that although all the methods are inaccurate, some of them seem to be more accurate than the others. The proposed evaluation methodology can easily be used in evaluating more fuzzy multiattribute decision making methods

Fuzzy Sets, Fuzzy Logic and Their Applications

The present book contains 20 articles collected from amongst the 53 total submitted manuscripts for the Special Issue “Fuzzy Sets, Fuzzy Loigic and Their Applications” of the MDPI journal Mathematics. The articles, which appear in the book in the series in which they were accepted, published in Volumes 7 (2019) and 8 (2020) of the journal, cover a wide range of topics connected to the theory and applications of fuzzy systems and their extensions and generalizations. This range includes, among others, management of the uncertainty in a fuzzy environment; fuzzy assessment methods of human-machine performance; fuzzy graphs; fuzzy topological and convergence spaces; bipolar fuzzy relations; type-2 fuzzy; and intuitionistic, interval-valued, complex, picture, and Pythagorean fuzzy sets, soft sets and algebras, etc. The applications presented are oriented to finance, fuzzy analytic hierarchy, green supply chain industries, smart health practice, and hotel selection. This wide range of topics makes the book interesting for all those working in the wider area of Fuzzy sets and systems and of fuzzy logic and for those who have the proper mathematical background who wish to become familiar with recent advances in fuzzy mathematics, which has entered to almost all sectors of human life and activity