An algebraic setting for the validity of Pavelka style completeness for some natural expansions of Lukasiewicz logic by new connectives and rational constants is given. This algebraic approach is based on the fact that the standard MV-algebra on the real segment [0, 1] is an injective MV-algebra. In particular the logics associated with MV-algebras with product and with divisible MV-algebras ar...

The multi-criteria decision-making (MCDM) problem has a solution whose quality can be affected by the experts’ inclinations. Under essential conditions, fuzzy MCDM method provide more acceptable and efficient outcomes to select best alternatives. This work consists of consensus-based technique for selecting evaluating suppliers in an incomplete preference relations (IFPRs) environment utilizing...

In 2000, Figallo and Sanza introduced the n×m−valued Lukasiewicz-Moisil algebras, which are a particular case of Matrix Lukasiewicz algebras, and a nontrivial generalization of n−valued Lukasiewicz-Moisil algebras. Here we start a research on the class of n × m−valued Lukasiewicz-Moisil algebras endowed with two modal operators (or 2mLMn×m−algebras). These algebras constitute a common generaliz...

Rough set theory is an important tool for dealing with granularity and vagueness in information systems. This paper studies a kind of rough set algebra. The collection of all the rough sets of an approximation space can be made into a 3-valued Lukasiewicz algebra. We call the algebra a rough 3-valued Lukasiewicz algebra. In this paper, we focus on the rough 3-valued Lukasiewicz algebras, which ...

The LLA Retina combines Lukasiewicz logic arrays (LLAs) with photo-sensor clusters to work as a fuzzy edge detection mechanism and several other applications. In this presentation we have explored various approaches to excite and evaluate the device with several types of light sources including visible and infra-red laser beams. Based on the detailed studies on the device, one particular config...

Carcinogenesis is a complex process that involves dynamically inter-connected modular subnetworks that evolve under the influence of micro-environmental, as well as, in many cases, cancer therapy-induced perturbations, in non-random, pseudo-Markov chain processes. An appropriate n-stage model of carcinogenesis involves therefore n-valued Logic treatments of such processes, nonlinear dynamic tra...

We investigate the combinatorics of interpolation in Gödel logic, the propositional logic whose algebraic semantics is the variety of Heyting algebras generated by chains. 1 Motivation In recent work, Busaniche and Mundici prove that Lukasiewicz logic has the Robinson property RP [4], exploiting the geometry of prime filters in the free finitely generated MV-algebra. In this note we recast thei...

The fundamentals of à Lukasiewicz-Moisil logic algebras and their applications to complex genetic network dynamics and highly complex systems are presented in the context of a categorical ontology theory of levels, Medical Bioinformatics and self-organizing, highly complex systems. Quantum Automata were defined in refs.[2] and [3] as generalized, probabilistic automata with quantum state spaces...

During the last two decades, Group for intelligent systems at Mathematical faculty in Belgrade has developed several theorem provers for different kind of formal systems. Lately, we have turned our attention to fuzzy logic and development of the corresponding theorem prover. The first step is to find the suitable axiomatization, i.e., the formalization of fuzzy logic that is sound, complete and...

Quantum-Dot Cellular Automata (QCAs) are becoming more and more one of the most promising candidates for the alternative processing platform of the future. Since their advent in the early 1990s the required technological processes, as well as the QCA structures that implement the basic and functionally complete set of binary logic functions, have been developed. This article, however, presents ...