In several advanced fields like control engineering, computer science, fuzzy automata, finite state machine, and error correcting codes, the use of fuzzified algebraic structures especially ordered semigroups plays a central role. In this paper, we introduced a new and advanced generalization of fuzzy generalized bi-ideals of ordered semigroups. These new concepts are supported by suitable exam...

a‎s we know, developing mathematical models and numerical procedures that would appropriately treat and solve systems of linear equations where some of the system's parameters are proposed as fuzzy numbers is very important in fuzzy set theory. for this reason, many researchers have used various numerical methods to solve fuzzy linear systems. in this paper, we define the concepts of midpoint a...

Limits and colimits of diagrams, defined by maps between sets, are universal constructions fundamental in different mathematical domains and key concepts in theoretical computer science. Its importance in semantic modeling is described by M. Makkai and R. Paré in [1], where it is formally shown that every axiomatizable theory in classical infinitary logic can be specified using diagrams defined...

in this paper we extend the notion of  degrees of membership and non-membership of intuitionistic fuzzy sets to lattices and  introduce a residuated lattice with appropriate operations to serve as semantics of intuitionistic fuzzy logic. it would be a step forward to find an algebraic counterpart for intuitionistic fuzzy logic. we give the main properties of the operations defined and prove som...

Synaptic algebras, introduced by D. Foulis, generalize different algebraic structures used so far as mathematical models of quantum mechanics: the traditional Hilbert space approach, order unit spaces, Jordan effect MV-algebras, orthomodular lattices. We study sharp and fuzzy observables on two special classes synaptic algebras: called generalized Hermitian algebras which are Banach duals. Rela...

This paper is an attempt to develop quantitative domain theory over frames. Firstly, we propose the notion of a fuzzy basis, and several equivalent characterizations of fuzzy bases are obtained. Furthermore, the concept of a fuzzy algebraic domain is introduced, and a relationship between fuzzy algebraic domains and fuzzy domains is discussed from the viewpoint of fuzzy basis. We finally give a...

Interval-valued fuzzy soft sets realize a hybrid soft computing model in a general framework. Both Molodtsov's soft sets and interval-valued fuzzy sets can be seen as special cases of interval-valued fuzzy soft sets. In this study, we first compare four different types of interval-valued fuzzy soft subsets and reveal the relations among them. Then we concentrate on investigating some nonclassic...

investigation of desertification trend needs understanding of phenomena creating changes singly or action and reaction together in the manner that these changes were ended up in land degradation. in investigation of pedological criterion onland degradation in quaternary rock units, first, a part of the rude-shoor watershed area was selected. after distinguishing target area, maps of slope class...

An inference method based on an equation image of a rule-base and the minimization of a cost index (inference error) is presented. The method has several advantages: it has intuitive insight, allows more powerful rules, and also presents an interesting algebraic (minimum distance) and functional (subsethood) formulation of the meaning of inference. Analysis of internal quality and completeness ...

Mathematical morphology is based on the algebraic framework of complete lattices and adjunctions, which endows it with strong properties and allows for multiple extensions. In particular, extensions to fuzzy sets of the main morphological operators, such as dilation and erosion, can be done while preserving all properties of these operators. Another, more recent, extension, concerns bipolar fuz...